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UBC Theses and Dissertations

Multi-level ambulance system design Kitt, Ronald Victor 1979

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MULTI-LEVEL AMBULANCE SYSTEM DESIGN by RONALD VICTOR KITT B. Comm., University of Alberta, 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE (BUSINESS ADMINISTRATION) i n THE FACULTY OF GRADUATE STUDIES THE FACULTY OF COMMERCE AND BUSINESS ADMINISTRATION (MANAGEMENT SCIENCE DIVISION) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1979 © Ronald V i c t o r K i t t , 1979 In presenting th i s thes is in pa r t i a l fu l f i lment of the reguirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes i s fo r f i nanc ia l gain sha l l not be allowed without my writ ten permission. Department of C^P^^n^iU-^ 6l^i<J J^^<U<>a!^- Clh^yc&i—'~' The Univers i ty of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date ABSTRACT The objective of this research was to study the opera-t i o n of the ambulance service i n the Greater Vancouver Regional D i s t r i c t . Attention has been focused on operational p o l i c i e s which a f f e c t the system's a b i l i t y to respond to c a l l s , espec-i a l l y to emergency c a l l s . The stated objective was accomplished by f i r s t reviewing the current demand for emergency ambulance services and the present operations. Next deterministic models were investigated and used to give " i n i t i a l " locations of depots. F i n a l l y a computer simulation model was developed and used to conduct experiments, examining a l t e r n a t i v e ambulance systems. This research revealed that 1. computer simulation i s an e f f e c t i v e t o o l for analysing ambulance systems, and 2. there i s a need for more emergency ambulance services, including more para-medics,, i n the Greater Vancouver Regional D i s t r i c t . TABLE OF CONTENTS Page ABSTRACT OF THE DISSERTATION ( i i ) LIST OF TABLES (vi) LIST OF FIGURES ( v i i i ) CHAPTER 1 INTRODUCTION 1 1.1. Introduction 1 1.1.1. Scope and Objectives of Research 2 1.1.2. Research Outlined 3 1.1.3. Function of the Ambulance System 5 1.1.4. The Role of Paramedic Units 5 1.2. Review of Ambulance System Models 7 1.2.-1. Review of Recent Literature 7 1.2.2. A p p l i c a b i l i t y to the G.V.R.D. 10 CHAPTER 2 EXISTING AMBULANCE SERVICES IN THE G.V.R.D. H 2.1. Ex i s t i n g Ambulance Service 11 2.1.1. The Network 11 2.1.2. ' Resources 12 2.1.3. Co-ordination and Management 13 2.2. Demand for Ambulance Services 13 2.2.1. Data C o l l e c t i o n 13 2.2.2. Table of Defi n i t i o n s 15 2.2.3. Current Demand 16 A. Temporal Variations 16 (i) Seasonal Variations 16 ( i i ) Hourly V a r i a t i o n of Demands 16 During the Day B. Demand for Paramedics 18 2.2.4. Demand Growth 18 2.3. Production and Evaluation 20 2.3.1. Production Components 20 Page 2.3.2. Analysis of Components 21 CHAPTER 3 THE COMPUTER SIMULATION MODEL 39 3.1. Use of Simulation i n the Analysis of Emergency Ambulance Systems 39 3.1.1. The Stochastic Elements of an Ambulance System 40 3.2. General Description of the Computer Simulation Model 40 3.2.1. General Outline 41 3.2.2. Inputs 49 3.2.3. Outputs 50 3.2.4. Model Val i d a t i o n 50 CHAPTER 4 THE AMBULANCE LOCATION PROBLEM 59 4.1. Es s e n t i a l Features of the Ambulance Location Problem 59 4.1.1. Analytic-Deterministic Approximations 60 4.2. The Maximal Covering Location Problem 60 4.3. Mathematical formulation of the MCLP 62 4.4. Use of the MCLP Model 64 4.5. The P-Median Location Model 74 4.6. Mathematical Formulation of the P-Median Model 74 4.7. Use of the P-Median Algorithm 81 CHAPTER 5 DESIGN OF EXPERIMENTS 88 5.1. Introduction 88 5.2. Experimental Design 89 5.3. Simulation S t a t i s t i c s 91 iv CHAPTER 6 EXPERIMENT RESULTS AND THEIR IMPLICATIONS 6.1. Introduction 6.2. The West Vancouver Ambulance Experiment 6.3. The E f f e c t s of Removing Three Night Crews 6.4. Moving a Paramedic Ambulance from Burnaby to Vancouver 6.5. Replacing at V.G.H. an Ordinary (EMA-2) Ambulance with a Paramedic (EMA-3) Ambulance under Two Conditions 6.6. Experiment #5 - Optimal Number of EMA-2 Units Required to Achieve a Given F r a c t i l e of Emergency C a l l s Answered i n Less Than Five Minutes 6.7. High Urban Density 6.8. Paramedics - Future Use 6.9. Summary BIBLIOGRAPHY APPENDIX Description of Regression on Travel Times Flow Chart of the Simulation v LIST OF TABLES Page TABLE 1 Current location of Ambulances i n the G.V.R.D. and Sh i f t s Operated 14 2 Daily Ambulance Demand Rate by Time of Day and Municipality 19 3 Average Response Time and Service Time by Municipality 22 4 Average Response Time and Service Time by Municipality Group 23 5 Average Operations Times by Type and Time of C a l l ( A l l Days) 26 6 Average Operations Times by Type and Time of C a l l (Vancouver, Burnaby and New Westminster only) 27 7 Average Operations Times by Type and Time of C a l l (Vancouver, Burnaby and New Westminster only - no paramedic c a l l s ) 28 8 Average Operations Times by Type and Time of Day (Weekdays Only) 29 9 D i s t r i b u t i o n of Ambulance Destinations by Municipality 31 10 D i s t r i b u t i o n of C a l l Origin by Destination ... 32 11 Comparison of Response Times by P r i o r i t y and Municipality 53 12 Comparison of Calls/Day by Station:Validation 57 13 Maximal Covering Linear Programming Solutions 67 14 Effects of Moving West Vancouver • Ambulances West 99 15 Ef f e c t s of Removing Three Night Crews 104 v i L i s t of Tables (continued) Page TABLE 16 Moving a Paramedic Vehicle from Burnaby (node 62) to VGH (node 14) 109 17 Replacing at VGH an Ordinary EMA-2 Ambulance with a Paramedic EMA-3 Ambulance under Two Conditions 115 18 Emergency Ambulance Ca l l s Answered i n 5 or Less Minutes (Night Only) 117 19 F r a c t i l e Response i n Rural Areas (Night Only) 122 v i i LIST OF FIGURES Page FIGURE 1 Average C a l l Rate (Calls/Hour) by Time of Day 17 2 Sequence of Events in Ambulance Service 20 3 D i s t r i b u t i o n of Response Times, A l l Municipalities 33 4 D i s t r i b u t i o n of Response Times (Vancouver, Burnaby and New Westminster) 34 5 D i s t r i b u t i o n of Response Times, Emergency C a l l , Paramedic C a l l s , A l l Mu n i c i p a l i t i e s ... 35 6 D i s t r i b u t i o n of Response Times, Transfer/ Ordinary C a l l s , A l l Mu n i c i p a l i t i e s 36 7 D i s t r i b u t i o n of Service Times, A l l Munic i p a l i t i e s 37 8 D i s t r i b u t i o n of Service Times (Vancouver, Burnaby and New Westminster) .... 38 9 Decision Table for Ambulance Movements for a Paramedic C a l l 48 10 Comparison of Cumulative D i s t r i b u t i o n of Actual Emergency Response Time versus Simulated Emergency Response Time 55 11 Present Ambulance Depot Locations 68 12 Maximal Covering Solution f or 19 Depots and a Four Minute Maximum Response Time 69 13 Maximal Covering Solution for 19 Depots and a Six Minute Maximal Response Time 70 14 Maximal Covering Solution for 21 Depots and a Six Minute Maximal Response Time 71 15 Maximal Covering Solution for 19 Depots and a Seven Minute Maximum Response Time .... 72 v i i i L i s t of Figures (continued) Page FIGURE 16 Maximal Covering Solutions 73 17 P-Median Solution for 19 Depots 86 18 P-Median Solution for 24 Depots 87 19 Emergency C a l l s Answered i n 5 or Less Minutes (Night Only) 119 20 Paramedic Calls Answered i n Less Than 5 Minutes (Night Only) 121 21 F r a c t i l e Response Under 5 Minutes for Rural Emergency C a l l s (Night Only) 123 22 F r a c t i l e Response Under 5 Minutes for Urban Emergency Calls (Night Only) 125 ix ACKNOWLEDGEMENTS The writer would l i k e to express his sincere thanks to Dr. D.H. Uyeno for his encouragement, advice and guidance throughout the months of thesis research and preparation. My sincere thanks also to Dr. I. Vertinsky for his constructive suggestions. The writing of a thesis requires the assistance of numerous individuals. In pa r t i c u l a r , the writer would l i k e to thank Mr. Carson Smith, Head of Operations of the Emergency Health Services Commission for his cooperation and assistance. He provided much of the voluminous amount of data and assisted in the development of experiments. x CHAPTER 1 1.1 INTRODUCTION Emergency ambulance services are an important component of the general health care system. Each and every day ambulance personnel provide l i f e - g i v i n g support to people in need. Victims of serious motor vehicle accidents, of cardiac arrests, of burns, of i n d u s t r i a l accidents and the l i k e a l l depend upon ambulance services for prompt medical attention. A prompt ambulance service results i n l i v e s saved. Two c r i t i c a l factors i n saving l i v e s are time and speed. These elements are a function of the a v a i l a b i l i t y of ambulance crews and t h e i r location. The main focus of t h i s research i s on the a v a i l a b i l i t y of ambulance crews and t h e i r location i n Vancouver. During the past f i v e years ambulance services i n the Greater Vancouver Regional D i s t r i c t (G.V.R.D.) have changed dramatically. The changes include: - The takeover of the r e s p o n s i b i l i t y for the provision of emergency ambulance service by the P r o v i n c i a l Government i n January of 1975, - a s i g n i f i c a n t increase i n the demand for ambulance services, 1 - the expansion of the service area, and - the introduction of paramedic units. These new circumstances have brought about a need for the examination of the operational aspects of the ambulance service. After the takeover by the Province, the charges for ambulance service were s i g n i f i c a n t l y reduced to $5.00 per c a l l and recently increased to $15.00 per c a l l . This change in structure explains, i n part, the increase i n demand from 61,700 c a l l s i n 1974 to 78,000 (estimated) c a l l s i n 1977. With an average of over 200 c a l l s per day ambulance a v a i l -a b i l i t y i s low. New service areas were also added, thus requiring that a larger geographical area be serviced. Another change within the ambulance service i s that paramedic units are now being u t i l i z e d . However, t h e i r function l i e s mainly i n attending to cardiac arrest victims. 1.1.1 SCOPE AND OBJECTIONS OF RESEARCH The primary objective of t h i s research i s to study the operation of the ambulance system. We s h a l l focus on opera-t i o n a l p o l i c i e s which a f f e c t the system's a b i l i t y to respond to c a l l s , e s p e c i a l l y to emergency c a l l s . A n a l y t i c a l models are used i n conjunction with simula-t i o n experiments to examine al t e r n a t i v e ambulance systems. The following sub-objectives were chosen: - to determine the effects on ambulance effectiveness of changes i n the number of ambulances and the i r location, and - to determine how to e f f e c t i v e l y u t i l i z e the services of paramedic teams. 1.1.2 RESEARCH OUTLINED Section 1.2 of thi s chapter reviews the recent l i t e r a -ture on ambulance system models. Included i s a b r i e f discus-sion on the relevance of these models to the s i t u a t i o n i n the G.V.R.D. Chapter 2 looks at the e x i s t i n g ambulance services i n the G.V.R.D. and discusses the data gathered for the study. Topics discussed are: - network structure of the G.V.R.D. and tr a v e l time data used, - current number and current locations of ambulances, - current demand for ambulance services, - temporal and s p a t i a l d i s t r i b u t i o n of c a l l s , - d i s t r i b u t i o n of c a l l destinations, - current "response time" l e v e l s , and - ambulance u t i l i z a t i o n . In Chapter 3 the simulation model used for the study i s described. Topics include: 3 - the need for a simulation, - the description of the simulation model, - assumptions made, and - v a l i d a t i o n of the model. The fourth chapter presents the ambulance location models, i n p a r t i c u l a r the following subjects are examined: - the es s e n t i a l features of the location problem, - two a n a l y t i c a l methods used for the study, and - the evaluation of the methods used. Chapter 5 comprises experiments with the a n a l y t i c a l models and the simulation. The s t a t i s t i c a l output from the simulation i s discussed. In the l a s t chapter, Chapter 6, the experimental re s u l t s are presented along with implications for p o l i c i e s . The chapter presents recommendations with respect to: - optimal locations, - the use of paramedic teams, - variations i n response times by municipality and type of c a l l ; - alternative dispatch rules, - s e n s i t i v i t y of response times to changes i n demand, and 4 1.1.3 FUNCTION OF THE AMBULANCE SYSTEM Ambulance systems have f i v e p r i n c i p l e functions: rescue, l i f e support, preliminary emergency care, transport to emergency health care f a c i l i t i e s , and treatment at emergency f a c i l i t i e s . (Functions of the paramedic ambulance service w i l l be discussed later.) Although r e s p o n s i b i l i t y for these, functions l i e s mainly with the ambulance service, police and f i r e departments compliment the ambulance service. With an e f f e c t i v e ambulance system, many l i v e s are saved. This can be i l l u s t r a t e d by a simple numerical c a l c u l a t i o n . Currently there are approximately 78,000 c a l l s per year for ambulance services i n the G.V.R.D. About 25% of a l l c a l l s are emergency c a l l s . Of these, roughly 2% involve l i f e sustaining circumstances. Therefore some 390 people per year depend on the ambulance service to save th e i r l i f e . 1.1.4 THE ROLE OF PARAMEDIC UNITS Paramedic teams are a group of sp e c i a l i z e d personnel trained to provide emergency service and f i r s t aid to victims who are i n near-death circumstances. Such cases include: - suspected heart attack, - sudden collapse, - major trauma, - drowning, 5 - o b s t e t r i c problems, and - unconsciousness. (Cardiac arrest cases furnish the majority of c a l l s the paramedic units attend to.) In these circumstances victims may require shock treatment, oxygen, drugs or minor surgery i n order to stay a l i v e . Ordinary ambulance personnel do not have the necessary q u a l i f i c a t i o n s or carry the special equipment (e.g. d e f i b r i l l a t i o n machine) to properly t r e a t the victim. When a li f e - t h r e a t e n i n g s i t u a t i o n occurs and a paramedic unit i s dispatched, on a r r i v a l the paramedics evaluate the patient's conditions and i n appropriate instances communicate with a physician. For cardiac arrest cases, the paramedics may perform cardiac pulmonary r e s u s c i t a t i o n . Early therapy of ci r c u l a t o r y arrests has proven to r e s u l t i n many saved l i v e s . Heart attack victims may also be placed under electrocardio-graphic monitoring. Drugs are administered i f necessary. For other l i f e - t h r e a t e n i n g circumstances minor surgery may have to be performed or oxygen may have to be given to the patient. Special extraction equipment may also be ca r r i e d by paramedics to get victims out of "hard to get places" such as from automobile wrecks. Members of the paramedic team can also provide valuable assistance i n the emergency ward. Summarizing the functions of a paramedic team we have: 6 - rapid response, - r e s u s c i t a t i o n from cardiac arrest, - early therapy of acute trauma and other li f e - t h r e a t e n i n g emergencies, and - transport of the patient to the ho s p i t a l . 1.2 REVIEW OF AMBULANCE SYSTEM MODELS 1.2.1 REVIEW OF RECENT LITERATURE Ambulance systems' models i n the l i t e r a t u r e can be c l a s s i f i e d into two categories. There are those that examine the queuing aspect of the problem and those that focus upon the location problem. With respect to the queuing aspect of the ambulance system both a n a l y t i c a l queuing models and simulation models have been developed and used. Fitzsimmons (2) developed both a queuing model and a simulation model to estimate a c t i v i t y l e v e l s . The queuing model predicted response time was dis t r i b u t e d for an actual operating system and the mean response time was i t e r a t i v e l y improved by the r e a l l o c a t i o n of the ambulances on the basis of a pattern search method. Global optimality could not be proven. Savas (24) studied New York City's emergency ambulance service. In the referenced system many ambulances were being dispatched from the hospitals. By using simulation he showed 7 that a substantial improvement i n mean response time could be attained by dispersing ambulance depots away from hospitals and throughout the service area. Chaiken and Larson (4) examined a number of urban emergency service systems and t h e i r operational problems. They suggest p o l i c i e s f o r : lo c a t i n g units, a l l o c a t i n g numbers, designing response areas, and r e a l l o c a t i n g units. Their p o l i c i e s are b a s i c a l l y derived from queuing models. A study by Swoveland et a l (29) uses simulation and a p r o b a b i l i s t i c branch and bound procedure to al l o c a t e ambulances. Output from the simulation provided information on system c h a r a c t e r i s t i c s under various ambulance assignments. The output was used to construct the objective function for the optimal location problem. Simulation was i n turn used to v e r i f y solutions from the branch and bound procedure. Kolesar (16) has developed square root laws for determining the number and location of emergency unit depots. His conclusion rests on the assumptions of low demand rate, and on a r r i v a l rates and service times being Poisson and exponen-t i a l l y d i s t r i b u t e d , respectively. The model can be used to give quick and rough approximations of response times. Literature on location analysis i s abundant, e s p e c i a l l y in the private sector. (I.E., Weber (35), Cooper(6), Kuhn 8 and Kuenne (18), e t c . ) 1 The warehouse problem i s a c l a s s i c example. Procedures to handle t h i s problem have been applied to public f a c i l i t y l o c a tion problems. Public f a c i l i t y location problems d i f f e r i n that t h e i r objective function i s to maximize the benefit to society as opposed to minimization of costs. Recently, most interest work i n public sector f a c i l i t y location analysis has been done by Revelle (19, 20, 21), Church (5) and Toregas (32, 33, 34). They have studied the use of the p-median, set covering, and maximal covering procedures i n locating ambulance depots. Although these models ignore the dynamic nature of the problem they do give an optimal solution to the s t a t i c problem. Using the maximal covering model one can f i n d the trade-off between the l e v e l of service and the number of ambulances used. For the ambulance problem the p-median model can be formulated so as to minimize average response time. Minimiza-t i o n of average response time is one of the major goals of the ambulance system i n the G.V.R.D. The maximal covering model finds the maximum number of people serviced within a s p e c i f i e d maximum response time by the ambulance system. By experimenta-t i o n one can f i n d the trade-off between the l e v e l of service and the number of ambulances needed. ±For an excellent bibliography on plant location see "Plant Location Family" Working Paper No. WP-12-77, Krarup, Jekob, Pruzan, and Mark, University of Calgary. 9 T h e u s e o f s i m u l a t i o n ( s t o c h a s t i c ) m o d e l s i n c o n j u n c t i o n w i t h l i n e a r p r o g r a m m i n g ( d e t e r m i n i s t i c ) m o d e l s w o u l d a p p e a r t o be a g o o d a p p r o a c h i n s o l v i n g a m b u l a n c e s y s t e m p r o b l e m s . B e r l i n a n d L e i b m a n (2) h a v e p r e v i o u s l y a t t e m p t e d s u c h a n a p p r o a c h w h e r e t h e y u s e d t h e s e t c o v e r i n g m o d e l t o l o c a t e d e p o t s a n d s i m u l a t i o n t o d e t e r m i n e u t i l i z a t i o n l e v e l s . A p - m e d i a n m o d e l i n c o r p o r a t e s more i n f o r m a t i o n t h a n a s e t c o v e r i n g m o d e l a n d , t h e r e f o r e , s h o u l d g i v e b e t t e r i n i t i a l s o l u t i o n s . 1.2.2 A P P L I C A B I L I T Y TO T H E G . V . R . D . M o s t o f t h e q u e u i n g m o d e l s i g n o r e t h e p r o b l e m o f c o n g e s t i o n ( i . e . a c a l l a r r i v e s w h i l e t h e a m b u l a n c e s t a t i o n c l o s e s t t o i t i s e m p t y ) . T h e y w o r k b e s t , t h e r e f o r e , when demand r a t e s a r e l o w . Many m o d e l s u t i l i z e t h e o r e t i c a l d i s t r i b u t i o n s w h i c h may n o t c o r r e s p o n d t o o b s e r v a t i o n s . T h e c o m b i n a t i o n o f m a t h e m a t i c a l p r o g r a m m i n g m o d e l s t o p r o v i d e "good" i n i t i a l s o l u t i o n s , a n d t h e e m p l o y m e n t o f a s i m u l a t i o n t o t e s t f o r o p t i m a l i t y a n d p r o v i d e d a t a n e c e s s a r y f o r l o c a l s e a r c h e s , i s c a l l e d f o r i n s y s t e m s c h a r a c t e r i z e d b y c o n g e s t i o n p r o b l e m s . T h e G . V . R . D . p r o v i d e s a n e x c e l l e n t e x a m p l e w h e r e s u c h a c o m b i n a t i o n o f t e c h n i q u e s i s n e e d e d . 10 CHAPTER 2 2 . 1 E X I S T I N G AMBULANCE S E R V I C E A t p r e s e n t , t h e e m e r g e n c y a m b u l a n c e s y s t e m s e r v i c e s t h e t o t a l G . V . R . D . a r e a . T h i s d i s t r i c t c o n s i s t s o f t h e l o w e r m a i n l a n d e x t e n d i n g e a s t t o A l d e r g r o v e . T h e m u n i c i p a l i t i e s s e r v i c e d b y t h e s y s t e m i n c l u d e : V a n c o u v e r , N o r t h V a n c o u v e r , W e s t V a n c o u v e r , B u r n a b y , New W e s t m i n s t e r , R i c h m o n d , D e l t a , S u r r e y , L a n g l e y , W h i t e R o c k , C o q u i t l a m , P o r t C o q u i t l a m , P o r t M o o d y , P i t t Meadows a n d M a p l e R i d g e . T h e t o t a l p o p u l a t i o n o f t h e a r e a i s a b o u t 1 , 1 7 2 , 0 0 0 . D u r i n g 1977 a b o u t 7 8 , 0 0 0 c a l l s w e r e s e r v i c e d b y t h e a m b u l a n c e s y s t e m . 2 . 1 . 1 T H E NETWORK The p h y s i c a l l a y o u t o f t h e r e g i o n c a n b e d e s c r i b e d f r o m t h e a m b u l a n c e s y s t e m ' s p o i n t o f v i e w b y a c o n n e c t e d n e t w o r k o f l o c a t i o n s a n d t r a v e l t i m e s b e t w e e n n o d e s i n t h e n e t w o r k . I n t h i s s t u d y we h a v e a d o p t e d t h e r e g i o n a l i z a t i o n scheme o f t h e G . V . R . D . B o a r d , d i v i d i n g t h e a r e a i n t o 169 s u b r e g i o n s . P o p u l a t i o n c e n t r o i d s o f e a c h s u b r e g i o n mark t h e n o d e s o n t h e a m b u l a n c e n e t w o r k . A m a t r i x g i v i n g t r a v e l t i m e s b e t w e e n a l l 11 pairs of nodes i n the system (the t r a v e l time matrix) was obtained from the G.V.R.D. Board. These times represented average t r a v e l times during the "morning rush hours". To examine the appropriateness of the information contained i n the matrix we have compared i t to t r a v e l times obtained from ambulance t r a v e l records (24-hour "a day records"). Travel times within each municipality were very s i m i l a r . However, s i g n i f i c a n t differences were found between the two sources of data for t r a v e l times between muni c i p a l i t i e s . Using the G.V.R.D. Board data (slower t r a v e l between municipalities) for planning ambulance services amounts to taking a more conserva-t i v e service posture. C l e a r l y ambulance allo c a t i o n s for periods of congested t r a f f i c w i l l make the service more equitable among mun i c i p a l i t i e s . 2.1.2 RESOURCES In the beginning of 1978 the ambulance service operated thirty-one cars, two of which were equipped as "paramedic units". Recently a t h i r d paramedic car has been added to the f l e e t . In addition to the f l e e t of the p r o v i n c i a l ambulance service there are several other ambulance services which have locations at U.B.C., Port Coquitlam and Port Moody. There are also volunteer services located i n West Vancouver. These peripheral services account for less than 2% of the t o t a l 12 c a l l s serviced i n the lower mainland. 2.1.3 COORDINATION AND MANAGEMENT The takeover by the p r o v i n c i a l government i n 1974 led to the adoption of a central dispatch system for the entire d i s t r i c t . (Previously services were "Balkanized".) The service operates 18 cars, 24 hours a day, nine additional cars are operated from 7:30 a.m. to 6:30 p.m., and f i v e cars from 12:00 a.m. to 11:00 p.m. Three of the cars operating 24 hours a day are paramedic units. The ears, which provide a contin-uous service, have two s h i f t s from 8:00 a.m. to 6:00 p.m. and from 6:00 p.m. to 8:00 a.m. The other vehicles operate during a one 11-hour s h i f t (see table 2.1). 2.2 DEMAND FOR AMBULANCE SERVICES 2.2.1 DATA COLLECTION The data used to analyze patterns of current demands and production components was obtained from dispatching forms which record the movements of each ambulance while i n service. The periods covered are from August 15 to August 24, 1977, and from September 1 to September 20, 1977. The s p e c i f i c i n f o r -mation obtained for each c a l l includes: - o r i g i n (location of patient), 13 TABLE 2.1 CURRENT LOCATION OF AMBULANCES IN GVRD AND SHIFTS OPERATED Shifts 0800-1800 Station Location # of Cars 1800-0800 0730-1830 1200-2300 Gl Vancouver 4 1 car 1 G2 Vancouver 1 1 G3 Vancouver 1 1 G4 Vancouver 1 1 G5 Vancouver 1 1 G6 Burnaby 3* 1* 1 G7 New Westminster 3* 1* 1 G7B New Westminster 1 1 G8 Vancouver 3 1 1 G9 Surrey 2 1 1 G10 Richmond 3 1 1 G i l Ladner 1 1 G12 Langley 1 1 G14 White Rock 1 1 G15 West Vancouver 1 1 G16 North Vancouver 2 1 1 G17 Haney 1 1 G18 Vancouver 1 1 G19 Coquitlam 1 1 one paramedic car located among these ** operates from 0700-1800 NOTE: This table does not include the non-provincially operated ambulances. 14 - destination of t r a v e l (location to which patient i s to be delivered), - sex and age of the patient, - p r i o r i t y r a t i n g of the c a l l ( i . e . transfer, non-urgent, emergency or paramedic c a l l ) , - time and date the c a l l was received, - time the ambulance l e f t i n response to the c a l l , °- time the ambulance arrived at the scene, - time the ambulance l e f t the scene, - time the ambulance arrived at i t s destination, - time the ambulance l e f t for i t s station, - time the ambulance arrived at i t s station, - time of cancellation of the c a l l ( i f applicable). 2.2.2 TABLE OF DEFINITIONS ANU (Ambulance Not Used): The s i t u a t i o n i n which the ambulance responds to the scene but i s not used for transport ( f i r s t aid may or may not be administered). Ambulance U t i l i z a t i o n : The percent of time an ambulance i s a c t u a l l y s e r v i c i n g a c a l l . Cancelled C a l l : A c a l l for an ambulance which i s cancelled before the ambulance reaches the scene. High P r i o r i t y C a l l (Code 3 or 4): Calls i n which the s i r e n i s used en route to the scene. Loading Time: The amount of time spent at the scene (time spent applying f i r s t aid, moving the patient into the ambulance, e t c . ) . Non-Primary Response: The s i t u a t i o n i n which a c a l l i s serviced by some ambulance other than the one whose depot i s closest to the scene of the c a l l (this may occur when the l a t t e r i s busy and therefore unavail-able to respond). Response Time: The elapsed time between a r r i v a l of the c a l l by the dispatcher and the a r r i v a l of the ambulance at the scene. Service Time: The elapsed time between a r r i v a l of the c a l l by the dispatcher and the time the ambulance clears the destination. Start-Up Time: The amount of time between the receipt of the c a l l by the dispatcher and the time the ambulance departs for the scene. Transfer C a l l : A non-urgent (often scheduled) c a l l i n which a patient i s transported between two points (e.g. from hospital to home) and does not receive f i r s t , a i d treatment. Unloading Time: The elapsed time spent at the point to which the patient i s transported (generally, time spent admitting patients into emergency wards). 2.2.3 CURRENT DEMAND A. TEMPORAL VARIATIONS i) Seasonal Variations: Analysis of monthly demand levels for 1976 and 1977 indicates that the demand i n the month of December i s the largest, probably due to the high stress and a c t i v i t y that the holiday season induces. Otherwise, no pattern i n month to month variations was discovered. i i ) Hourly Variation of Demands During the Day: Figure 2.1 provides average c a l l rates by time of day for the t o t a l 16 region. The lowest demand for the day i s approximately at 5:00 a.m. From 5:00 a.m. u n t i l 11:00 a.m. there i s a sharp and steady r i s e i n the number of c a l l s . Demand for transfer c a l l s seem to create a l o c a l peak around 11:00 a.m. Following a small decline, demand l e v e l increases to i t s global peak at approximately 2:00 p.m. From that time on, demands generally decline. B. DEMANDS FOR PARAMEDICS At the present time there are three paramedic cars, with the t h i r d car being added only recently. The two o r i g i n a l paramedic cars are stationed i n Burnaby and New Westminster. These two cars were i n i t i a l l y i n t r o -duced to serve those c a l l s requiring s p e c i a l procedures for which they were equipped. However, the heavy general demand for ambulance services required t h e i r deployment for a l l types of demands. A sample of t h e i r service records obtained for February 1978 revealed that the cars responded to an average of 19 c a l l s a day. These c a l l s consisted of 9% transfer c a l l s , 40% non-urgent c a l l s and 51% emergency c a l l s . Two to three c a l l s a day ( a l l emergency c a l l s ) required the use of the specia l i z e d equipment of the paramedic units and the spe c i a l i z e d t r a i n i n g of t h e i r attendants. 2.2.4 DEMAND GROWTH PATTERN The v a r i a t i o n i n hourly c a l l rates for each municipality are provided i n table 2.2. The day period 8:00 a.m. to 6:00 p.m. i s the highest demand period i n a l l m u n i c i p a l i t i e s . Comparing current day rates with those reported four years ago, one notes that demands i n Vancouver increased less r a p i d l y (about 50%) than demands i n New Westminster, Richmond, Delta, Surrey, 18 Average § c a l l s / h o u r M u n i c i p a l i t y 12M-8AM 8AM-6PM 6PM-12M Average of c a l Number 1s/day Vancouver 2 • 5 5 6 . 2 5 4 . 8 7 112 . 1 7 North Vancouver 0 . 2 3 0 .54 0 . 3 7 9 .he West Vancouver 0 . 2 3 0.18 k, . 0 0 Burnaby 0 .hi 1.02 0 . 8 0 18, . 33 New Westminster 0, .22 0 . 7 8 0 . 4 9 12. .42 Richmond 0. .16 0.70 0 . 4 3 10. 92 Delta 0.24 0.12 3 . 62 Surrey o . 30 0 . 5 8 0.60 12. 75 Langley 0. 15 0 . 2 5 0 . 1 9 k. 86 Coquitlam 0. 11 0 . 2 3 0.17 k. 25 P i t t Meadows - _ Maple Ridge 0.20 0. 12 3 . 33 White Rock - 0.22 0.09 3 . 21 Port Coquitlam - - - 0. 9 6 Port Moody -For missing v a l u e s , sample less than 10 c a l l s . TABLE 2. 2 D a i l y Ambulance Demand Rate by Time of Day and M u n i c i p a l i t y 19 Coquitlam and White Rock (60% - 100% increases). These r e l a t i v e changes represent recent s h i f t s i n the s p a t i a l d i s t r i b u t i o n of population i n the lower mainland. 2.3 PRODUCTION AND EVALUATION 2.3.1 PRODUCTION COMPONENTS Emergency ambulance service (EMS) i s one element of the ov e r a l l emergency medical care system. The focus of t h i s research, i s on the transportation function of an EMS system and, i n p a r t i c u l a r , the response time of ambulances used s o l e l y for ground transportation of patients. Other functions of the EMS such as treatment and rescue add to the q u a l i t y of service provided but are not examined here. Response time, a key at t r i b u t e of service quality, is calculated as the time the c a l l i s received by the dispatcher to the time an ambulance arrives at the scene. (See figure 2.2.) Figure 2.2 amb. amb. amb. amb. c a l l amb. arrives leaves arrives leaves rec'd leaves scene scene hospital hospital s t a r t - t r a v e l load t r a v e l unload return up to time to patient to time scene hosp. base _ _ Response - -Time - - - - - - - - - service Time 20 2.3.2 ANALYSIS OF COMPONENTS The average response time per time period per munici-p a l i t y i s shown i n tables 2.3 and 2.4. For most municipalities, the average response time i s greatest during the middle of the day and i s smallest during the morning hours of the day. These figures are highly correlated with the number of c a l l s during the same period. Congestion of demand i s c l e a r l y the dominant problem of the system as i t operates now. In Vancouver, Burnaby and New Westminster, the response times, compared to four years ago, have a l l s i g n i f i c a n t l y increased. Longer response times i n Richmond, Delta, and Langley r e f l e c t the low population density of the area (hence, r e s u l t i n g i n a longer t r a v e l time within subregions). Also given i n tables 2.3 and 2.4 i s the average service time by municipality. There i s l i t t l e v a r i a t i o n i n these times. Richmond, Delta, Langley, P i t t Meadows and Port Coquitlam a l l have high service times due to the long t r a v e l l i n g distances. Service times i n Burnaby and New Westminster include paramedic c a l l s which are usually longer than normal c a l l s . Vancouver's long service time can be explained, i n part, by the high number of transfer c a l l s which take longer to service (about an average of 70 minutes, see table 2.5). Figures 2A, 2B, 2C, 2D, 2E, and 2F give frequency and Average Response Time* (in minutes) Mun ic ipa l i t y 12M-8AM Time of Day 8AM-6PM 6PM-12M Overal1 (24 Hours) Average Serv ice Time Vancouver North Vancouver West Vancouver Burnaby New Westminster Richmond Delta Surrey Lang ley Conquitlam P i t t Meadows Maple Ridge White Rock Port Coquitlam Port Moody 8.8 8.9 11.0 1 1.2 12.3 12. 1 15.5 10.4 14.7 11.2 11.8 16.4 18.6 15.6 17.7 12.2 24.9 11.3 13 10 9 8.5 9-9 13 18.8 26.6 13-5 10.4 15.9 10.2 10.2 14.8 12.0 10.0 11.3 14.5 17.7 17.7 15.8 11.7 20.8 10.8 11.6 10.9 21.4 47.2 44.2 50.6 51 55.5 57 60.4 46.8 67.5 48.2 57.1 43.4 65.8 TABLE 2.3 Average Response Time and Serv ice Time by Muni c i pa l i ty (For miss ing va lues , sample less than 10 c a l l s ) * does not inc lude t r ans fe r c a l l s having a zero response time. Average Response Time- (in minutes) to Munic ipa l i ty Vancouver Time of Day Overa l l Average 12M-8AM 8AM-6PM 6PM-12M (24 Hours) Se rv i ce Time North Vancouver and West Vancouver Burnaby and New Westminster Richmond and Delta Surrey, Langley and White Rock Coguitlam, Port Moody, Port Coguit lam, P i t t Meadows and Maple Ridge 8.8 9.8 11.0 11.3 12.6 10.8 •14.7 11.4 17-4 16.2 14.8 13.2 9-0 8.9 15.3 23.4 12.0 12.4 12.1 10.5 15.8 17.1 13.6 12.6 47.2 46.2 52.8 58.0 50.9 54.2 TABLE 2.4 Average Response Time and Serv ice Time by Mun i c i pa l i t y Groups * does not include t r ans fe r c a l l s having a zero response time. cumulative d i s t r i b u t i o n s for response times for the whole G.V.R.D. and for the area of Vancouver, Burnaby, and New Westminster. (The frequency d i s t r i b u t i o n s show the percentage of c a l l s taking a ce r t a i n number of minutes. The cumulative d i s t r i b u t i o n s display the percentage of c a l l s i n which the response time did not exceed a s p e c i f i c value.) The cumulative d i s t r i b u t i o n s indicate that: - 50% of transfer c a l l s are responded to within 20 minutes - 84% of a l l non-urgent c a l l s are responded to within 20 minutes - 99% of a l l emergency and paramedic c a l l s are responded to within 20 minutes and further, - 85% of a l l c a l l s are responded to within 10 minutes. In figure 2E one can observe the impact of response times to transfer c a l l s on the t o t a l d i s t r i b u t i o n of response times. Erequency and cumulative d i s t r i b u t i o n s for service times are displayed i n figures 3A, 3B, 3C, and 3D. Service times for a l l c a l l s (except transfers) i s very similar to emergency c a l l s . Let us now examine average operation times by type of c a l l and time of day. These s t a t i s t i c s are noted i n tables 2.5 to 2.8. Table 2.5 contains data derived from observations for the t o t a l G.V.R.D. Average start-up times are lowest i n 24 the morning period and highest during the middle part of the day when the large majority of c a l l s occur. The high average start-up time for transfer c a l l s i s due to ambulance service s e r v i c i n g more urgent c a l l s f i r s t (transfer c a l l s are low p r i o r i t y ) . Response times for a l l categories i s highest during the middle part of the day when the c a l l load i s heaviest. Average service times transfer c a l l s have the highest average service times. Table 2.6 has s t a t i s t i c s for Vancouver, Burnaby, and New Westminster. The average response times for normal and emergency c a l l s are lower than for the t o t a l G.V.R.D. and indicate that the outlying regions have a larger response time due to longer t r a v e l distances. In table 2.7 the paramedic c a l l s are excluded from the data. Note that the average response time for emergency c a l l s i s 5.96 minutes (5 minutes and 58 seconds). Table 2.8 gives figures for average operation times for weekdays only. Average response times are higher than the average for a l l days. This was expected as weekdays furnish the periods of heaviest demand for c a l l s . Variations for average time spent at the scene do not d i f f e r s i g n i f i c a n t l y between tables 2.5 to 2.8. When paramedic c a l l s are excluded, average time at the scene goes down for emergency c a l l s . This indicates that the paramedic procedures take longer to perform than the normal c a l l procedures. 25 Time of Day Priority 12AM-8AM 8AM-6PM 6PM-12M Transfer Normal Emergency All Priorities % of calIs 17.8% 55.6% 26.7% 24.4% 51.6% 24.0% 100% Average start-up times Average response times Average time at scene Average service time 2.09 10 10.4 46.2 7.6 15.1 10.2 51.7 4.4 11.4 10 48 19 26.5 13.2 70.9 4.9 13.2 9.8 1.1 6.8 9.8 47.8 43.7 5.7 13.2 10.2 49.7 TABLE 2.5 Average Operations Times (in Minutes) by Type and Time of C a l l " (Al1 Days) * Startup and Response times do not include transfer calls which had a zero startup or response time. Time of Day P r i o r i t y 12AM-8AM 8AM-6PM 6PM-12M Transfer Normal Emergency A l l P r i o r i t i e s * of c a l l s 18.IS 54.7% 27.1% 2k.0% 53.7% 22.3% 100% Average s t a r t -up times 2.2 8.2 4.1 20.1 4.9 1.2 6 Average response time 9.4 15.5 10.6. 27.1 12.7 6.2 13 Average time at scene 9-9 10.2 9.7 12.7 9.7 9-3 10 Average se rv i ce time 44.2 51.7 45-7 69.6 46.8 41.9 """" 48.7 TABLE 2.6 Average Operations Times (in Minutes) by Type and Time of Cal l " (Vancouver, Burnaby and New Westminster Only) * Startup and Response times do not include t rans fer c a l l s which had a zero startup or response time. CO Time of Day P r i o r i t y 12AM-8AM 8AM-6PM 6PM-12M Transfer Normal Emergency AM P r i o r i t i e s % of c a l l s 17.89% 55-19% 26.9% 24.8% 55.4% 19.8% 100% Average s t a r t -up times 2.2 8.45 4.3 20.1 4.89 1.1 6.2 Average response times 9-4 . 15„7 10.75 27.1 12.7 5.96 13 .2 Average time at scene 9-65 10.2 9-49 12.7 9-7 8.8 9.9 Average se rv i ce time 43-2 51.77 45.4 69-5 46.7 40.4 ' 48 .5 TABLE 2,7 Average Operations Times (in Minutes) by Type and Time of C a l l " : (Vancouver, Burnaby and New Westminster Only. No paramedic c a l l s ) •i'r ;"' :. * Startup and Response times do not include t rans fer c a l l s which had a zero startup or response time. Time of Day P r i o r i t y 12AM-8AM 8AM-6PM 6PM-12M Transfer Normal Emergency A l l P r i o r i t i e s % of c a l l s 15.7% 58.9% 25.4% 28.7% 48.5% 22.8% 100% Average s tar t -up times Average response times 2. 1 10.3 8.8 16.5 4.1 11.2 1 9 - 9 27.6 5.5 14 1.1 6.8 6.6 14.2 Average time at scene Average se rv i ce time 10 46 10.2 53.1 10.2 48.5 13.2 72.6 9-7 9-5 48.5 43.4 10.2 50.9 TABLE 2,8 Average Operations Times (in Minutes) by Type and Time of Day* (Only Weekdays) " Startup and Response times do not include t rans fer c a l l s which had a zero startup or response time. The s p a t i a l d i s t r i b u t i o n s of c a l l destinations i s given i n table 2.9 ( i . e . , where the ambulances go a f t e r picking up t h e i r patients). From l e f t to r i g h t the hospital abbreviations stand f o r : Vancouver General, St. Paul's, Burnaby General, St. Mary's, Lion's Gate, Royal Columbian, Shaughnessy, Richmond General, Langley Memorial, Maple Ridge, Peace Arch, and other (including Surrey h o s p i t a l s ) . ) . Hospitals whose emergency rooms are st a f f e d to provide v i r t u a l l y any kind of emergency treatment necessary are: Vancouver General, St. Paul's, Lion's Gate and Royal Columbian. Table 2.10 i s the complement of table 2.9, giving the d i s t r i b u t i o n of c a l l o r igins by h o s p i t a l . 30 HOSPITALS Munic ipa l i ty VGH SHY SPH Vancouver 46. 46 8. 36 26. 42 North V a n c o u v e r 6 . 95 0. 53 2. 67 Vest Vancouver 0. 0 0. 0 2. 35 3urnaby 10. 83 2. 56 1 . 14 view Westmi nster 6. 35 1. 19 0. 79 Ri chmond 25. 11 5. 73 5. 29 Del ta 11 27 2. 82 0. 0 Surrey 2 73 1. 17 0. 39 Langley 6 12 2. 04 3. 06 Coqu i tlam 1 25 2. 50 0. 0 P i t t Meadows 0 0 0. 0 0. 0 Maple Ridge 3 03 1 . 52 1. 52 White Rock 4. 55 0. 0 1. 52 Port Coquitlam 5 56 0. 0 0. 0 Port Moody 0 0 0. 0 0. 0 BGH SMH LGH RCH SMY 2.77 0.20 1 .24 0 .20 0 .64 0.0 0.0 71.66 0.0 0.53 1.18 0.0 83-53 0.0 0.0 39-89 0.85 0.0 4 .84 25-93 3.97 4.37 2.20 . 18.25 42.86 0 .88 0.44 0.0 0.44 2.20 1.41 23.94 0.0 0.0 8.45 0.0 56.25 1 .02 0.78 16.80 0.0 2 .04 0.0 0.0 19.39 0.0 1.25 0.0 6.25 77-50 0.0 0.0 0.0 0.0 33-33 0.0 0.0 0.0 0.0 7.58 0.0 3.03 0.0 0.0 4.55 0.0 0.0 0.0 22.22 66.67 0.0 0.0 0.0 0.0 100.0 RGH LMH MRH PADH Othe 0.69 0.15 0. 1 0. 1 12.6 0.0 0.53 0 . 0 0 . 0 17. 1 0.0 0.0 0 .0 0 .0 12.« 0.0 0.0 0.28 0 .0 12.J 0.0 1.59 1.59 0 .0 19.C 47 .14 0.0 0 .44 0 .0 10.1 43.66 0.0 0.0 0.0 8.1 0.0 3.52 0 .39 9 . 77 8..J 0.0 6 3 . 2 7 0.0 1.02 2.( 0.0 0.0 1.25 0.0 10.( 0.0 0.0 6 6 . 6 7 0.0 o.c 0.0 0 .0 7 8 . 7 9 0.0 7-f 0.0 0 .0 0.0 75.76 10.1 0.0 5.56 0 . 0 0.0 OA 0.0 0 .0 0 . 0 0.0 O.C TABLE 2.9 D i s t r i b u t i o n of Ambulance (Rows sum to 100%) Dest inat ions by Mun i c ipa l i t y Hosp i ta l s u n i c i p a l i t y VGH SHY SPH BGH SMH LGH RCH SMY RGH LMH MRH PADH ancouver 8 6 . 07 82. 44 9 4 . 51 26. 6 7 2 . 16 10. 46 5. 06 3-50 9- 21 3. 7 5 3. 13 2.56 or th Vancouver 1. 1 9 0. 49 0. 89 0. 0 0 . 0 5 6 . 07 0 . 0 0.27 0. 0 1. 25 0. 0 0.0 est Vancouver 0. 0 0. 0 0. 35 0. 4 8 0. 0 29. 71 0 . 0 0 . 0 0. 0 0. 0 0. 0 0.0 urnaby 3- 4 8 4. 39 0. 71 66. 67 1. 62 1. 26 21 . 52 2 4 . 4 6 b. 0 0. 0 1. 56 0.0 ew Westminster 1. 47 1. 4 6 0. 35 4. 76 5. 95 ' 0. 0 58. 23 29.03 0. 0 5. 00 6. 25 0.0 i chmond 5. 23 6. 34 2. 12 0. 95 0. 54 2. 09 1. 27 1.34 70. 39 0. 0 1. 56 0.0 e l t a 0. 73 0. 98 0. 0 0. 4 8 9. 19 0. 0 0 , 0 1.61 20. 39 0. 0 0. 0 0.0 urrey 0. 6 4 1. 4 6 0. 1 8 0. 0 77. 8 4 0. 0 2. 53 11.56 0. 0 11. 25 1. 56 32 .05 angley 0. 55 0. 98 0. 53 0. 0 1. 08 0. 4 2 0. 0 5.11 0. 0 77. 50 0. 0 1 .28 oqui tlam 0. 09 0. 98 0. 0 0. 0 0. 54 0. 0 6. 33 16.67 0. 0 0. 0 1. 56 0.0 i t t Meadows 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 o: 0 0.27 0. 0 0. 0 3. 13 0.0 aple Ridge 0. 18 0. 49 0. 18 0. 0 0. 0 0. 0 0. 0 1.34 0. 0 0. 0 8 1 . 25 0.0 h i t e Rock 0. 28 0. 0 0. 18 0. 0 1. 08 0. 0 0. 0 0.81 0. 0 0. 0 0. 0 65. 10 ort Coquitlam 0. 09 0. 0 0. 0 0. 0 0. 0 0. 0 5. 06 3.23 0. 0 1. 25 0. 0 0.0 ort Moody 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 0 0,81 0. 0 • 0, 0 0. 0 0.0 verage # cal1s/day 45. 4 6 8. 54 23. 54 8. 75 7. 1 71 9. 96 3. 29 1 5 . 5 0 6. 33 3. 33 2. 67 3-25 O J N J TABLE 2.10 D i s t r i b u t i o n of Ca l l O r i g in by Dest inat ion (-i.e., by Hospita l ) (Columns sum to 100%) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 Minutes Frequency D i s t r i b u t i o n FIGURE 2A 1 1 1 J I I I I 1 I I I I I I 1 1 f •] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 Minutes FIGURE 2B Cumulative D i s t r i b u t i o n D i s t r i b u t i o n of Response times ( A l l Municipalities) 33 a l l c a l l s , a l l , except transfer c a l l s emergency c a l l s only. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 Minutes Frequency D i s t r i b u t i o n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 Minutes FIGURE 2C Cumulative Distributions Distributions of Response times (Vancouver, Burnaby and New Westminster only) 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Minutes Frequency. D i s t r i b u t i o n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 Minutes FIGURE 2D Cumulative D i s t r i b u t i o n D i s t r i b u t i o n of Response times emergency c a l l s ( A l l Municipalities) only paramedic c a l l s only 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 Minutes FIGURE 2E Frequency D i s t r i b u t i o n Minutes FIGURE 2F Cumulative D i s t r i b u t i o n D i s t r i b u t i o n of Response times transfer c a l l s ( A l l Municipalities) only ordinary c a l l s only. 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 Minutes FIGURE 3A Frequency D i s t r i b u t i o n 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 20 Minutes FIGURE 3B Cumulative D i s t r i b u t i o n D i s t r i b u t i o n of Service times ( A l l Municipalities) 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Minutes FIGURE 3C Frequency D i s t r i b u t i o n Minutes FIGURE 3D Cumulative D i s t r i b u t i o n D i s t r i b u t i o n of Service times (Vancouver, Burnaby and New Westminster only) 38 a l l c a l l s a l l c a l l s , except transfer emergency c a l l s only CHAPTER 3 THE COMPUTER SIMULATION MODEL 3.1 USE OF SIMULATION IN THE ANALYSIS OF EMERGENCY AMBULANCE SYSTEMS  One important evaluation c r i t e r i o n of an ambulance system i s i t s response time. There are six major factors which a f f e c t response time of ambulances: - the frequency of c a l l s , - the geographical d i s t r i b u t i o n of c a l l s , - the number of ambulances available for service, - the loc a t i o n of hospitals, - the location of ambulance depots, and, - the general p o l i c i e s which govern ambulance services. The ambulance system i s a complex stochastic system with many possible management options. Management of an ambulance system involves an array of interdependent decisions concerning resource inputs to the system and t h e i r deployment. As the performance of an ambulance system i s multi-faceted i t i s d i f f i c u l t to capture the complexity of the system through simple a n a l y t i c a l models. Computer simulation offers an a l t e r -native method. Through computer simulation i t i s possible to obtain predictions of alternative demand contingencies and pol i c y responses. The simulation offers a "laboratory world" i n which alt e r n a t i v e p o l i c i e s can be tested instantaneously and changes introduced without the high costs of t r i a l and error i n the r e a l world. 3.1.1 THE STOCHASTIC ELEMENTS OF AN AMBULANCE SYSTEM Secondary responses ( i . e . , ambulances responding to demands that are re g u l a r l y served by other ambulances whose depots are closer) r e s u l t i n g from congestion i n the system i n h i b i t the use of analytic models. Furthermore, many of the stochastic variables of the system are d i s t r i b u t e d without correspondance to any known t h e o r e t i c a l d i s t r i b u t i o n . There-fore, i n the ambulance simulation, empirical d i s t r i b u t i o n s are used d i r e c t l y . The simulation uses as inputs, the empirical d i s t r i b u -tions of the following variables: - i n t e r - a r r i v a l times of c a l l s (by type and location, and - loading and unloading times. 3.2 GENERAL DESCRIPTION OF THE COMPUTER SIMULATION MODEL A GPSS (General Purpose Simulation System) computer 40 simulation model was b u i l t to analyze the behavior of the ambulance system i n the G.V.R.D. GPSS was chosen as the simulation language since i t s elements are homomorphic to the ambulance system. Two basic elements of GPSS are: movement (units of t r a f f i c ) and service stations ( f a c i l i t i e s ) . In the ambulance system model the unit of t r a f f i c i s the patient and the service stations are the ambulances. A patient or c a l l represents a transaction. A complete transaction is a movement of the ambulance from the l o c a t i o n where a demand originates to the destination, and back again to the depot. Two other basic elements of GPSS are queues and a time clock. Queues i n the ambulance model are represented by the following: response times, service times, and time spent waiting for an ambulance to become free. The time clock automatically sequences a l l events. In an ambulance system the sequence of events for each transaction i s s i m i l a r . 3.2.1 GENERAL OUTLINE The simulation model consists of two major parts. Part one handles the non-paramedic c a l l s , while part two handles the paramedic c a l l s . Both non-paramedic and paramedic ears can be used to service c a l l s of either type.-^ i T h i s p o l i c y i s under control of the user and the model can be altered so designated cars answer only one type of c a l l . 41 Let us f i r s t consider the operation of part one of the model. A non-paramedic c a l l enters the model through the job-tape, and i s routed to part one where a check i s made to see i f any ambulances are available for service within a radius of 30 minutes t r a v e l from the scene. The closest non-paramedic ambulance i s designated to service the c a l l . If no ordinary ambulances are available a search i s made to see how many paramedic ambulances are available. If no ambulances can service the c a l l the transaction i s queued by p r i o r i t y (emergency, normal, and transfer) and by c a l l order. For the ambulance designated to service the c a l l , the tr a v e l time to the scene i s determined. If the ambulance was at the depot at the time the c a l l was received, a start-up time i s added to the t r a v e l time. For emergency c a l l s the t r a v e l time i s multi p l i e d by a constant ( K 1) re speed-up to indicate that i t w i l l be using the sire n while en route to the c a l l . While t r a v e l l i n g to the scene the c a l l may be cancelled. Cancellation may also occur once the ambulance arrives at the scene. In either case, the c a l l i s terminated and the ambulance checks for other c a l l s to be serviced. I f the c a l l i s cancelled a f t e r the ambulance arrives at the scene i t s response time i s calculated. Once the ambulance arrives at the scene the patient i s loaded and transported to a s p e c i f i c destination (e.g., the hospital) where the patient i s unloaded. Response time i s 42 calculated when the car arrives at the scene and service time i s calculated after the patient i s unloaded. After unloading the patient the ambulance checks for other waiting c a l l s . Waiting paramedic c a l l s are serviced f i r s t , then emergency c a l l s , then normal c a l l s and f i n a l l y transfer c a l l s . If there are no c a l l s waiting to be serviced, the ambulance travels back to the depot and waits for the next c a l l . When a paramedic c a l l i s processed through the model i t is routed to part two of the model. Since both-*- paramedic and non-paramedic cars may answer these c a l l s , part two i s s p l i t into a stream for paramedic cars and a stream for non-paramedic cars. The following decision rules are used: 1. Contingency: there i s an ambulance of each type available response -(A) If an ordinary ambulance i s closer i t i s dispatched. After i t arrives a decision i s made whether to I. cancel the ordinary ambulance and wait, i f necessary, for the para-medic ambulance; paramedic ambulance carri e s patient, or I I . cancel the paramedic ambulance; ordinary ambulance ca r r i e s patient. (B) If the paramedic ambulance i s closer, i t i s dispatched and i t ca r r i e s the patient. 2. Contingency: ordinary but no paramedic ambulance -•-The model builder can control the p o l i c y regulating which cars can answer paramedic cars v i a a te s t block. 43 i s available Response: dispatch ordinary ambulance and queue for a paramedic one (A) If an ordinary ambulance arrives before a paramedic ambulance i s sent - cancel the c a l l for the paramedic ambulance and l e t the ordinary one carry the patient. (B) If a paramedic ambulance i s sent before an ordinary arrives and I. paramedic ambulance arrives f i r s t -cancel the ordinary ambulance, or II. ordinary ambulance arrives f i r s t 1) cancel the ordinary ambulance and wait, i f necessary, for paramedic ambulance, paramedic ambulance carries patient, or 2) cancel the paramedic ambulance and l e t ordinary carry patient. 3. Contingency: paramedic ambulance but no ordinary ambulance i s available Response: dispatch the paramedic ambulance. 4. Contingency: no ambulance of any type i s available Response: queue for both types (A) If paramedic ambulance available f i r s t , only dispatch that ambulance (B) If ordinary ambulance i s available f i r s t , do the same as i n the s i t u a t i o n described i n 2. Let us examine the case where there i s an ambulance of each type available and the ordinary ambulance i s closer. A paramedic c a l l enters the model. I t is routed to the 44 paramedic section. Two transactions are created. One trans-action ( c a l l i t transaction A) enters the ordinary car stream and the other transaction ( c a l l i t transaction P) enters the paramedic car stream. F i r s t transaction A enters the queues and finds an ordinary ambulance that i s available within t h i r t y minutes. The f a c i l i t y number and the time to the scene are saved and then the transaction stops. Now transaction P i n the paramedic car stream i s executed. It notes the ordinary f a c i l i t y , enters the queues, and finds a free paramedic ambulance. Then response time i s determined and i s compared to the response times for the two ambulances. In t h i s case the ordinary ambulance i s closer. Transaction P then creates a duplicate (say transaction Q). Transaction P i s then loaded on a user chain. Transaction Q advances to the scene. While the paramedic i s t r a v e l l i n g , transaction A checks to see i f a paramedic was available and subsequently moves to the section where both cars are available. Then i t compares the response times and finds that the ordinary ambulance i s closer. The f a c i l i t y (ambulance) i s captured (made unavailable for other c a l l s ) and also advances to the scene. Afte r the ordinary ambulance arrives i t leaves the queues and waits for another minute to decide whether to cancel or not. If the paramedic ambulance has not arrived, the ordinary ambulance cancels the paramedic en route i n 75% of the time. Transaction P i s removed from the user chain and sent to look for another c a l l . Transaction A proceeds to load the patient, carry and unload him i n the ho s p i t a l . Then i t looks for another c a l l . In the meantime, transaction Q on the paramedic stream arrives at the scene and searches the user chain for transaction P. Since i t does not f i n d i t , i t concludes that the c a l l f o r a paramedic ambulance i s cancelled and the transaction terminates. Twenty-five per cent of the time the ordinary ambulance randomly cancels i t s e l f . This r e f l e c t s the actual proportion of times th i s occurs i n r e a l - l i f e s i t u a t i o n s . Transaction A is then put on a user storage chain. When the paramedic car arrives at the scene i t searches the user chain for transaction P. It finds i t and transaction Q terminates. Transaction P departs the queues, tabulates response time and checks to see i f the ordinary ambulance has decided to cancel i t s e l f . When th i s i s the case, transaction P takes transaction A o f f the user chain and subsequently services the c a l l . After unloading at the hospital, i t searches for another c a l l . Transaction A counts the cancella t i o n as an ambulance not used and the ordinary car searches for another c a l l . In the above i l l u s t r a t i o n i t i s shown that there are two cars simultaneously pursuing one c a l l and thus there i s a need for two streams. The paramedic section of the model i s also represented i n figure 3.1. The possible states of an ordinary ambulance 46 when a car arrives are: unavailable (N/A) and available. These are the headings for columns one and two. Rows one and two give the state for a paramedic ambulance. Column three represents an a r r i v a l of an ordinary ambulance at the scene. - i f no paramedic ambulance has been dispatched, the paramedic ambulance i s cancelled and the ordinary ambulance carries the patient. - If a paramedic ambulance has been dispatched, the ordinary ambulance makes a decision whether to cancel the paramedic or not. Row two (columns two and three) states that i f neither ambulance i s available and the paramedic i s available f i r s t , then the ordinary i s cancelled. Row three, column two, represents the s i t u a t i o n where an ordinary ambulance was dispatched and a paramedic was dispatched l a t e r but arrived at the scene before the ordinary ambulance, the ordinary ambulance i s cancelled. 47 FOR A PARAMEDIC CALL ORDINARY AMBULANCE N/A EN ROUTE DECIDING Await Developments Cancel Ordinary Await DeveloDments Await Developments Cancel Ordinary Cancel Paramedic Await Developments ^ Cancel Paramedi Wait f o r . Paramedic and cancel Ordinary Await Developments ^ Cancel Paramedi Wait fo r Paramedic and cancel Ordinary (Same i f both ava i lab le Paramedic closer) FIGURE 3.1 48 3.2.2 INPUTS The inputs to the model consisted of information con-cerning 4800 actual c a l l s which took place between August 16, 1977 and August 23, 1977 and between September 3, 1977 and September 19, 1977. These c a l l s were entered on a f i l e for the use of the simulation model. For each c a l l or transaction the following information was provided: scene of the c a l l , municipality of the c a l l , destination (hospital), type or p r i o r i t y of the c a l l (1 - transfer, 2 - normal, 3 - emergency and 4 - paramedic). The i n t e r - a r r i v a l time, the time i t took to load and unload the patient, and i n the case where the c a l l was cancelled the time from dispatch to cancellation was recorded. For missing loading or unloading data, a value was estimated from the empirical d i s t r i b u t i o n . The model also used t r a v e l time data. This data was used to determine the time needed to t r a v e l from the place of dispatch to the node representing the scene and from there to the h ospital. The model also contained general information on a l l the ambulances. This information included the location of depots, the number of ambulances at each depot, the type of ambulance located at each depot and the periods when each ambulance i s available. 49 3.2.3 OUTPUTS The simulation recorded response times, service times, number of c a l l s answered by each ambulance, the average u t i l i z a t i o n per ambulance, and s t a t i s t i c s on length of queues. Outputs of the simulation were: the o v e r a l l average response times per type of c a l l , a d i s t r i b u t i o n of response times per type of c a l l , the average response time per type of c a l l per municipality and the average response time for a l l c a l l s per subregion. For service time only the o v e r a l l averages and t h e i r associated frequency d i s t r i b u t i o n were recorded. For each subregion and each municipality, s t a t i s t i c s on the maximum and average contents of the queue were recorded along with the t o t a l entries. Other s t a t i s t i c s gathered included the t o t a l number of c a l l s , by type, that had to stand i n the queue and the average time spent waiting i n these queues. 3.2.4 MODEL VALIDATION The conventional measure of v a l i d i t y i s the degree of correspondence between the simulated system and the referent system. Higher correspondence can be achieved by increasing the complexity and d e t a i l of the model. The appropriate l e v e l of correspondence i s decided by the value of the added i n f o r -mation. This pragmatic c r i t e r i o n of v a l i d a t i o n states that refinements should be stopped when no net benefits can be 50 obtained by r e f i n i n g the model to improve i t s correspondence to r e a l i t y . In the ambulance simulation several measures were taken to ensure v a l i d i t y . F i r s t , the model and i t s desired output were discussed with management (in p a r t i c u l a r the desired degree of s p a t i a l r esolution). Second, when possible, empiri-c a l d i s t r i b u t i o n s were used, and therefore, loss of information derived from data inputs was decreased. F i n a l l y , test of correspondences between simulated and actual time series were conducted. This was done for each component of the model and the model as a whole. In the computer simulation model start-up times were adjusted for each type of c a l l to c a l i b r a t e the model. Start-up time i s the time from when a c.all i s dispatched to leave for the scene and the actual time i t did leave. Data gathered from the ambulance service records contained information on the time a c a l l was received, the time the c a l l was dispatched and the a r r i v a l time at the scene. With t h i s information one could only estimate response times which included start-up times. The start-up time could not be is o l a t e d and was, there-fore, used as a residual to c a l i b r a t e the model. The t r a v e l times used i n the simulation were obtained from the G.V.R.D. These were compared against actual data records from the ambulance service. It was found that t r a v e l times for short distances were very s i m i l a r . (See Appendix.) 51 A te s t was also conducted to compare t r a v e l times by day and night for both urban and r u r a l m u n i c i p a l i t i e s . It was found that the t r a v e l times for r u r a l municipalities during the day needed to be adjusted downward by 10%, t r a v e l times for urban municipalities during the evening needed to be adjusted down-ward by 10% and t r a v e l times for r u r a l municipalities needed to be adjusted downward by 25%. The f i n a l set of variables for which correspondences were tested were: - actual and simulated average response times, - actual and simulated emergency c a l l d i s t r i b u t i o n s , - actual and simulated response times by type of c a l l by municipality, and - actual and simulated number of c a l l s answered by each f a c i l i t y . The comparison of the actual and simulated average response times by type of c a l l and municipality are presented i n table 3.1. The comparison of the average response time for each type of c a l l shows that the simulated times d i f f e r from the actual by 12 seconds for emergency c a l l s , by 19 seconds for ordinary c a l l s , by 12 seconds for transfer c a l l s , and by less than 10 seconds for paramedic c a l l s . Average response times by type of c a l l for Vancouver only, which produced by far the greatest block of c a l l s i n any municipality, were almost COMPARISON OF RESPONSE TIMES BY PRIORITY AND MUNICIPALITY ( a l l times are i n minutes) TRANSFER CALL ORDINARY CALL EMERGENCY CALL Actual Simulated Actual Simulated Actual Simulated Average 19.46 19. 21. 25 02 12.69 12. 13. 43 00 6.62 6. 21 Municipality-Vancouver* 19.91 19. 68 11.35 10. 64 5.49 5. 47 North Vancouver 10.94 18. 23 9.54 11. 51 6.55 6. 15 West Vancouver 32.53 20. 61 10.94 15. 93 8.17 10. 28 Burnaby 22.51 18. 86 15.4 12. 02 7.72 6. 58 New Westminster 20.97 16. 87 17.12 11. 63 6.53 6. 28 Richmond 22.55 19. 19 17.2 13. 26 7.1 7. 68 Delta 19.13 19. 61 18.39 13. 91 10.19 8. 85 Surrey 10.54 17. 34 13.02 12. 02 7.3 7. 27 Langley 16.3 23. 79 23.78 17. 85 11.24 11. 29 Coquitlam 13.15 19. 64 12.38 12. 16 6.57 6. 72 P i t t Meadows * 23.0 20. 20 * Maple Ridge 14.0 22. 40 13.5 18. 94 6.42 7. 17 White Rock 22.86 21. 16 11.44 9. 16 7.67 7. 70 Port Coquitlam * 21.44 15. 71 * Port Moody * 15.5 14. 62 5.0 9. 78 Number of Calls ; 1015 2541 996 Vancouver* proportion 47% 62% 54% of c a l l s Actual Simulated Paramedic 8 min. 6.10 min. Service time 49.7 min. 49.80 min. *Less than 10 c a l l s TABLE 3.1 53 i d e n t i c a l for emergency c a l l s , d i f f e r e d by 43 seconds i n ordinary c a l l s and d i f f e r e d by 13 seconds i n transfer c a l l s . In general, simulated response times for emergency c a l l s for each municipality were very s i m i l a r to actual response times. Since emergency c a l l s have the highest p r i o r i t y and thus are of the highest concern to management, these results are very encouraging. Comparing response times by municipality for ordinary c a l l s , one finds that the differences range from 43 seconds up to 5.93 minutes i n Langley (a r u r a l d i s t r i c t ) . For transfer c a l l s (lowest p r i o r i t y c a l l s ) one finds differences of up to 12 minutes i n West Vancouver. But, on the average, the differences are small, since there were only 227 paramedic c a l l s a comparison of response time by municipality would not be meaningful. The o v e r a l l average service time difference between actual and simulated data was less than three minutes. The comparison of the d i s t r i b u t i o n of simulated emer-gency response times with actual times i s displayed i n figure 3.2. Due to a % minute start-up time and a minimum inter-node t r a v e l time of 1.2 minutes, the simulation started to record response times from the 2 minute l e v e l and upwards by 1 minute i n t e r v a l s . The r e s u l t i n g discrepancy, however, narrows down for higher response times. With a difference of less than 5% for the range of 5 minutes to 20 minutes, i t was concluded that the two d i s t r i b u t i o n s are s i m i l a r . 54 COMPARISON OF CUMULATIVE DISTRIBUTION OF ACTUAL EMERGENCY RESPONSE TIME VERSUS SIMULATED EMERGENCY RESPONSE TIME Cumulative Percentage ioo%h Response time in Minutes FIGURE 3.2 55 Another t e s t for v a l i d a t i o n was the comparisons of simulated and actual c a l l s per day per sta t i o n . These are shown i n table 3.2. The average t o t a l number of c a l l s per day answered i n the simulation i s almost the same as i n the actual data. In a comparison of actual and simulated data conducted for each station, two stations with s i g n i f i c a n t differences were discovered. One i s the Burnaby s t a t i o n . Burnaby and New Westminster have the only paramedic cars. Often when a paramedic c a l l occurs, both an ordinary and a paramedic car w i l l t r a v e l to the scene, and therefore, the c a l l i s counted as two c a l l s by the simulator. This, i n part, explains the discrepancy. Station G8 (located at the south end of the second narrows bridge) also shows a large discrepancy. This is due to the fact that the ambulances from t h i s s t a t i o n are being c a l l e d to handle some of the numerous Vancouver c a l l s , thus being routed away from home. Also these cars are crossing into North Vancouver where the t r a v e l times are longer. In the present system these cars may r a r e l y go into North Vancouver, but t h i s constraint was not inserted i n the simula-t i o n . For a l l other stations the average numbers of simulated c a l l s per day were very similar to the numbers of actual c a l l s . A f i n a l test was to evaluate the impact of the length of the run. It was found that the standard deviations lowered with more c a l l s and time series started to s t a b i l i z e a f t e r 56 COMPARISON OF CALLS/DAY BY STATION: VALIDATION Simulation Model August Data September Data Ca l l s per day Ca l l s per day Ca l l s per day Gl - Vancouver 31.85 31.8 34.5 G2 - Vancouver 18.19 20.5 20.8 G3 - Vancouver 8.47 10.4 9.5 G4 - Vancouver 13.17 12.1 12.43 G5 - Vancouver 12.77 12.7 12.47 G6 - Burnaby 19.98 15.2 13.33 G7 - New Westminster 20.07 18.0 20.47 G8 - Vancouver 22.98 29.3 28.40 G9 - Surrey 11.11 12.2 12.17 GIO - Richmond 13.22 10.7 . 11.70 G i l - Delta 2.91 4.1 2.73 G12 - Langley 4.93 5.1 5.50 G14 - White Rock 4.93 4.7 4.33 G15 - West Vancouver 2.78 4.1 4.17 G16 - North Vancouver 11.20 9.4 10.40 G17 - Haney 3.54 4.8 4.17 G18 - Vancouver 10.53 10.2 9.0 G19 - Coquitlam 7.75 5.6 6.43 Ca l l s per day 220.38 220.9 222.5 TABLE 3.2 57 3500 c a l l s . S e n s i t i v i t y tests were also conducted. The following parameters were examined: start-up times, speed-up factors for emergency c a l l s , number of c a l l s per day and t r a v e l times. The response v a r i a t i o n of start-up times were li n e a r , as expected, the model was sensitive to changes i n the speed-up factor for emergency c a l l s and changes i n the t r a v e l times. The model was very sensitive to changes i n the number of c a l l s per day i n d i c a t i n g that the r e a l system operates near capacity. 58 CHAPTER 4 THE AMBULANCE LOCATION PROBLEM This chapter considers the problem of locating ambulances so as to minimize mean response time. 4.1 ESSENTIAL FEATURES OF THE AMBULANCE LOCATION PROBLEM The deterministic location problem assumes the following: - the closest ambulance i s always dispatched, - an ambulance i s always available at the station when a c a l l i s received, - a l l c a l l s have the same p r i o r i t y , and - the rate of c a l l s i s constant throughout the day. In contrast, i n the stochastic formulation i t i s recognized that: - ambulances are not always available at the i r s t a t i o n when a c a l l i s received, - the p r o b a b i l i t y that an ambulance is at i t s s t a t i o n depends upon the incidence rate, - the response time for a c a l l depends - upon the number of ambulances which are busy when a c a l l i s received, and, - since during peak periods the hos p i t a l becomes a departure point for ambulances 59 responding to c a l l s , the location of hospitals a f f e c t mean response time. The stochastic formulation indicates that the assignment of ambulances i s a dynamic problem. The d e t e r m i n i s t i c - s t a t i c formulation can serve only as a crude approximation to the stochastic system. This approximation i s v a l i d only for systems with l i t t l e or no congestion problems. In the next section of this chapter two deterministic approximations to the problem are considered. 4.1.1 ANALYTIC-DETERMINISTIC APPROXIMATIONS Two models are considered: 1. Maximal covering location model, and, 2. P-Median Model. The two models are crude approximations to the stochastic assign-ment problem and are used to i d e n t i f y "good" i n i t i a l solutions. 4.2 THE MAXIMAL COVERING LOCATION PROBLEM In solving public f a c i l i t y location problems two surro-gate measures of value are: t o t a l weighted distance and the distance of the most distant user from a service f a c i l i t y . Total weighted distance i s used i n the p-median model which w i l l be discussed l a t e r . The maximal covering location problem (MCLP) uses maximal service distance as the surrogate measure 60 for the value of a given configuration of locations. The model allocates p f a c i l i t i e s to positions on the network such that the maximum number of people w i l l f i n d service within a stated distance or response-time standard. If a l l of the population is serviced within the response-time standard then the maximum distance which an ambulance would have to t r a v e l to reach the patient would r e f l e c t the worst possible performance of the system. With the MCLP model a trade o f f curve may be developed showing various levels of coverage within desired distances for a range of f a c i l i t i e s . For example, ten depots may service 80% of the population within a sp e c i f i e d distance while 15 depots may service 100% of the population within a s p e c i f i e d distance. Another aspect of the model i s that of 100% population coverage within a maximum time. If only 90% of the population is within f i v e minutes of service but 2% are 30 minutes away then the q u a l i t y of service to these 2% i s much lower than to the majority. A constraint may be added i n the model to ensure that a l l c i t i z e n s get service within a s p e c i f i e d maximum distance or response-time. Advantages of the MCLP model are: - i t can be solved by l i n e a r programming - i t does not e n t a i l an excessive burden of computations (180 constraints i n th i s study) - population and maximal service distance are both used - i t indicates the maximum extent of demand coverage to be expected from a number of f a c i l i t i e s less than the minimum number needed to cover a l l demand. Disadvantages of the MCLP model are: - i t assumes one ambulance per depot - i t assumes the ambulance is always available - i t does not take into account congestion (in areas of high demand the solution may show that one ambulance can cover the entire region) - one ambulance can cover several high demand areas i f these areas are i n close proximity of each other (such as the case i n downtown Vancouver) , - f r a c t i o n a l solutions may be encountered. Next i s a mathematical representation of the model followed by a discussion of the use of the model and an evaluation of the mode1. 4.3 MATHEMATICAL FORMULATION OF THE MCLP DEFINE: I = set of nodes P = number of f a c i l i t i e s (depots) "" = frequency of demand of node i (population at node i or # of c a l l s per day at node i ) = 1 i f demand node i i s covered by a f a c i l i t y 0 otherwise Y j = 1 i f a f a c i l i t y i s allocated to s i t e j 0 otherwise 62 N. = { j l d.. i S . , j « J} J = a set of p o t e n t i a l f a c i l i t y s i t e s S = a s p e c i f i e d maximum response distance (or time) d^j = smallest distance (or time) between node i and node j Zj_ = number or percentage of population served or "covered" within the desired service distance Problem 1 1. Maximize Z. = >_ a. X. 1 1 1 l « I subject to 2. Z. Yj > X i V ± € I i € N-; 3. 2_ Y j = P 4. X i # Yj 6 (0,1) , € J , V ± € I Interpretation 1. - Maximize number of people served or "covered" within the desired service distance. 2. - Allow X i to be covered only when a f a c i l i t y i s within the desired service distance. 3. - A s p e c i f i e d number of depots. A t h i r d constraint may be added namely: 5. 21 Y j * 1 • V i * 1 j * M i where M i = 0 1 d i i * T > S } 63 Which w i l l ensure that no one i s farther than a response d i s -tance T to his closest f a c i l i t y . Adding t h i s l a s t constraint provides some degree of equity to the population not served within service distance S. Problem 1 has an equivalent formu-l a t i o n derived by substituting 1 - Xj_ = x i -Problem 2 Minimize subject to I £ I a i x i j *N ± j * J Xi, + X l — = P 1 v. Y J J (0,1) v ± I, X^ = 1 i f demand node i i s not covered by a 4 f a c i l i t y within S distance 0 otherwise This problem seeks to minimize the population l e f t "uncovered" i f p f a c i l i t i e s are to be located on the network. Problem 2 is the dual of Problem 1. Either formulation may be programmed. For the purpose of t h i s study Problem 2 was programmed. 4.4 USE OF THE MCLP MODEL The MCLP model was adopted for t h i s study to provide: - i n i t i a l "good" depot locations which could be s t a r t i n g points for the simulation, and 64 - a trade o f f curve of the percentage of population covered versus a range of number of f a c i l i t i e s . Input data for the dual of the MCLP was the demand at each of the 169 nodes and a t r a v e l time matrix. In each p a r t i c u l a r sub-region the demand was equal to the number of c a l l s i n that sub-region divided by the t o t a l number of c a l l s for the whole of the G.V.R.D. Thus the demand was a percentage of the t o t a l c a l l s . The t r a v e l time matrix contained i n the shortest time to t r a v e l between subregions and the average internode t r a v e l time was roughly two minutes. At the time of the study there were 19 depots i n Vancouver which are indicated i n figure 4.1. Also shown are the high density regions. I t appeared reasonable to i n i t i a l l y solve the MCLP model for 19 depots and at a maximum response time of two minutes. The solution was in t e r e s t i n g . P r a c t i c a l l y a l l of the depots were i n the high density region and v i r t u a l l y none i n the outlying regions. Further, only 57% of the population was covered. Thus i t was decided to increase the maximum response distance. The results were similar with only 64% of the density covered. Further increases in maximum response time were added and two depots were added. See figures 4.2, 4.3, 4.4, 4.5, 4.6 and table 4.1. As the maximum response time increased one depot covered a few very densely populated regions. This revealed some serious draw-backs i n using the MCLP model. The analysis revealed that: 1. At a very small maximum response time each depot was only covering one node. Thus the MCLP model allocated the depots to the 19 nodes with the highest demand many of which were very close together. 2. As the maximum response time increased one depot now could cover a few or several subregions of high demand. Outlying depots were allocated to nodes of highest demand i n those regions. The d e f i c i e n c i e s of the MCLP model are therefore the following: 1. At a low maximum response time outlying regions are not considered. 2. In outlying regions no consideration i s being made of nodes surrounding the high population node, i . e . t r a v e l time to these other nodes -subregions were larger and one depot covered one subregion. 3. As maximum response time increased, one depot could cover several high demand regions. In places, one depot covered 10% of demand whereas other places one depot only covered h% of demand. 4. No consideration of time of day of c a l l s or type of c a l l s . (Depots were also allocated at hospitals since they have many transfer c a l l s . ) These results were discouraging since one would need a very high number of depots and a possible rearrangement of sub-regions to get a better f i t . The p-median model was t r i e d and compared to the MCLP model. 66 TABLE 4.1 MAXIMAL COVERING LINEAR PROGRAMMING SOLUTIONS Number of Maximum % Demand % Demand F a c i l i t i e s Response Time Covered Not Covered 19 2 (minutes) 57% 43% 19 4 . 64% 36% 19 5 75% 25% 19 6 86% 14% 19 7 92% 8% 19 8 96% 4% 19 10 99% 1% 19 15 100% 0 21 4 66% 34% 21 5 78% 22% 21 6 88% 12% 21 7 94% 6% 67 PRESENT A:4BULANCE DEPOTS • Present depot locations High demand zones FIGURE 4.1 68 MAXIMAL COVERING SOLUTION FOR 19 DEPOTS AND A FOUR MINUTE MAXIMUM RESPONSE TIME 64% of Demand Covered FIGURE 4.2 * 69 MAXIMAL COVERING SOLUTION FOR 19 DEPOTS AND A SIX MINUTE MAXIMAL RESPONSE TIME 86% of Demand Covered FIGURE 4.3 70 MAXIMAL COVERING SOLUTION FOR 21 DEPOTS AND A SIX MINUTE MAXIMAL RESPONSE TIME 88% of Demand Covered FIGURE 4.4 MAXIMAL COVERING SOLUTION FOR 19 DEPOTS AND A SEVEN MINUTE MAXIMUM RESPONSE TIME S = 7 minutes 12.78 P = 19 depots FIGURE 4.5 72 MAXIMAL COVERING SOLUTIONS PERCENTAGE OF POPULATION COVERED 0$ < °/° o t f t f * 6 6% 7 8 88 94 57% 64 75 86 92 96 • • • • • 99% i 1 T 1 r — — i 1 1 1 ' 2 3 4 5 6 7 . 8 9 10 11 12 Minutes FIGURE 4.6 Radius of Coverage 4.5 THE P-MEDIAN LOCATION MODEL This network model i s designed for determining f a c i l i t y -locations and has a structure s i m i l a r to the integer formula-t i o n of the p-median problem of Revelle and Swain (1970). The optimization problem i s to minimize t o t a l response time. 4.6 MATHEMATICAL FORMULATION OF THE P-MEDIAN MODEL DEFINE: I = set of nodes P = number of f a c i l i t i e s (depots) aj_ = frequency of demand at node i - (population at node i or # of c a l l s per day at i) dj.j = smallest distance (or time) between node i and node j x^j = f 1 when a f a c i l i t y j serves node i \ 0 otherwise J = a set of potential f a c i l i t y s i t e s S = a s p e c i f i e d maximum response distance (or time) For each node i , the service set Nj. i s defined as N I = { i / d i j * S, j e j } Yj = f 1 when a depot i s placed at node j L 0 otherwise 74 Problem 3 1. Minimize = £ a i d i j x i j i * I j 6 J s .t. 2. S. x i j = 1 ' v i fe 1 j *N ± Yj = P 3 j «J 4. yj - x ± j > 0 , j N i # i I 5. x ± j € (0,1) , Vj 6 J, V ± € I Yj €. (0,1) , Vj 6 J Interpretation The problem i s to locate p f a c i l i t i e s on a network of demands so as to minimize t o t a l distance (response time) from depots to demand nodes. The f i r s t constraint demands that each community be assigned to one and only one depot for service; that i s , the assignment cannot be p a r t i a l . A second constraint s p e c i f i e s and fixes the number of depots ( f a c i l i t y sites) available. The t h i r d constraint ensures that communities are served by locations designated as depots and that depots s a t i s f y some constraint of maximum response time. 1 With a maximum response time constraint the solution guarantees that no points of demand w i l l be far away from the nearest f a c i l i t y . "'"The d e f i n i t i o n of a feasible service set N. reduces the i ... „ 2 size of the problem from an otherwise larger problem with N variables and N 2 + 1 constraints. The amount of reduction depends upon the sizes of N^* s. 75 One deficiency i n the above formulation i s that i t does not consider congestion. An alternative formulation i s to take into account the problem of demand congestion. This formulation uses a surrogate index to the impact of queues. The measure chosen i n the a l t e r n a t i v e formulation implemented i n t h i s study (problem 4) was the distance or response time from the nth closest demand node. Thus the surrogate index acts as a sub-sidy for each f a c i l i t y node. Problem 4 a i d i j x i j i 6 I j € J 1. Minimize Z~ = — : subject to 2. 5_ x. . = 1 V. I J x 3. £ y = P j € J 4. yj - X i j ^ O ^ f e N ^ i f e l 5. x ± j e (0,1) , V ± € I, Vj € J •Yi C (0,1) , Vj fe J where dj_j i s the distance (or time) to the nth closest node. This may be determined by n where K i s a constant, n is the # of demand K ' ~ nodes and p i s the # of f a c i l i t y nodes. P i s a constant which adjusts for geographical and t e r r a i n 7 6 " /3 2. d i j Y j factors. Problem 4 gives the f a c i l i t y locations a f t e r adjusting for congestion. The adjustment i s subtracted from the f i r s t term (tot a l distance) to give the model the e f f e c t of moving depots from congested areas towards less congested regions and remote areas of sparse population. Often i n high demand regions an ambulance i s busy and i s unable to respond to c a l l s immedi-ately. Servicing of such a c a l l depends on how far away the second closest ambulance i s (assuming he i s fr e e ) . Without an adjustment term, f a c i l i t i e s w i l l tend to be located i n the center of demand regions. Outside regions are considered "secondary". With the subsidy term, depots move towards outside regions. This i s i l l u s t r a t e d by the following example. Let the network be defined as follows: 10 1 05 2 3 7 4 \ 8 06 10 10 Thus,.the shortest distance matrix would be: 77 1 2 3 4 5 6 7 1 1 4 2 10 10 2 2 1 1 4 11 11 2 3 4 1 2.5 10.5 10 2 4 2 4 2.5 8 8 2 5 10 11 10.5 8 10 10 6 10 11 10 8 10 10 7 2 2 2 2 10 10 And l e t the demand at each node be: dm 1 2 3 4 5 6 7 dm 100 175 100 50 50 50 200 725 We w i l l l e t n be determined by using the time to the second closest node. We are t r y i n g to solve the following objective function for problem (4). Minimize ^ dm * ds • X - ( £ dm) yB ^ ds X where dm = 725 ds = distance between nodes X = location of depots - f i n d 2 l& = 0.10 Four feasible solutions are as follows: 78 depots 2, 7(subsidy) 4,7(subsidy) 5, 7(subsidy) 2, 4(subsidy) 2--1 100 20 200 20 200 100 100 20 2 17.5 350 52. 5 350 192.5 52.5 3 100 20 200 25 200 100 100 25 7--4 100 15 10 100 40 75 5 500 55 400 50 50 400 55 6 500 55 4 0 0 50 500 50 400 55 7 40 40 200 400 40 no sub- 1300 min. 1550 1350 1400 1st sidy closest answer subsidy -222. 5 -247.5 -732. 5 -322. 5 2nd closest t o t a l 1077. 5 1302.5 627. 5 min. 1077. 5 By use of a subsidy term, one of the depots moves to an out-l y i n g region. Using the same network l e t us assume that c a l l s occur at node 2 f i r s t and then at node 5. The solution of problem 3 places depots at node 2 and node 7. For problem 4 the solution would be at nodes 5 and 7. In problem 3, i f an ambulance at node 2 services a c a l l at node 2, a second c a l l at node 5 would require the ambulance at node 7 to t r a v e l a f a i r distance. However, with depots at nodes 5 and 7 a c a l l at node 2 would be serviced by the ambulance' at 7 and a second c a l l at node 5 would be serviced immediately. Certainly most c a l l s occur i n nodes 1, 2, 3 and 7 and t h i s is where ambulances are needed.''" The p-median model has some advantages over the maximal covering model. This can be well i l l u s t r a t e d i n the following "'"The choosing of & and the "2nd" closest distance versus say the "3rd" or "4th" has a d e f i n i t e bearing on the solution. 79 simple examples. Consider the following network: Demand 1 100 5 10 A - no demand 2 100 6 10 B - no demand 3 100 7 10 C - no demand 4 100 8 10 D - no demand Maximal covering solution for three ambulances with maximum response of 5 Solution depots at A B D Objective function 100% of population covered. P-median solution for three ambulances Solution depots at 2 4 C Objective function = 4.75 or average response time = 4.75 minutes. The major congestion problem i s at 1, 2, 3, 4 and t h i s i s where ambulances are needed. If the maximal response time i s lowered to 3, the maximal covering w i l l s t i l l place only one ambulance i n the congested region. If the maximal response time i s decreased any lower than the maximal covering solution w i l l be at three of the f i r s t four depots and ignore the outlying region. I t does appear that the p-median model, which determines the response time i t s e l f , uses time and distance more e f f e c t -80 i v e l y . When the p-median algorithm was solved (without subsidy) for 19 depots, depots were located i n a l l outlying regions and not congested i n downtown Vancouver as solutions from the maximal covering model. The disadvantages of formulating the ambulance problem as a p-median are: - It involves a very large number of constraints. The LP problem may have to be solved i n two parts or by making i n i t i a l guesses at depot points. If N i s the number of demand nodes and P i s the number of f a c i l i t y nodes, then the possible lower bound on the number of constraints P(N-P) = 20(170-20) - 3000. - The formulation requires experiments for c a l i b r a t i n g and for the determin-ation of the appropriate closest node. - The service distance (or time) constraint may eliminate a l l feasible solutions. - The formulation may r e s u l t i n f r a c t i o n a l solutions. - There are many possible optimal solutions, and, - The formulation assumes one ambulance per depot. 4.7 USE OF THE P-MEDIAN ALGORITHM The LP formulation of the p-median problem requires some N 2+l constraints. In the G.V.R.D. N i s equal to 169, thus the number of constraints i s over 25,000. Due to the sparseness of 81 the matrix, the cost of solving t h i s LP i s p r o h i b i t i v e . (Solving the problem for N equal to 40 costs $50.00.) An alte r n a t i v e to solving the problem i s to include every t h i r d or fourth node i n the model instead of a l l 169 nodes. But since the nodes already represent large regions the approximation i s almost u n r e a l i s t i c . An e f f i c i e n t algorithm for solving the p-median problem i s available at U.B.C. R.A. Whitaker i n research undertaken while i n the geography department at U.B.C. formulated a programme which computes solutions to the p-median problem subject to some side constraints. Heuristic procedures were u t i l i z e d to estimate the medians. The basic procedure i s as follows i n p-median estimation problems. 1. Pick an i n i t i a l set of nodes at which to locate P service bases. 2. Assign a l l other nodes to be serviced by the nearest service base. 3. A l t e r service base locations i n such a way as to check for possible improvements. Both steps 1 and 3 require Heuristic procedures. Singer (1968)-'- has created a method to obtain i n i t i a l set of nodes (Step 1) by which the P service bases are spaced the maximum distance apart. This spread i s p a r t i c u l a r l y useful i n the ambulance set t i n g since i t ensures that the i n i t i a l f easible solution for ambulance locations covers less dense r u r a l areas. •'•Singer, S. multi-centers and multi-medians of a graph with an app l i c a t i o n to optimal warehouse location, mimeographed paper presented at the annual meeting of Tims and Orsa, San Francisco, June, 1968. 82 For step 3 Singer employed c y c l i c perturbation of one node service base at a time. In his adaptation of Singer's algorithm, Whitaker allows t h i s as an option since several of his examples did not require perturbation to obtain optimality. Whitaker allowed constraints to be placed on the amount of service provided at each base. This was handy for the ambulance location problem since the number of ambulances was not p a r t i c u l a r l y large and thus service was rather "lumpy". With the constraints, i t was possible to solve for an i n i t i a l set of base nodes through the a p p l i c a t i o n of the transportation method of l i n e a r programming. Whitaker used the Ford-Fulkerson algorithm. Whitaker also mentioned a maximum distance constraint in his d i s s e r t a t i o n . His suggested method was simply based on r e s t r i c t i o n of the nodes for which demand was allocated to any base to the neighbourhood of the base. This was not imple-mented i n the published version of the program. A method to employ the maximum distance constraint i s through the use of the t r a v e l time matrix. By multiplying t r a v e l times for each node outside a given radius by a 5*" factor, ( C > 1) one i s implementing a distance penalty. Thus t r a v e l times to and within r u r a l areas are increased. Since the p-median algorithm is minimizing, the depots are .:• spread out. By increasing t r a v e l times the e f f e c t i s that the r u r a l areas are subsidized and thus i s the same as adding 83 the surrogate i n the LP formulation. Thus by adding the maxi-mum distance constraint i t i s also taking into account conges-t i o n . Attempts were made to run the Whitaker p-median algorithm (WPMA) with the service constraint i n place over a l l possible base locations. Results were uniformly poor, running from no solution a f t e r computer time had been spent under f a i r l y moderate constraints to an absurd solution i n which f i v e ambulances were i n the west point grey area. It was decided instead to s e l e c t i v e l y apply constraints to s p e c i f i c nodes i n the otherwise unconstrained problem, expecting that the workload (number of nodes serviced) at these s p e c i f i c nodes would be below the maximum s p e c i f i e d and the workload o v e r a l l to be spread more equitably among the depots. However, there were great differences i n the workload per station, with a range of 1 to 31 nodes serviced by a s p e c i f i c s t a t ion. The next step was to force some nodes into the solution. Inclusion of d i f f e r e n t sets of nodes i n the sol u t i o n resulted i n r a d i c a l differences of response time and i n number of nodes serviced by p a r t i c u l a r stations. Unfortunately, there was no way of placing upper bounds on these "forced i n " nodes. Further options exercised were the extended search, with weight s h i f t and perturbation. The extended search option c a l l s for searching throughout the whole region locating medians 84 instead of searching only in the immediate area surrounding a s p e c i f i c node. Perturbation tests c a l l for checking surrounding nodes to see i f there would be any improvement i n response time. Although the service constraints, applied o v e r a l l or to i n d i v i d u a l nodes could not be used successfully, the remaining unconstraint problem, with perturbation, produced "good" re s u l t s as i n i t i a l solutions. This became e s p e c i a l l y evident as the number of f a c i l i t i e s (depots) i n the s o l u t i o n increased. The congested areas were well "covered" and more depots were placed i n low density areas. See figures 4.7 and 4.8. The solutions from the p-median were inputted into the computer simulation. Now the congestion aspect on the p-median solution was observed. With these results the p-median solution was altered to account for congestion and inputted back into the simulation. The p-median solutions were used i n the experiments which are discussed i n Chapter 6. 85 P-MEDIAN SOLUTION FOR 19 DEPOTS Average response time 4.0 7 minutes FIGURE 4.7 86 P-MEDIAN SOLUTION FOR 24 DEPOTS Average Response time 3.58 minutes FIGURE 4.8 87 CHAPTER 5 DESIGN OF EXPERIMENTS 5.1 INTRODUCTION To conduct experiments a number of d e c i s i o n s must be made: - d e t e r m i n a t i o n of s t a r t i n g c o n d i t i o n s of the model, - d e t e r m i n a t i o n of l e n g t h o f the run, - d e t e r m i n a t i o n o f parameters so t h a t the e f f e c t o f one v a r i a b l e can be s t u d i e d w ithout compounding i t s e f f e c t w i t h simultaneous changes i n other system v a r i a b l e s , - d e t e r m i n a t i o n o f parameters t o expose d i f f e r e n t system responses, and, In a d d i t i o n one must ensure t h a t the model r e p r e s e n t s the r e a l world system and has j u s t s u f f i c i e n t d e t a i l t o examine the important f e a t u r e s of the system. In Chapter 3 the l e n g t h of the runs was d i s c u s s e d . With over 4500 t r a n s a c t i o n s run, and the model b e g i n n i n g a t midnight when t h e r e were few c a l l s s t a t i s t i c s c o u l d be gathered from the s t a r t of the run without having any s i g n i f i c a n t e f f e c t . 88 S e n s i t i v i t y analysis was also discussed i n Chapter 3, The ambulance model was designed to be an abstraction of the r e a l system, with the emphasis being on the evaluation of response time and u t i l i z a t i o n . The model i s s u f f i c i e n t l y detailed so as to highlight changes i n behavior caused by experimentation with system parameters. 5.2 EXPERIMENTAL DESIGN There are f i v e experiments reported here: 1. Determining the effects of moving the West Vancouver ambulance westward. 2. Determining the effects of removing the three night crews. 3. Moving one Burnaby paramedic ambulance to the Vancouver General Hospital (V.G.H.). 4. Replacing one V.G.H. ordinary ambulance with a paramedic ambulance under two .conditions. 5. Determining the number of depots and ambulances required to have an emergency response time of five minutes for at least 90% of the c a l l s . Simulation was used i n a l l f i v e experiments. The p-median and maximal covering models give answers on where to locate depots optimally whereas the f i r s t four experiments are not concerned with optimality. In experiment (1) a simulation run was made for each move of the ambulance from i t s present lo c a t i o n to a westward 89 node. For experiment (2) two d i f f e r e n t sets of night crews were removed and a separate simulation run was made for each. Experiment (3) required only one run. Replacing an ordinary ambulance with a paramedic i n experiment (4) was done i n i t i a l l y with the paramedic unit only on emergency and paramedic c a l l s . A test was made with the paramedic unit helping out on ordinary ( p r i o r i t y 2) c a l l s when not otherwise busy. For the t h i r d experiment the following procedure was employed: 1. The p-median algorithm was run, with perturbation and extended search, to determine the optimal locations for a large number of ambulances. 2. The number of depots i s the same as the number of night crews. Thus only the night s h i f t transactions were run on simulation for a range of ambulances u n t i l 90% of the emergency c a l l s were answered within f i v e minutes. This established the number of depots. 3. For each depot ambulances were added (0-3) depending upon the demand surrounding the depot location. The simulation model was now run with transactions for the f u l l day. Ambulances were added u n t i l 90% of the emergency c a l l s were answered within f i v e minutes. The results obtained from these experiments cannot be considered exact. Response times and the placement of depots and ambulances during various parts of the day may vary s l i g h t l y since a computer simulation cannot take into account a l l issues. Some of these are: - Small adjustments i n i n d i v i d u a l locations are often necessary to secure adequate 90 adequate accommodation for the depot to account for l o c a l t r a f f i c conditions, etc. - Considerations other than response time may influence the location of ambulance depots. For example, for reasons of t r a i n i n g and l i a i s o n , i t may be desirable to locate a ce r t a i n number of ambulance depots adjacent to emergency rooms. - Some or a l l of the depot locations selected for the evening or early morning periods may be r e s t r i c t e d to the depot locations selected for the daytime period. - The objective of minimizing average response time may be disputed. For example, i t may be f e l t that a small decrease i n response time i n an outlying region may be worth more than a r e l a t i v e l y larger increase for the region as a whole. This i s c l e a r l y a p o l i t i c a l decision. 5.3 SIMULATION STATISTICS For each c a l l the simulation recorded the type of c a l l i t was, the subregion and municipality of occurrence, the time i n queue, the response time for the ambulance, and the service time. The number of c a l l s each ambulance answered and type of c a l l answered was also recorded. The output s t a t i s t i c s consisted of the following: - mean response time per type of c a l l , - a d i s t r i b u t i o n of response times per type of c a l l , - the average response time per type of c a l l per municipality, - the average response time for a l l c a l l s 91 per subregion, - the service time only - the o v e r a l l averages and t h e i r associated frequency d i s t r i b u t i o n , - maximum, average and t o t a l c a l l s for each subregion and municipality, and - t o t a l number of c a l l s , by type, that had to wait i n queue and the average time spent waiting i n these queues. 92 CHAPTER 6 EXPERIMENT RESULTS AND THEIR IMPLICATIONS 6.1 INTRODUCTION In t h i s chapter the re s u l t s of f i v e experiments are presented. A l l of the experiments use simulation. With simulation d i f f e r e n t aspects of the ambulance service can be investigated as well as the t o t a l system. I t should be noted here that i n the experiments the dispatch p o l i c y was to send the closest available ambulance. Each ambulance was r e s t r i c t e d to a 30 minute radius. Thus i f a l l ambulances were busy within a 30 minute radius of a c a l l that c a l l i s queued. The experiments highlight several problems (e.g. -congestion) and permit evaluation of alt e r n a t i v e strategies and p o l i c i e s . The chapter concludes with i d e n t i f i c a t i o n of areas which merit research i n the future. 6.2 THE WEST VANCOUVER AMBULANCE EXPERIMENT The objective of the West Vancouver ambulance experiment was to determine the effects on the system of moving the West 93 Vancouver depot westward. A l l of factors i n the simulation were kept constant. Currently the West Vancouver ambulance i s located at node 43 (see figure 6.1). It services the nodes i n the West Vancouver region and helps out on c a l l s i n North Vancouver when that ambulance i s busy. Also, i f required, i t may t r a v e l into Vancouver to service a c a l l . The hospital i s located at node 51 (see figure 6.1) where the North Vancouver depot i s located. The experiment was c a l l e d upon since c a l l s west of node 43, e s p e c i a l l y at node 39, required the West Vancouver ambulance to t r a v e l from node 43 to node 39 and then to node 51. Thus patients at node 39 wait quite awhile before reaching the hos p i t a l . The results are given i n table 6.1. The e f f e c t of moving the ambulance from node 43 to node 41 decreases the average emergency response time i n West Vancouver. However, movements to other nodes have the opposite e f f e c t of increasing the average emergency response time for West Vancouver. The explanation requires understanding how the West and North Vancouver ambulances intera c t and also the unique road network i n West Vancouver. F i r s t as the ambulance i s moved westward the ambulance v i n North Vancouver answers some c a l l s that previously would have been answered by the unit at node 43. The North Vancouver car needs to t r a v e l further westward r e s u l t i n g i n both increased response time and t o t a l service time. Its a v a i l a b i l i t y i s thus 94 lessened and other c a l l s are now queued. A few hours may be l o s t before the North Vancouver ambulance i s back to i t s normal period of a v a i l a b i l i t y . Overall, the average emergency response time for North Vancouver increases. Now with the North Vancouver unit covering more t e r r i -tory, West Vancouver's ambulance has some pressure relieved. Its a v a i l a b i l i t y increases. It i s also more c e n t r a l l y located i n West Vancouver and consequently, the West Vancouver average emergency response time decreases. Horseshoe Bay, node 39, also has i t s response time lowered with the depot located at node 41. This r e s u l t was f u l l y expected and desired. The average response time for ordinary and transfer c a l l s i n West Vancouver enlarged. Some of these c a l l s occur i n nodes 40 and 42 which are located on the high road i n West Vancouver. The unique road network i n West Vancouver has a lower road through nodes 45, 43 and 41. The upper road goes through nodes 44, 42, 40, 39 and 38. These two roads run somewhat p a r a l l e l to each other and getting from the upper road to the lower or vice versa i s very d i f f i c u l t . There are very few d i r e c t roads connecting the major a r t e r i e s . With the ambulance at node 41, i t has more d i f f i c u l t y getting to the upper nodes than i t did with the depot at node 43. Another p a r t i a l explanation for the augmented response time for ordinary and transfer c a l l s i s that the West Vancouver ambulance now has to t r a v e l further to answer c a l l s i n North Vancouver i f that ambulance i s busy. 95 Also, any transfers from the hospital to, a West Vancouver location require the West Vancouver ambulance to spend more time on the road. Spending more time servicing c a l l s leads to less a v a i l a b i l i t y and an increase i n response time. These reasons apply to the deterioration i n service l e v e l when the ambulance i s moved to other West Vancouver subregions. The road network i s a major factor i n increasing response times. At nodes 40, 38 and 39 a l l response times and West Vancouver's service time appreciate, with the exception of the response time at Horseshoe Bay. Locating an ambulance at nodes 38 or 39 s i g n i f i c a n t l y increases response and service times due to: the d i f f i c u l t y of getting to the lower road, the long response time required i n answering c a l l s i n North Vancouver, and the increased service time as a r e s u l t of the ambulance having to t r a v e l a long distance back to i t s depot. Nodes 43, 44, 47 and 48 have the majority of c a l l s i n West Vancouver. A depot at either node 38 or 39 obviously w i l l increase the response time for a l l c a l l s . The t r a v e l time from the hospital to the depot i s increased. As a re s u l t , the t o t a l time the ambulance is available to answer c a l l s decreases. Consequently, response times appreciate s i g n i f i c a n t l y . The North Vancouver ambulance also has more pressure on i t with a depot at 38 or 39. I t has to t r a v e l further into West Vancouver, time to t r a v e l back to the hospital increases, 96 and, thus, t o t a l service time increases. Total a v a i l a b i l i t y -i s depreciated. Overall response and service times increase. Only Horseshoe Bay residents p r o f i t from the movement of the West Vancouver ambulance. Response and service times for the t o t a l G.V.R.D. do not a l t e r . The best p o l i c y for a l l West and North Vancouver ambulances i s not to move the West Vancouver ambulance. Of course, experiments can be done relo c a t i n g the North Vancouver ambulance or adding more, ambulances which may a l t e r the results obtained. 98 EFFECT OF MOVING WEST VANCOUVER AMBULANCE WESTWARD (Results i n Minutes) West Vancouver emergency s a i l response time North Vancouver emergency s a i l response time North Vancouver ambulance service time North Vancouver number of s a i l s serviced West Vancouver ambulance service time West Vancouver number of s a i l s serviced Horseshoe Bay subregion response time for a l l c a l l s North Vancouver ambulance response time for transfer s a i l s North Vancouver ambulance response time for normal s a i l s West Vancouver ambulance response time for transfer s a i l s West Vancouver ambulance response time for normal s a i l s Current Depot Depot Depot Node 43 Node 41 Node 40 Horseshoe Bay Depot Depot Node 38 Node 39 7.39 8.98 9.14 10.75 9.55 5.91 6.11 6.14 6.39 6.27 51 51 51 51 51.6 269 269 269 269 269 66 75.03 76.2 94.83 94 57 57 57 57 57 23.08 21.68 22.01 20.98 19.97 16.9 16.9 16.9 16.9 16.9 15.89 15.89 15.89 15.89 15.89 31.03 31.53 31.54 32.99 32.35 15.15 15.95 16.28 19.01 17.47 TABLE 6.1 99 6.3 THE EFFECTS OF REMOVING THREE NIGHT CREWS Experiment #2 consisted of two separate simulation runs each with three night crews removed. The evening s h i f t runs from 12 midnight u n t i l 7:30 a.m. There are 15 ordinary ambul-ances and two paramedic crews on duty during the night s h i f t . The depot locations and corresponding s h i f t s are stated i n Table 6.2. Paramedic crews were not removed i n the experiment. The depots where ambulances are removed are i n nodes 6, 23 and 166 i n the f i r s t experiment and nodes 15, 31 and 166 i n the second run. (See figure 6.1 for node locations.) The results gathered are l i s t e d i n Table 6.3. The removal of three night crews causes dramatic r e s u l t s . A l l average response times for a l l c a l l s and i n a l l regions of the G.V.R.D. increase s i g n i f i c a n t l y . Let us begin examination of these results by stating that a l l nodes where ambulances were removed did have a high demand. Node 23 i s a downtown node and i s near St. Paul Hospital. Node 6 i s a residence region with the V.G.H. and Shaunagsy nearby. Node 166 i s where the Langley ambulance i s . This ambulance has a very large s p a t i a l t e r r i t o r y to p a t r o l . Node 15 i s r e s i d e n t i a l with the Shaunagsy and V.G.H. nearby and i s less than ten minutes from downtown Vancouver. At node 31, the demand rate i s also high as i t i s i n the heart of the "red l i g h t " d i s t r i c t . Thus the removal of an ambulance r e a d i l y 100 puts a s t r a i n on nearby crews. With other crews having to pick, up the slack, t h e i r a v a i l a b i l i t y to service other c a l l s decreases. Consequently, more c a l l s need to wait for an ambulance to become free. The increased queuing time results i n increased response time. The most s i g n i f i c a n t increase i n average response time i s for ordinary ( p r i o r i t y II) c a l l s . Vancouver and Burnaby are hardest h i t with increases. Since the majority of c a l l s are i n these two regions, t h i s r e s u l t i s not surprising. The amount of increase i s . . Vancouver has the greatest proportion of ordinary c a l l s . Further, the largest percentage of a l l c a l l s are non-emergency c a l l s . Two Vancouver night crews are removed i n each simulation run, leaving only f i v e crews i n Vancouver on the night s h i f t . This i s a 28% decrease i n ambulance crews for Vancouver. These remaining f i v e crews answer emergency c a l l s f i r s t . Then i f no other emergency c a l l s are on queue, the ordinary c a l l i s responded to. With only f i v e crews available each crew answers more c a l l s decreasing i t s a v a i l a b i l i t y . Combining t h i s fact with the fact that most c a l l s are ordinary c a l l s , one can r e a d i l y appreciate the s i g n i f i c a n t increase i n Vancouver's average response time. Burnaby's average response time f o r ordinary c a l l s also increased due mainly to only f i v e crews available i n Vancouver. Obviously Vancouver needed help and got some from Burnaby. 101 Increased t r a v e l time for Burnaby increases i t s response time. Also, Burnaby has one paramedic serving i n the evening and i t s e l f has a f a i r number of ordinary c a l l s . C a l l s i n Burnaby suffer as a r e s u l t of the Burnaby ambulance t r a v e l l i n g to Vancouver. This includes both non-paramedic and paramedic c a l l s . The paramedic unit i n Burnaby helps out on ordinary c a l l s when i t i s not busy. The removal of a night crew i n Vancouver makes the Burnaby crew work more, creating more work for the paramedic unit. As a r e s u l t , the average response time for the paramedic unit i s augmented. The chain reaction can be extended to include the ordinary and paramedic unit i n New Westminster. Also with less crews i n Vancouver, a paramedic crew may have to t r a v e l there to answer a paramedic c a l l . With the paramedics answering more ordinary c a l l s , the paramedic c a l l i n Vancouver may get queued r e s u l t i n g i n a long wait.. The increased work for a l l units causes an increase i n emergency response time, but not as s i g n i f i c a n t l y . This i s due to the high p r i o r i t y and low number of emergency c a l l s . Response time for r u r a l regions increases s i g n i f i c a n t l y . The large increase i n r u r a l emergency response time can be attributed to the removal of a unit at node 166. It was the only night crew i n Langley. Now the closest ambulances are i n White Rock and Surrey who, while covering t h e i r own large regions, are required to t r a v e l the long haul to cover for the absence 102 of the Langley ambulance. Further, Surrey and White Rock no longer get help from the ambulance at Langley. If they get any help i t would be from the ambulance at New Westminster. The large s p a t i a l area required to cover coupled with the loss of 1/3 of the ambulance crews explains the s i g n i f i c a n t increase i n average r u r a l emergency response times. It goes without saying that the average ordinary response time increased. This experiment strongly indicates that the removal of crews from the night s h i f t i s not viable. The reaction i s far reaching. If anything possible crews need to be added and experiments can be e a s i l y done with the simulation program. The second r e s u l t of the experiment i s that concerning paramedic crews. In order for these crews to be most e f f e c t i v e i n saving l i v e s in cases such as cardiac arrests, they must be available as much as possible. Removal of night crews i n Vancouver or Surrey results i n less a v a i l a b i l i t y . 103 EFFECTS OF REMOVING THREE NIGHT CREWS (Results i n Minutes) Remove Nodes Remove Nodes Present 6,23,166 15,31,166 Overall emergency response time 6.21 7.61 7.78 Urban emergency response time 6.08 7.26 7.43 Rural emergency response time 6.77 9.21 9.35 Vancouver emergency response time 5.80 7.29 7.50 Burnaby emergency response time 6.04 6.87 7.74 New Westminster emergency response time 6.19 6.58 6.58 Overall normal* response time 13.00 17.99 18.64 Vancouver normal response time 10.99 16.44 17.44 Burnaby 11.85 18.48 18.15 New Westminster 16.56 17.48 20.60 Overall paramedic response time 6.09 7.41 7.11 Vancouver paramedic response time 5.26 6.59 6.43 Burnaby 6.38 17.02 8.05 New Westminster 6.29 7.84 8.43 TABLE 6.3 * P r i o r i t y 2 c a l l s - non-emergency 104 6.4 MOVING A PARAMEDIC AMBULANCE FROM BURNABY TO VANCOUVER In experiment #3 a Burnaby paramedic crew, node 62, i s relocated at the Vancouver General Hospital (V.G.H.), node 14. Presently there are no paramedic cars i n Vancouver. The para-medic unit was to help out on other c a l l s when i t was not busy and was given a 15 minute radius maximum for answering para-medic c a l l s . Paramedic c a l l s outside the 15 minute maximum would be treated as emergency c a l l s , answered by other vehicles. Currently, the Vancouver d i s t r i c t has the highest per-centage! of a l l types of c a l l s , including emergency. Some of these emergency c a l l s are paramedic type but were treated as emergency since no paramedic ambulances were available to.answer the c a l l . (An experiment done by the dispatchers l a b e l l i n g these c a l l s bore out t h i s fact.) Any paramedic vehicles t r a v e l l i n g to Vancouver came from far away Burnaby. Victims of cardiac arrests i n Vancouver cannot wait for a paramedic crew to come from Burnaby. For paramedic crews to be e f f e c t i v e , response time must be as low as possible, i d e a l l y within three minutes. Adding a paramedic ambulance at the V.G.H. gives Vancouver one more a l l day crew, four daytime and two night time at node 14. Burnaby, node 62, would be reduced to two day crews and no night crews. A l l other factors remain constant. The results have been tabulated i n Table 6.4. 105 Two s i g n i f i c a n t results a r i s e . F i r s t , both the average emergency and paramedic response times increase. Second, the average response times for ordinary and transfer c a l l s are reduced. Response time for emergency c a l l s increases due to the loss of an a l l day ambulance in Burnaby. Without the paramedic unit at node 62, average response time for emergency and para-medic c a l l s i s increased s i g n i f i c a n t l y i n Burnaby. This indicates how much work the paramedic unit was doing i n Burnaby. Now the remaining cars have to pick up for the loss and are having d i f f i c u l t y keeping up with the increased work-load. Further, the fact there i s no car i n Burnaby at night probably s i g n i f i c a n t l y affects Burnaby's average response time. During the day, t h i s ambulance can be covered f o r . At night, ambulances must come from Vancouver to answer a c a l l i n Burnaby. The increased t r a v e l time d i r e c t l y aug-ments response and t o t a l service time. Thus Vancouver's aver-age emergency response time s u f f e r s . Also, North Vancouver suffers an increase i n i t s emergency response time. This i s possibly due to the ambulance i n North Vancouver crossing the second narrows bridge to answer a c a l l i n Burnaby during either the busiest part of the day when most ambulances are occupied, or at night when no ambulance i s available. The increase i n Burnaby's and North Vancouver's emergency response time is not f u l l y balanced by the reduced response 106 time experienced i n Vancouver r e s u l t i n g i n an o v e r a l l appreci-ation i n the average emergency response time. Vancouver i s benefited by the additional unit at the V.G.H. Both i t s emergency and paramedic response time are reduced, although marginally. Most of thi s r e s u l t can be attributed to the very high demand for a l l c a l l s i n Vancouver. A l l ambulances i n t h i s municipality are busy and t h e i r a v a i l -a b i l i t y i s low. It must be kept i n mind that the paramedic unit helps out on ordinary c a l l s . A reduction i n the average paramedic response time took place i n New Westminster. Most l i k e l y the paramedic unit was no longer required to make any long t r i p s to Vancouver. The increase i n the West Vancouver paramedic response time i s mainly due to the 15 minute radius for the Vancouver paramedic. Previously paramedic c a l l s i n West Vancouver may have been answered by the Burnaby unit. Since that unit no longer exists there either the West or North Vancouver ambulance answers the paramedic c a l l s . Since there are few paramedic -calls i n that region, i t i s not l i k e l y that the paramedic c a l l got t i e d up in the queuing l i s t causing the increased response time. In order to improve the paramedic average response time, i t appears that more of these types of vehicles are necessary. It i s also seen i n Table 6.4 that the average response time for ordinary and transfer c a l l s i s reduced. With the high number of ordinary c a l l s and transfer c a l l s i n Vancouver and the 107 additional vehicle helping out on ordinary c a l l s , t h i s r e s u l t i s not surp r i s i n g . The majority of c a l l s are ordinary c a l l s and most ordinary c a l l s occur i n Vancouver. An additional ambulance takes some of the workload o f f of the other cars. As a r e s u l t , a l l cars are more available to service c a l l s and consequently, less c a l l s need be queued. Thus average response time for ordinary and transfer c a l l s i s reduced. In summary the addition of a paramedic unit at the V.G.H. helps Vancouver residents but Burnaby suffers somewhat. It may be worthwhile to have an a l l day vehicle i n Burnaby. This would help out both Vancouver and Burnaby, e s p e c i a l l y on the evening s h i f t . 108 TABLE 6.4 Moving paramedic vehicle from Burnaby (node 62) VGH (node 14) Average Transfer Response Time Avg. Ordinary Response time Avg. Emergency Response Time Avg. Paramedic Response Time Vancouver Emergency R. T. North Van. Emerg. R. T. West Van. Emerg. R. T. Burnaby Emerg. R. T. New West. Emerg. R. T. Vancouver Para. R. T. North Van. Para. R. T. West Van. Para. R. T. Burnaby Para. R. T. New West. Para. R. T. Base Run 20.46 12. 73 6.33 6.08 5.86 5.91 7.39 6.44 5.81 5.18 5.15 4.14 6.91 6.29 Move Para at (62) Para at (14) 20.36 12.71 6.41 6.17 5.84 6.82 7.39 7.29 5.81 5.12 5.15 6.28 7.62 6.23 109 I "7 6.5 REPLACING AT V.G.H. AN ORDINARY (EMA-2) AMBULANCE WITH A PARAMEDIC (EMA-3) AMBULANCE UNDER TWO CONDITIONS For the fourth experiment a paramedic unit replaces an a l l day ordinary unit at node 14. Presently there are no paramedic cars i n Vancouver. The loss of an EMA-2 vehicle i n Vancouver leaves the municipality with ten EMA-2 cars serving during the day s h i f t and only s i x EMA-2 units on the night s h i f t . No other municipalities experience any changes i n the volume of vehicles. The EMA-2 ambulance at node 14 answered a l l types of c a l l s . For th i s experiment the paramedic ambulance has two dispatch p o l i c i e s : 1. the paramedic crew only answers emergency and paramedic c a l l s , and 2. the paramedic crew helps with ordinary ( p r i o r i t y II) c a l l s when i t i s not busy. I t does not answer any transfer c a l l s . Two simulation runs were required, one with p o l i c y (1) and the other under p o l i c y (2). With a paramedic i n Vancouver, more emergency type c a l l s w i l l be deemed as requiring a para-medic crew. Previously, since Vancouver had no paramedic, these c a l l s were serviced as emergency c a l l s . A study done by the dispatchers gave the proportion of paramedic c a l l s per day in Vancouver. Thus i n the simulation, a c e r t a i n percentage of emergencies were given paramedic status to more accurately represent the r e a l s i t u a t i o n . The r e s u l t i n g s t a t i s t i c s are 110 stated i n Table 6.5. Under condition (1), a l l c a l l types, except emergency, show an increase i n average response time. Emergency type c a l l s show a marginal decrease i n average response time. The reason for this i s apparent. Vancouver has l o s t one a l l day vehicle to answer non-emergency c a l l s . Having an EMA-2 unit which handles a l l types of c a l l s r e l i e v e s the pressure on other ambulances, freeing them up to help out on paramedic and emergency c a l l s more. Vancouver has the majority of ordin-ary and transfer c a l l s . Even with the EMA-2 unit, the vehicles are quite busy, e s p e c i a l l y during the middle part of the day when the greatest majority of transfer c a l l s occur. Now with one less EMA-2 vehicle the ordinary and transfer c a l l s are being queued up even more. Further, on the night s h i f t the six EMA-2 vehicles have to cover up for the l o s t vehicle. The higher u t i l i z a t i o n of the remaining EMA-2 cars reduces t h e i r a v a i l a b i l i t y and as a re s u l t , average response time for non-emergency c a l l s appreciates. On a community by community basis for emergency response time, most municipalities are unaffected. Vancouver, Burnaby and New Westminster experience marginal improvements i n th e i r emergency response time. The explanation here i s that the paramedic unit at node 14 only answers emergency and paramedic c a l l s . Its a v a i l a b i l i t y i s thus greater than that of an EMA-2 unit. Less emergency c a l l s as a r e s u l t are queued and average 111 response time for emergency c a l l s improves i n Vancouver. Ambulances i n Burnaby increase t h e i r a v a i l a b i l i t y s l i g h t l y since long t r i p s into Vancouver are no longer necessary. The vehicles have a smaller radius to cover and t h i s d i r e c t l y improves t h e i r response time. New Westminster's vehicle now no longer have to t r a v e l into Burnaby to help out there. Thus the p o l i c y employed by the EM\-3 vehicle at V.G.H. res u l t s i n three municipalities lowering t h e i r average response times for emergency c a l l s . Paramedic response time, on the contrary, i s increased. By having the simulation create more paramedic c a l l s , the number of these types of c a l l s queued i s increased. With an increase i n paramedic c a l l s i n Vancouver, paramedic response time i s increased. In New Westminster, the paramedic response time i s also increased. With a higher number of paramedic c a l l s i n Burnaby, the EMA-3 unit i n New Westminster i s helping out there. Travel time i s increased. With help from New Westminster, Burnaby's average paramedic response time i s reduced s l i g h t l y . This p o l i c y has some implications. F i r s t , the high number of transfer c a l l s i n Vancouver creates a big problem when a vehicle i s taken away. Perhaps some other form of transpor-t a t i o n i s needed for these types of c a l l s . Special cars may be added to handle transfer c a l l s during the 11 a.m. to 2 p.m. s h i f t when most transfers are released from the hospitals. Second, as more paramedic units are added, more paramedic c a l l s 112 occur. The public requests for paramedics increases. The screening for these types of c a l l s i s c r i t i c a l i n order for the EMA-3 vehicles to be of utmost effectiveness. For the second condition, the new EMA-3 unit gives f i r s t p r i o r i t y to emergency and paramedic c a l l s and only answers ordinary ( p r i o r i t y II) c a l l s when a l l other nearby ambulances are busy. The s i t u a t i o n i s e s p e c i a l l y c r i t i c i z e d during the day s h i f t . The paramedic unit must help out due to the high frequency of c a l l s during the day and there is s t i l l a loss of an ordinary unit. The EMA-3 does not answer any transfer c a l l s . With the paramedic unit helping on ordinary c a l l s (the majority of c a l l s ) the emergency response time i n Vancouver increases, from the base run. Burnaby has a very minute increase i n i t s emergency response time. A l l other areas are scarcely or not at a l l affected. The r e s u l t i s an increase i n the o v e r a l l emergency response time. The majority of emergency c a l l s occur i n the Vancouver region. The average response time for ordinary c a l l s i s decreased with the help of the paramedic unit. Ordinary ambulances i n Vancouver are free to answer ordinary c a l l s since the paramedic i s mainly s e r v i c i n g emergency c a l l s . Other areas are not affected. Paramedic response time i n Vancouver, Burnaby and New Westminster increases. North Vancouver experiences a drop i n i t s paramedic response time due to a paramedic unit being 113 close by i n Vancouver. The increase i n average paramedic response time for the three high demand municipalities can be attributed to the increase i n the number of paramedic c a l l s . In Vancouver, with the EMA.-3 unit p a r t i c i p a t i n g i n servicing ordinary c a l l s , the increase i s more apparent. Further i m p l i -cations of the Vancouver EMA-3 unit helping out on non-emergency c a l l s are that Vancouver may now be getting help from the Burnaby EM7A-3 crew. Burnaby's response time increases. As a re s u l t , the paramedic i n New Westminster may have to t r a v e l i n Burnaby. Overall, everybody's average response time for para-medic c a l l s increases. These re s u l t s indicate that 1. more EMA-2 vehicles are required i n Vancouver, e s p e c i a l l y during the day s h i f t , 2. a study should be conducted to see i f some other form of transportation for transfer patients can be obtained, 3. the e f f e c t i v e use of paramedic vehicles requires e f f e c t i v e screening of c a l l s by dispatchers, 4. Vancouver does require paramedic vehicles, and 5. with the adaptation of p o l i c i e s (2) and (3), the most e f f e c t i v e use of paramedics would be for them to only answer emergency and paramedic type c a l l s . 114 TABLE 6.5 Replace VGH EMA-2 w/EMA-3 under two conditions Change VGH All-Day Change VGH All-Day Ordinary Ambulance Ordinary Ambulance into Paramedic into Paramedic Ambulance Ambulance Base Run Paramedic Amb. Answers Paramedic & Emergency Calls Only Paramedic Ambulance Helps w/Ordinary Calls When Not Busy Average Transfer Response Time 20.46 n 21.48 20. 73 Average Ordinary R. T. 12.73 14.15 12.61 Average Emergency R. T. 6.33 6.27 6.36 Average Paramedic R. T. 6.08 6.59 6.70 Vancouver Emerg. R.T. 5.86 5.83 5.91 North Vancouver Emerg. R.T. 5.91 5.91 5.91 West Vancouver Emerg. R. T. 7.39 7.39 7.39 Burnaby Emerg. R.T. 6.44 5.99 6.46 New West. Emerg. R. T. 5.81 5.60 5.81 Vancouver Para. R. T. 5.18 6.15 6.27 North Van. Para. R. T. 5.15 5.21 4.90 West Van. Para. R. T. 4.14 4.14 4.14 Burnaby Para. R. T. 6.91 6.75 7.08 New West. Para. R. T. 6.29 6.68 6.58 No. of Para. C a l l s Answered by EMA-3 176 277 280 115 6.6 EXPERIMENT #5 - OPTIMAL NUMBER OF EMA-2 UNITS REQUIRED TO ACHIEVE A GIVEN FRACTILE OF EMERGENCY CALLS ANSWERED IN LESS THAN FIVE MINUTES  This experiment proceeded i n two stages. F i r s t a number of experiments were run to optimally locate ambulances to service night s h i f t demands. These locations were i n i t i a l l y obtained using the p-median model. The solution set from the p-median was then implemented i n the simulation. Experiments with the simulation lead to some r e a l l o c a t i o n of the depots taking the impact of congestion into account. I n i t i a l l y the idea was that only one ambulance per base would be required for the night s h i f t . But, very heavy demand rates i n some urban nodes made i t more e f f i c i e n t to stack ambulances at some bases. (See figure 6.1L) A l t e r n a t i v e l y one could subdivide the nodes, but t h i s could r e s u l t i n ambulances a few blocks apart. In r u r a l areas one ambulance per base remained appropriate (figure 6.100. While stacking was necessary, ambulances were added to make the number of cars at a base roughly proportionate to demand. F i g -ures 6.8 and 6.9 provide the f r a c t i l e response surfaces for emergency and paramedic a l l s , respectively. In figure 6.8, for instance, the 60th f r a c t i l e l i n e has been estimated by i n t e r p o l a t i o n . For any combination of bases and ambulances on t h i s l i n e one would expect about 60% of the c a l l s to be answered i n f i v e or less minutes, provided the bases were optimally located and the ambulances optimally allocated. 116 Only a lim i t e d range of alternatives were examined due to the heavy expense of computation. Examination of figure 6.8 reveals some intere s t i n g fa c t s . The present number of ambulances and bases, 19, answer 42.2% of a l l emergency c a l l s i n f i v e minutes or less at night. TABLE 6.6 EMERGENCY AMBULANCE CALLS ANSWERED IN 5 OR LESS MINUTES (NIGHTS ONLY) # of Depots # of Ambulances Added Ambulances % Increases Added % Increase 19 19 4 (23) 7.1% 12(31) 6.1 23 23 4 (27) 12.6% 12(35) 3.2 27 27 4 (27) 7.4% 31 31 4 (31) 8.1% TABLE 6.7 # of Ambulances Bases Added Bases % Increase 23 23 4 (27) - 2.3% 27 23 4 (27) - 4.5% 31 27 4 (31) - 1.9% 235 31 4 (35) - 5.2% Adding four ambulances to the 19 depots, 19 ambulances combin-ation results i n an 7.1% increase i n the number of emergency c a l l s answered. When another eight ambulances are added the marginal increase is 6.1%. This r e s u l t i s explained by the fact that when the f i r s t four ambulances were added they took 117 a good deal of pressure o f f the f i r s t o r i g i n a l 19 ambulances. With the addition of eight more ambulances most c a l l s nearby the depots were taken care of quickly but there s t i l l were not enough ambulances i n r u r a l areas when t r a v e l times are longer. Looking at the case where one starts with 23 depots and 23 ambulances and increases the number of cars to 27, one gets an increase i n the number of c a l l s answered within f i v e minutes of 12.6%. ODf eight more cars are added the percentage increase is only 3.2%. Here again the e f f e c t of diminishing marginal returns i s apparent. The addition of four cars helps immensely i n the urban areas. To reduce response time further one needs the placement of ambulances i n r u r a l areas only a few miles apart. The number of c a l l s i n r u r a l areas, however, does not j u s t i f y having ambulances i n close proximity to each other. A l l figures i n Table 6.6 and Table 6.7 support stacking of ambulances i n urban areas. The demand i s heaviest i n urban areas and stacking of ambulances there results i n at least a 7.1% increase in the number of emergency, c a l i s answered i n f i v e minutes or l e s s . Figure 6.8 also reveals that going from the 50th f r a c t i l e curve to the 65th f r a c t i l e the curve i s becoming f l a t t e r . Perhaps an a l t e r n a t i v e measurement would be to s p l i t the urban emergency and r u r a l emergency response times. Service Standards for both of these areas would have to be developed by a person from the Emergency Health Services. 118 Emergency C a l l s Answered i n 5 or Less Minutes (Night Only) 39 •+-No. of Bases FIGURE 6 .8 119 In figure 6.9 the f r a c t i l e s for paramedic c a l l s i s depicted. Again stacking of ambulances i n urban areas has a big e f f e c t . With 23 ambulances and 19 bases only 41.6% of a l l emergency c a l l s are answered i n f i v e minutes or l e s s . Adding eight cars increases the percentage to 49.9%. For the 23 cars and 23 bases the percentage of c a l l s answered within f i v e minutes i s 52.4%. Adding 12 ambulances increases the number of c a l l s answered by 12.5%. In figure 6.9 i t can be seen that the 70th f r a c t i l e curve i s f l a t compared to the other f r a c t i l e s . At t h i s f r a c t i l e i t i s becoming evident that to get any s i g n i f i c a n t increase i n paramedic c a l l s answered within f i v e minutes a great number of cars and bases would need to be added. Again i t can be said that perhaps urban and r u r a l regions should be examined separately. Another al t e r n a t i v e can be that c e r t a i n cars be designated to answer only emergency c a l l s and/or only paramedic c a l l s . Table 6.8 reveals that with nine r u r a l ambulances only 53.7% of r u r a l c a l l s are answered i n less than f i v e minutes. Further increases of 3, 4 and 2 ambulances show diminishing marginal increases although doubling of the number of ambulances has an o v e r a l l e f f e c t of 18.5%. In figure 6.10 i t can be seen that increasing the number of ambulances from 40 to 60 has no e f f e c t on the r u r a l response time for emergency c a l l s . No e f f e c t i s also observed when 120 Paramedic Calls Answered in Less Than 5 Minutes (Night Only) 23 27 31 35 No. of Bases r FIGURE 6.9 121 FRACTILE RESPONSE IN RURAL AREAS (NIGHT ONLY) Number of Rural Ambulances F r a c t i l e Under 5 Minutes % Increase 9 53.7 7.4 12 61.1 5.5 16 66.6 5.6 18 72.2 TABLE 6.8 122 F r a c t i l e Response (Night Only) Under 5 Minutes f o r Rural Emergency C a l l s 61.1 * 72.2 (18 rural ambulance 53.7 no e f f e c t * 66.6 \ no effect (16 rural ambulances) *61.1 (12 rural ambulances) x 5 3 . 7 ( 9 rural ambulances) 20 30 T o t a l // of Bases AO TT 50 60 F I G U R E 6 . 1 0 123 with 47 bases the number of ambulances i s increased from 47 to 70. The only a l t e r n a t i v e to reducing r u r a l response time is to increase the number of r u r a l ambulances as indicated i n f i g -ure 6.10. With 70 ambulances i n the region and only 12 i n r u r a l areas the number of c a l l s answered i s 61.1%. Transferring s i x of the urban cars to r u r a l areas increases the number of r u r a l emergency c a l l s answered to 72.2%. Whereas buses and ambulances are required i n r u r a l areas only cars help i n urban areas. Figure 6.11 i l l u s t r a t e s the stacking e f f e c t of ambulances i n urban areas. A 20 car increase at the 40 base l e v e l results i n a 10.9% increase i n emergency c a l l s answered and a 23 car increase at the 47 base l e v e l r esults i n a 12.9% increase i n the number of emergency c a l l s answered within f i v e minutes. Increasing the number of bases at the 60 and 70 ambulance l e v e l results i n a decrease i n emergency c a l l s answered. Comparing the 47 base and 70 ambulance l e v e l between emergency r u r a l c a l l s and emergency urban c a l l s one sees that only 61.1% of emergency r u r a l c a l l s versus 84.3 emergency c a l l s are answered. The reason i s obvious. Large distances i n r u r a l areas cause large response times. Urban areas have a heavy demand problem. Stacking i s an e f f e c t i v e means of reducing emergency response time i n urban areas. Having obtained the response surface i n 6.8, i t i s now possible to pick l i k e l y areas for further i n v e s t i g a t i o n of the 124 F r a c t i l e Response Under 5 Minutes f o r Urban Emergency (Night Only] X 8 4 ; 3 . X 8 3-9 8 1 . 2 X 8 0 . 4 X 71.4 * 70.3 20 30 40 4 7 50 60 70 T o t a l // of Bases FIGURE 6.11 125 number of ambulances to assign to gain equivalent f r a c t i l e responses over the entire day. The appropriate t e s t i n g point, that which balances the number of bases and the number of ambulances on any given f r a c t i l e contour l i n e , must be decided by the ambulance management. For the purposes of th i s experi-ment, several combinations were chosen as s t a r t i n g points for all-day runs. Starting from the 23-base 27-ambulance combina-tion, the addition of 14 ambulances resulted in an all-day f i v e -minute f r a c t i l e for emergency c a l l s of 54.8%, a drop of 4.8% over the night s h i f t . With a s t a r t of 27 bases and 27 ambulance 14 more ambulances caused a drop of 2.4%, with a s t a r t of 27 bases and 31 ambulances, the drop was 0.1%. The important observation i s that the night s h i f t respons surface and the all-day response surface have similar properties During the day s h i f t the frequency of c a l l s increases but the proportion of emergency c a l l s i s not large. There i s a s i g n i -f i c a n t increase i n the number of transfer c a l l s but the f r e -quency of other types of c a l l s do not increase s i g n i f i c a n t l y . I t i s becoming evident from th i s experiment and others that either more ambulances or sp e c i a l i z e d ambulances are needed i n urban areas. With the high frequency of urban c a l l s c e r t a i n l y more ambulances are needed. To further reduce respons time for emergency type c a l l s (including paramedic c a l l s ) per-haps a number of cars should only be used to answer emergency c a l l s . Another alt e r n a t i v e i s to obtain other forms of trans-126 portation for transfer patients. As the population i n the G.V.R.D. grows and demand increases the ambulance service must examine innovative al t e r n a t i v e p o l i c i e s i n order to remain e f f e c t i v e . Some alternative p o l i c i e s are discussed i n the following sections. 6.7 HIGH URBAN DENSITY Congestion i s the major problem of the present ambulance system. There are not enough ambulances i n either the day s h i f t or night s h i f t to meet demand. As a r e s u l t ambulance a v a i l a b i l i t y i s low and the number of queued c a l l s i s s i g n i f i -cant. As population increases demand w i l l increase. Some p o l i c i e s to further investigate are: 1. Set separate goals for urban and r u r a l response times. By d i v i d i n g up the region one can focus more e f f e c t i v e l y on the problems of one area. 2. Increase the number of vehicles as indicated by the results of experiment #5 for the day s h i f t . The optimal number w i l l have to be decided by ambulance service management. 3. Use of other than ambulance personnel to trans-port transfer patients. This would a l l e v i a t e much congestion between the hos p i t a l discharge hours from 11 a.m. to 2 p.m. 6.8 PARAMEDICS - FUTURE USE From the experiments conducted and data gathered i t i s evident that there i s strong demand for more paramedic units. 127 Presently i n the G.V.R.D. there are two paramedic units. These units are being used for other types of c a l l s when other vehicles are busy. Another factor which results i n loss of time for paramedics i s the high number of cancelled c a l l s these vehicles answered. In order to e f f i c i e n t l y use the paramedic units e f f e c t i v e screening of c a l l s must f i r s t take place. This may take place when dispatches become more experienced. A second p o l i c y i s to use paramedics only for designated paramedic c a l l s . In order to f a c i l i t a t e obtaining t h i s goal more ambulances are needed. F i n a l l y more paramedic-ambulances are required. By gathering data from dispatchers on where and when paramedics are required one can determine through the simulation where these vehicles should be located. Placements of paramedic crews at hospitals i s a useful p o l i c y since paramedics are well q u a l i f i e d to help out i n emergency rooms. 6.9 SUMMARY The ambulance system i s a very complex system. In order to study i t e f f e c t i v e l y many factors must be taken into account. These factors include: the frequency of c a l l s , the s p a t i a l and time d i s t r i b u t i o n of c a l l s , the types of c a l l s and the operational procedures of ambulances. Simulation i s a means of taking into account these factors and the int e r - r e l a t i o n s h i p s involved. 128 In the G.V.R.D. congestion i s a major problem. Using simulation one i s able to investigate the problem e f f e c t i v e l y and t r y out d i f f e r e n t strategies to see how problems can be dealt with. From the f i v e experiments done i n Chapter 6 of t h i s study, i t was demonstrated how simulation can be used to examine i n d i v i d u a l regions, various periods, and the t o t a l system. Areas of concern revealed by the simulation are the high frequency of urban c a l l s , the high number of transfer c a l l s during the day s h i f t and the increasing demand for paramedic vehicles. 129 BIBLIOGRAPHY 1. B e r l i n , G.N., Leibman, J.C. "Mathematical Analysis of Emergency Ambulance Location" Socio-Economic Planning Sciences Vol. 8, Dec. 1974. 2. B e r l i n , G.N., Revelle, C , Elzinga, J . "Determining Ambulance Locations for On-Scene and Hospital Care" Environmental Planning Association Vol. 3, Aug. 1976. 3. Carbone, R. "Public F a c i l i t i e s Location Under Stochastic Demand" Infor Vol. 12 No. 3, Aug. 1976. 4. Chaiken, J . , Larson, R. "Methods for A l l o c a t i n g Urban Emergency Units: A Survey" Management Science Vol. 19, Dec. 1972. 5. Church, R., Revelle, C. "The Maximal Covering Location Problem" Papers of the Regional Science Association Vol. 32, F a l l 1974. 6. Cooper, L. "Location-Allocation Problems" Operations Research, Vol. 11, No. 3 (May-June 1963) pp. 333-343. 7. Daverkow, S.G. "Location and Cost of Ambulances Serving a Rural Area" Health Services Research Vol. 12 No. 7, F a l l 1977. 8. Fitzsimmons, J . "A Methodology for Emergency Ambulance Deployment" Management Science Vol. 19, Feb. 1973. 9. Garfinkel, R.S., Neebe, A.W., Rao, M.R. "An Algorithm for the M-Median Plant Location Problem" Transportation Science Vol. 8, Aug. 1974. 10. Groom, K.N. "Planning Emergency Ambulance Services" Operational Research Quarterly Vol. 28 No. 3 I I . 11. Hakimi, S. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph" Operations Research Vol. 12, May-June 1974. 12. Hakimi, S. "Optimum D i s t r i b u t i o n of Switching Centers i n a Communications Network and Some Related Graph Theoretic Problems" Operation Research Vol. 13, June 1965. 130 13. Khumawala, B.M. "An E f f i c i e n t Algorithm for the P-Median Problem with Maximum Distance Constraints" Geographical Analysis Vol. 5, Oct. 1973. 14. Khumawala, B.M., Neebe, A.N., Dannenbring, D.G. "A Note on Elshaieb's New Algorithm for Locating Sources Among Destinations" 15. Kleinman, J.C., Wilson, R.W. "Are 'Medically Underserved Areas' Medically Underserved?" Health Services Research, Summer 1977. 16. Kolesar, P., Blum, E.H. "Square Root Laws for F i r e Engine Response Distances" Management Science Vol. 19 No. 12, Aug. 1973. 17. Krarup, J . , Pruzun, P.M. "Selected Families of Discreet Location Problems Part IIIK: The Plant Location Family" Working Paper No. WP-12-77, Faculty of Business, University of Calgary, Aug. 1977. 18. Kuhn, H.W., Kuenne, R.E. "An E f f i c i e n t Algorithm for the Numerical Solution of the Generalized Weber Problem i n S p a t i a l Economics" Journal of Regional Science, Vol. 4 (1962) p. 21-34. 19. Revelle, C.S., Marks, D., Leibman, J . "An Analysis of Private and Public Sector Location Problems" Management Science Vol. 16. 20. Revelle, C.S., Swain, R. "Central F a c i l i t i e s Location" Geographical Analysis Vol. 2, Jan. 1970. 21. Revelle, C.S., Toregas, C , Falkson, L. "Applications of the Location Set-Covering Problem" Geographical Analysis Vol. 8, Jan. 1976. 22. Rojeski, P., Revelle, C.S. "Central F a c i l i t i e s Location Under an Investment Constraint" Geographical Analysis Vol. 2, 1970. 23. Rushton, G., Goodchild, M. , Ostresh, L. "Computer Programs for Location-Allocation Problems" Monograph No. 6, Department of Geography, University of Iowa, July 1973. 24. Savas, E. "Simulation and Cost-Effectiveness Analysis of New York's Emergency Ambulance Service" Management Science Vol. 15, Aug. 1969. 131 25. Schuler, R.E., Holaman, W.L. "Optimal Size and Spacing of Public F a c i l i t i e s i n Metropolitan Areas: The Maximal Covering Location Problem Revisited" Papers of the Regional Science Association Vol. 39, Summer 1978. 26. Scott, A.J. "Location-Allocation Systems: A Review" Geographical Analysis, 1970. 27. S i l e r , K.F. "Level-Load Retrieval Time: A New C r i t e r i o n for EMS F a c i l i t y S i t e s " Health Services Research, Winter 1977. 28. Swain, R.W. "A Parametric Decomposition Approach for the Solution of Uncapacitated Location Problems" Management Science Vol. 21, Oct. 1974. 29. Swoveland, C , Uyeno, D., Vertinsky, I., Vickson, R. "Ambulance Location: A P r o b a b i l i s t i c Enumeration Approach" Management Science Vol. 20 No. 4, Dec. 1973. 30. Tan, E. "A Strategy for Ambulance System Designs: An Investigation of the Ambulance System i n the Greater Vancouver Regional D i s t r i c t " Master's Thesis, University of B r i t i s h Columbia, 1974. 31. T e i t z , M. , Bart, P. "Heuristic Methods for Estimating the Generalized Vertix Median of a Weighted Graph''- Operations Research Vol. 16, Sept.-Oct., 1968. 32. Toregas, C , Revelle, C.S. "Location Under Time or Distance Constraints" Papers of the Regional Science Association Vol. 28, F a l l 1972. 33. Toregas, C , Revelle, C.S. "Binary Logic Solutions to a Class of Location Problems" Geographical Analysis Vol. 5, A p r i l 1973. 34. Toregas, C , Swain, R.W., Revelle, C.S., Bergman, L. "The Location of Emergency Service F a c i l i t i e s " Operations Research Vol-. 19, Oct. 1971. 35. Weber, A. translated as "Alfred Weber's Theory of Location of Industries" by C.I. F r i e d r i c h , Chicago, 1929. 36. Whitaker, R.A. "An Algorithm for Estimating the Medians of a Weighted Graph Subject to Side Constraints, and an Application to Rural Hospital Locations i n B.C." PHD Thesis, University of B r i t i s h Columbia, March 1971. 132 APPENDIX 133 1. Description of Regression on Travel Times In a separate study, 1 a regression equation was developed that could be used to predict response times. The data used was gathered from data forms f i l l e d out by the ambulance dr i v e r s . A sample size of one hundred and twenty-one t r a v e l times was obtained. For each ambulance c a l l , there is a separate response time and a time for t r a v e l l i n g from the scene to the f i n a l destination ( i . e . h o s p i t a l ) . The factors considered were: (i) distance t r a v e l l e d , ( i i ) type of c a l l , ( i i i ) time of day, and (iv) where the tr a v e l took place. The regression equations obtained were: (T for time and D for distance) response time T = 5.8754 i f non-emergency c a l l 2.9894 i f emergency c a l l R 2 = 0.69563 scene to f i n a l T = 3.7002 i f not on 7 a.m.-6 p.m. s h i f t destination 0.23498D + 3.7002 D i f on 7 a.m. -6 p.m. s h i f t R 2 = 0.726Z These equations are graphed on figures A and B. The regression equations were used to compare the actual t r a v e l times (travel times to be used by the simulation model) and the predicted t r a v e l times. This could be done since the G.V.R.D. tr a v e l time matrix had a corresponding distance matrix. Nodes were chosen from various regions of the G.V.R.D. 134 (the dispatch area). Obtained for each of these nodes was a predicted t r a v e l time to every other node i n the G.V.R.D. The predicted t r a v e l times were then compared to the actual t r a v e l times. The routine "ACTFIT" from the U.B.C. T.S.P. package . was used to compare the t r a v e l times. It was observed that the actual t r a v e l times were greater than the predicted t r a v e l times. For nodes within a few miles of the source node the mean error was almost zero. As one moved further away from the source node the actual t r a v e l times exceeded predicted t r a v e l times by an o v e r a l l mean error of 9.8 minutes for downtown source nodes. The regression indicates that the t r a v e l time data being used for the simulation model i s conservation. This res u l t s from the fact that the data i s r e f l e c t i n g morning rush hour t r a f f i c . Thus the net e f f e c t of using t h i s data i s that response times outputted by the simulation model should be conservative. 135 = 5.8754 D = 2.9894 D 0 1 2 3 4 5 6 7 8 9 ]D U 12 13 14 15 16 Distance (miles) FIGURE A / ^ 0.23498D + 3.7002 D T = 3.7002 D 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Distance (miles) FIGURE B Generate c a l l s i begin p one c a l rocessing 1 at a time FLOW CHART OF THE SIMULATION paramedic c a l l a l l other c a l l s no Add 20 minutes delay to t r a n s f e r c a l l s Yes i Adjust t r a v e l time for emergency c a l l s i Add startup time i Dispatch the ambulance Store c a l l s on l i s t s by p r i o r i t y Yes? ordinary ambulance handles c a l l D-Xact f o r the c a l l i s used as device to see i f any other c a l l s need to be. answered, i f more, Xact i s t e r -minated and Ambulance returns home cancelled Xact ( Stop ) 137 © one of each No dispatch both free Yes Dispatch paramedic only only ordinary free only paramedic free store on l i s t of calls to be serviced! Paramedic ambular can be dispatched while ordinary is enroute Dispatch paramedic only by p r i o r i t y cancel paramedic 303 Yes ordinary ambulance handles Vcall 2L. paramedic handles c a l l completed c a l l Xact is used to check i f any other paramedic cal l s must be served. If none, Xact i s terminated and ambu-lance returns home. ^ ( Stop ) 30% v Yes Dispatch paramedic paramedic ambulance handles c a l l > t ordinary ambu-lance cancels on paramedic arrival 138 paramedic cance l paramedic i f any o r d i n a r y ambulance handles c a l l ord inary: ambu-l a n c e - i s c a n c e l l e d paramedic ambu-lance handles ' c a l l 139 

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