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A strategy for ambulance system designs : an investigation of the ambulance system in the greater Vancouver… Tan, Eddy 1974

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A STRATEGY FOR AMBULANCE SYSTEM DESIGNS:  An i n v e s t i g a t i o n  o f the Ambulance System i n the  G r e a t e r Vancouver Regional  District  by  BSc.,  Eddy Tan U n i v e r s i t y of V i c t o r i a , 1972.  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN BUSINESS ADMINISTRATION IN THE MANAGEMENT SCIENCE DEPARTMENT OF THE FACULTY OF COMMERCE We accept t h i s t h e s i s as conforming r e q u i r e d standard  THE UNIVERSITY OF BRITISH  to the  COLUMBIA  September 1974 A. D.  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l  f u l f i l m e n t o f the requirements  an advanced degree at the U n i v e r s i t y of B r i t i s h C o l u m b i a , I agree the L i b r a r y I further  s h a l l make i t f r e e l y a v a i l a b l e f o r  agree t h a t p e r m i s s i o n f o r e x t e n s i v e  r e f e r e n c e and copying of t h i s  of t h i s t h e s i s f o r written  It  i s understood that c o p y i n g or  thesis  Department of  C OA1 » 7 C- r~t f  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  Date  4-€£/  /0 -  / / 7 </ c  or  publication  f i n a n c i a l g a i n s h a l l not be a l l o w e d without my  permission.  that  study.  f o r s c h o l a r l y purposes may be granted by the Head of my Department by h i s r e p r e s e n t a t i v e s .  for  (ii)  ABSTRACT OF THE DISSERTATION This d i s s e r t a t i o n design parameters  i s a study o f the e f f e c t s  and c o n t r o l p o l i c i e s  i n t h e p l a n n i n g and  o p e r a t i o n o f emergency ambulance s y s t e m s . is  c h a r a c t e r i z e d by a s e q u e n c e  notification patient  o f an i n c i d e n t  A computer s i m u l a t i o n validated  f o r the  Experiments  The a m b u l a n c e  system  o f events b e g i n n i n g w i t h the  and e n d i n g w i t h  t o an e m e r g e n c y m e d i c a l  of alternative  the d e l i v e r y  of the  facility.  model was s u b s e q u e n t l y d e v e l o p e d and  G.V.R.D.  are conducted  using this  Simulation  a L o c a l Search A l g o r i t h m which  determined  optimal locations to  evaluate the e f f e c t  of the following  *  number o f a m b u l a n c e s  *  dispatching  *  demand  Results  on s y s t e m  M o d e l and  performance:  policies  rate  f r o m t h e above e x p e r i m e n t s  lead  to the following  recommendations: *  Ambulance s e r v i c e  *  A m b u l a n c e s s h o u l d be l o c a t e d response  *  location  different Periodic  strategically  level  of response  *  to minimize  t i m e , t h e number  o f a m b u l a n c e s s h o u l d be d i f f e r e n t i n  p e r i o d s o f the day. review of the level  and s p a t i a l  o f demand s h o u l d be made and a d j u s t m e n t s in  basis.  time.  For a given desired and  *  s h o u l d be p r o v i d e d on a r e g i o n a l  t h e number and l o c a t i o n s  of  i n part  on an a n a l y s i s  b e t w e e n c o s t and r e s p o n s e  time.  s h o u l d be made  ambulances.  The d e t e r m i n a t i o n o f t h e p r o p e r r e s p o n s e s h o u l d be b a s e d  distribution  time  level  of the t r a d e o f f  (iii) TABLE OF CONTENTS Page ABSTRACT OF THE DISSERTATION  (i i )  L I S T OF TABLES  (  L I S T OF FIGURES  ( vi)  L I S T OF MAPS  v)  (vii)  CHAPTER 1  INTRODUCTION  1  1.1.  Introduction  1  1.1.1. 1.1.2. 1.1.3.  1 2 3  1.2.  CHAPTER 2  Scope and O b j e c t i v e s o f R e s e a r c h Research O u t l i n e F u n c t i o n o f t h e Ambulance S y s t e m  Ambulance S y s t e m M o d e l s  6  1.2.1. 1.2.2. 1.2.3.  6 8  Q u e u i n g Model S i m u l a t i o n Model O p t i m i z a t i o n Method t o L o c a t e Ambulances  EXISTING AMBULANCE SERVICES  IN G.V.R.D.  10  2.1.  Existing  2.2.  Demand F o r Ambulance S e r v i c e s  13  2.2.1. 2.2.2. 2.2.3.  13 15 16  2.2.4. 2.3.  CHAPTER 3 3.1.  Ambulance S e r v i c e  8  Data C o l l e c t i o n Definitions C u r r e n t Demand a. Temporal V a r i a t i o n s (i) Seasonal V a r i a t i o n s (ii) Day o f Week V a r i a t i o n s (iii) Time o f Day V a r i a t i o n s Demand Growth P a t t e r n  Production  and E v a l u a t i o n  10  20 24  2.3.1. 2.3.2.  P r o d u c t i o n Components A n a l y s i s o f Components  24 26  2.3.3.  Ambulance U t i l i z a t i o n  34  COMPUTER SIMULATION Use o f S i m u l a t i o n  MODEL  i n System A n a l y s i s  36 36  (iv)  3.2.  General D e s c r i p t i o n Models 3.2.1. 3.2.2.  3.3.  o f Computer S i m u l a t i o n  Ambulance C a l l G e n e r a t o r Main S i m u l a t o r  Model V a l i d a t i o n f o r t h e Ambulance S y s t e m 3.3.1. 3.3.2. 3.3.3. 3.3.4.  CHAPTER 4  Page 37 37 37  Vancouver 40  G e n e r a l V a l i d i t y o f t h e Model S t a t i s t i c a l Test D e t e r m i n i n g the Length o f the Simulation Period C o r r e s p o n d e n c e o f R e a l W o r l d and S i m u l a t e d Data  41 41 42 42  THE AMBULANCE LOCATION PROBLEM  48  4.1.  E s s e n t i a l Features i n the L o c a t i o n o f Ambulances  48  4.2.  An A n a l y t i c a l Time  48  4.3.  A Local Search A l g o r i t h m  50  4.4.  Experimental E v a l u a t i o n of the A l g o r i t h m  51  4.5.  S e n s i t i v i t y o f A l g o r i t h m to Choice o f Starting Locations  52  DESIGN OF THE EXPERIMENT  54  5.1.  Introduction  54  5.2.  Experimental Design  55  5.3.  The C o l l e c t i o n  57  CHAPTER 5  CHAPTER 6  Approximation  t o Mean R e s p o n s e  of Simulation S t a t i s t i c s  EXPERIMENT RESULTS AND THEIR IMPLICATIONS  58  6.1.  O p t i m a l Ambulance L o c a t i o n  58  6.2.  Variations  71  6.3.  Dispatch Rules  76  6.4.  Sensitivity i n Demand  80  6.5. 6.6.  i n R e s p o n s e Time by M u n i c i p a l i t y  o f R e s p o n s e Times t o Changes  T r a d e - o f f s Between A n n u a l and R e s p o n s e Time Summary and C o n c l u s i o n s .  Operating  Cost 81 84  ( v  )  LIST OF TABLES Page Table  1  Ambulance  2  Ambulance S e r v i c e by M u n i c i p a l i t y  12  3  D a i l y Ambulance Demand R a t e by Time o f Day and M u n i c i p a l i t y  19  Distribution Municipality  o f A m b u l a n c e D e s t i n a t i o n s by 21  5  Distribution  of Call Origin  6  A v e r a g e R e s p o n s e Time Municipality  4  7  Companies S e r v i n g  t h e G.V.R.D  by D e s t i n a t i o n . . . .  and S e r v i c e Time by  Call  8  Ambulance U t i l i z a t i o n by Time o f Day  9  CHI S q u a r e Goodness o f F i t T e s t o f R e s p o n s e Time P r o b a b i l i t y D i s t r i b u t i o n A v e r a g e and 9 0 t h F r a c t i l e R e s p o n s e Time by M u n i c i p a l i t y and by Number o f A m b u l a n c e s (8 a.m. - 6 p.m., a l l c a l l s )  11  12  13  14  22 28  A v e r a g e O p e r a t i o n Times by Type and Time of  10  11  A v e r a g e and 9 0 t h F r a c t i l e R e s p o n s e Times by M u n c i p a l i t y and by Number o f A m b u l a n c e s (6.p.m.midnight, a l l calls) A v e r a g e and 9 0 t h F r a c t i l e R e s p o n s e Times by M u n i c i p a l i t y and by Number o f A m b u l a n c e s ( m i d n i g h t - 8 a.m., a l l c a l l s )  33 35 46 72  73  74  A v e r a g e R e s p o n s e Time by M u n i c i p a l i t y w i t h O p t i m a l P l a c e m e n t o f 21 A m b u l a n c e s f o r T r u e , S q u a r e d , and Cubed T r a v e l Times  77  O p t i m a l P l a c e m e n t o f Ambulance D e p o t s by Time o f Day and Number o f A m b u l a n c e s  86  (vi)  L I S T OF FIGURES Page Fig.  1  A v e r a g e G.V.R.D. C a l l Time o f Day  Rate ( c a l l s / h o u r )  by 18  2. D i s t r i b u t i o n All Calls  o f Response Time, C u r r e n t D a t a ,  3  Distribution Emergency  o f Response Time, C u r r e n t D a t a ,  4  D i s t r i b u t i o n o f R e s p o n s e Time Ambulance S y s t e m  5  Standard  6  E f f e c t o f P r o b a b i l i t y o f an i n c i d e n t by K - t h c l o s e s t Ambulance  31  f o r G.V.R.D.  D e v i a t i o n v e r s u s number o f c a l l s  32 45 47  dispatch 53  7  D i s t r i b u t i o n o f R e s p o n s e Time w i t h O p t i m a l P l a c e m e n t o f A m b u l a n c e s (8 a.m. - 6 p.m.)  60  8  D i s t r i b u t i o n o f R e s p o n s e Time w i t h O p t i m a l P l a c e m e n t o f A m b u l a n c e s (7 p.m. - m i d n i g h t )  61  9  D i s t r i b u t i o n o f R e s p o n s e Time w i t h O p t i m a l P l a c e m e n t o f A m b u l a n c e s ( m i d n i g h t - 8 a.m.)  62  A v e r a g e R e s p o n s e Time by Number o f A m b u l a n c e s by Time o f Day, f o r a l l c a l l s  66  A v e r a g e R e s p o n s e Time by Number o f A m b u l a n c e s by Time o f Day, f o r emergency c a l l s o n l y  67  E f f e c t o f Number o f A m b u l a n c e s on R e s p o n s e T i m e , S e r v i c e Time and Ambulance U t i l i z a t i o n (8 a.m. - 6 p.m.) ,  68  E f f e c t o f Number o f A m b u l a n c e s on R e s p o n s e Time, S e r v i c e Time and Ambulance U t i l i z a t i o n (6 p.m. - m i d n i g h t )  69  E f f e c t o f Number o f A m b u l a n c e s on R e s p o n s e T i m e , S e r v i c e Time and Ambulance U t i l i z a t i o n ( m i d n i g h t - 8 a.m.)_  70  10 11 12  13  14  15  M u n i c i p a l V a r i a t i o n i n A v e r a g e R e s p o n s e Time by Number o f A m b u l a n c e s f o r a l l c a l l s (8 a.m.-6pcmB)75  16  T r a d e o f f Between A v e r a g e R e s p o n s e Times and Annual O p e r a t i n g Cost  82  (vii)  L I S T OF MAPS Page Map  1  C u r r e n t Ambulance L o c a t i o n s  63  2  O p t i m a l P l a c e m e n t o f 21 (8 a.m. - 6 p.m.)  64  3 4  Ambulances  O p t i m a l P l a c e m e n t o f 21 Ambulances w i t h S q u a r e d T r a v e l Time (8 a.m. - 6 p.m.)  78  O p t i m a l P l a c e m e n t o f 21 Ambulances w i t h cubed T r a v e l Time (8 a.m. - 6 p.m.)  79  -  1 -  CHAPTER 1 1.1.  Introduction An e f f e c t i v e  ambulance s e r v i c e i s a v i t a l  community.  I t provides l i f e - g i v i n g  Without  it,  hundreds  victims  unable t o get medical a t t e n t i o n  part o f every  s u p p o r t t o people i n need.  o f people would  d i e each y e a r - a c c i d e n t i n time.  Time i s t h e e s s e n c e o f e v e r y a m b u l a n c e s e r v i c e . speed w i t h which  an a m b u l a n c e c a n r e s p o n d t o a c a l l  In t h e G r e a t e r Vancouver ambulance system's on b o t h p l a n n i n g  Regional D i s t r i c t  ability  primary objective  management and c o n t r o l cally  ability  of t h i s  operation of this Three *  research  and management p o l i c i e s  t o r e s p o n d t o emergency  calls.  o b j e c t i v e s , i t was n e c e s s a r y  of alternative  within  ambulance  of design parameters  to determine:  on t h e a m b u l a n c e  s y s t e m p e r f o r m a n c e , i . e . , t h e number o f  *  the e f f e c t system  systems  community m e d i c a l s y s t e m .  s u b - o b j e c t i v e s were e s t a b l i s h e d  and t h e i r  affect  and m e t h o d o l o g i e s f o r t h e p l a n n i n g and  subsystem  the e f f e c t s  i s to study the  o f t h e ambulance system and, s p e c i f i -  simulation studies  to p r o v i d e knowledge  T h i s s t u d y i s an  of Research  I n o r d e r t o meet t h e r e s e a r c h to conduct  depends  i s so.  d e t e r m i n e how i t s p l a n n i n g  the system's  (G.V.R.D.), t h e  and management p o l i c i e s .  Scope and O b j e c t i v e s  The  i s crucial.  t o r e s p o n d t o emergency c a l l s  a t t e m p t t o e x p l a i n why t h i s 1.1.1.  The  ambulances  location of dispatching policy  performance  on a m b u l a n c e  - 2  *  the in  sensitivity  response to change i n the  i.e., 1.1.2.  Section  different  calls.  Outline  1.2.  of t h i s  chapter r e l a t e s the  t h e o r e t i c a l frameworks:  model, and  demands f o r s e r v i c e  the occurrence r a t e o f ambulance  Research  to three  of ambulance system performance  an o p t i m i z a t i o n s t u d i e s on the  model.  subject  ambulance system  a queuing model, a s i m u l a t i o n A b r i e f review of  three  of ambulance systems i s a l s o  included. Chapter 2 contains which i s now  being  an a n a l y s i s of the  provided  ambulance s e r v i c e  i n the G.V.R.D.  Included  is a  d i s c u s s i o n about: *  who  provides  the  ambulance s e r v i c e  *  the  temporal and  *  the  d i s t r i b u t i o n of c a l l  *  current  spatial  call  f o r help  i s placed  ambulance a r r i v e s on the ambulance  origin  destinations  "response time" l e v e l s ( i . e . ,  when the  *  d i s t r i b u t i o n of c a l l  the time from  to the  time  the  scene)  utilization.  Chapter 3 i s devoted to the d e s c r i p t i o n of the model used i n t h i s study. a simulation  The  *  why  *  a general  *  a d i s c u s s i o n of the  chapter a l s o  simulation  discusses:  i s used  d e s c r i p t i o n of the  simulation  model  assumptions made  * a v a l i d a t i o n o f the model Chapter 4 contains includes:  the  "optimization  algorithm"  and  - 3 *  *  analytical  a p p r o x i m a t i o n o f mean r e s p o n s e  simulation  results  comparison  b e t w e e n t h e v a l u e o f mean r e s p o n s e  obtained  from the s i m u l a t i o n  time  from  time  and t h e a n a l y t i c a l  approximation *  the " a l g o r i t h m s t e p s " t o l o c a t e ambulances w i t h t h e o b j e c t i v e o f m i n i m i z i n g mean r e s p o n s e  *  experimental evaluation of the "algorithm"  Chapter 5 c o n t a i n s experiments. the  This chapter develops  p l a n o f the experiments using the s i m u l a t i o n  optimization simulation  algorithm.  implications, *  output from the  Chapter 6 contains experimental r e s u l t s , and c o n c l u d i n g r e m a r k s .  the average for  The s t a t i s t i c a l  each  o v e r a l l response  of three levels  time i n each  *  the s e n s i t i v i t y  of response  health  municipality  times  time t o l e v e l  o f demand  ( e . g . , by how much does a v e r a g e  response  i o r a t e when c a l l  are doubled.  r a t e s p e r hour  F u n c t i o n o f t h e Ambulance  care f a c i l i t i e s ,  Until quite recently  private  deter-  functions:  rescue,  emergency c a r e , t r a n s p o r t t o emergency  and t r e a t m e n t a t emergency  responsibility  among a number o f p r i v a t e G.V.R.D.:  time  System  a m b u l a n c e s y s t e m has f i v e p r i n c i p l e  support, preliminary  examines:  of service  t h e i m p a c t o f d i s p a t c h r u l e s on r e s p o n s e  The  policy  This chapter also  *  1.1.3.  and t h e  i s explained.  Finally,  life  time  facilities.  f o r these functions  resided  and p u b l i c o r g a n i z a t i o n s w i t h i n t h e  ambulance companies,  police  and f i r e  departments.  - 4 -  and h o s p i t a l The service  emergency  departments.  i m p o r t a n c e o f an e f f e c t i v e c a n be i l l u s t r a t e d  and e f f i c i e n t  ambulance  by a s i m p l e n u m e r i c a l c a l c u l a t i o n .  C u r r e n t l y , t h e r e a r e r o u g h l y 45,000 a m b u l a n c e c a l l s in  t h e G.V.R.D.  priority" is  Of t h e s e , a p p r o x i m a t e l y 10,000 a r e " h i g h  o r "emergency" c a l l s  required  t o speed  -  -  calls  calls  r e s p o n s e by h i g h l y  trained  crucial  t o the maintenance  of the patient's  sake o f argument, t h i s  or  d i e , depending  ambulance p e r s o n n e l i s life.  p e r c e n t a g e were o n l y  240 c a l l s  of the c a l l .  t h e r e i s some p e r c e n t a g e i n w h i c h  a rapid  into  i n which the s i r e n  t h e ambulance t o t h e scene  Of t h e s e h i g h p r i o r i t y  translate  per year  p e r year i n which  on t h e q u a l i t y  I f , f o r the  2%, t h a t  would  t h e p a t i e n t may  o f t h e ambulance  service.  F u r t h e r e v i d e n c e o f t h e i m p o r t a n c e o f ambulance is  service  c o n t a i n e d i n a s t u d y by F r e y e t . a l . o f 150 d e a t h s ( 5 ) . I t was f o u n d t h a t  result-  ing  from a u t o m o b i l e a c c i d e n t s  the  v i c t i m s w o u l d p r o b a b l y have s u r v i v e d h a d t h e q u a l i t y o f  a m b u l a n c e s e r v i c e been h i g h e r . S y s t e m s Task  Force  the 1.  The r e c e n t r e p o r t o f t h e H e a l t h  f o r improved  us now b r i e f l y  ambulance  18% o f  ( t h e " F o u l k e s r e p o r t " ) has a l s o s t r e s s e d t h e  i m p o r t a n c e o f and need Let  live  ambulance s e r v i c e ( 4 ) .  c o n s i d e r each o f t h e f i v e  functions of  system.  Rescue In  some e m e r g e n c i e s  ment a r e r e q u i r e d treatment.  just  specialized  to get a p a t i e n t  F o r example,  from a w r e c k e d  certain  skills  and e q u i p -  t o a point of safe  a v i c t i m may h a v e t o be e x t r i c a t e d  automobile o r r e s c u e d from a c l i f f .  Since these  - 5 -  s i t u a t i o n s may and  r e q u i r e very r a p i d response and  equipment r e q u i r e d  are  often the  s i n c e the  skills  same as those used to  f i r e s , many m u n i c i p a l i t i e s c u r r e n t l y r e l y on  the  fire  fight  department  to provide rescue s e r v i c e . 2.  Life  Support  In the  first critical  moments a f t e r an emergency, immediate  response i s often necessary to maintain l i f e . icularly The  true  i f breathing  has  primary c o n s i d e r a t i o n  This  stopped or there  i s part-  i s heavy  then i s to reach the v i c t i m q u i c k l y  render f i r s t a i d to r e s t o r e b r e a t h i n g  or stop b l e e d i n g .  cases r a p i d response i s e s s e n t i a l but  a sophisticated  training i s generally fire  not.  Frequently  fire  wide range of emergencies, however, broader and more complex t e c h n o l o g i c a l  Since each s p e c i a l l y equipped and the decision-maker must be between t r a i n i n g and 3.  Preliminary This  but  function  equipment costs  c o n s i s t s not  also the d e c i s i o n on  path:  the  patient? facility?  How  combat  aware of the and  the  of and the  more s o p h i s t i c a t e d  support are  required. expensive,  trade-offs  r a p i d i t y of response.  Care  only  of the p r o v i s i o n of f i r s t  appropriate  What s e r v i c e s should be  level  trained unit i s quite  constantly  Emergency Medical  To  and  In such  rescue v e h i c l e s  department personnel perform t h i s f u n c t i o n .  t r a i n i n g and  bleeding.  preliminary  aid,  treatment  done at the scene to s t a b l i z e the  q u i c k l y must the p a t i e n t be moved to a treatment  Must the  treatment f a c i l i t y  be  forewarned of the  patient's  arrival? 4.  Transport to the Once the p a t i e n t  to the  Emergency Health Care i s i n the  emergency f a c i l i t y ,  Facility  ambulance and  f i r s t aid may  be  i s being  continued  transported and  - 6 a d d i t i o n a l i n f o r m a t i o n may be gathered. 5.  Treatment at an Emergency Health Care F a c i l i t y It  i s not common to regard the treatment at the emergency  facility  as part o f the emergency ambulance s e r v i c e system.  However, there are i n s t a n c e s i n which the attendants have s u f f i c i e n t medical t r a i n i n g and experience to be o f continued value to the p a t i e n t by a s s i s t i n g the emergency room 1.2.  staff.  Ambulance System Models The f o l l o w i n g  i s a d e s c r i p t i o n o f two models r e l a t e d to the  ambulance system and a d i s c u s s i o n of an o p t i m i z a t i o n 1.2.1.  method.  Queuing Model  The ambulance system can be c o n c e p t u a l i z e d as a queuing system i n the f o l l o w i n g (i)  A patient a call  (ii)  (customer) " a r r i v e s " at the moment he p l a c e s  f o r an ambulance;  S e r v i c e begins at the moment the ambulance i s dispatched to  (iii)  the p a t i e n t ;  S e r v i c e ends when the p a t i e n t and In  ing  sense:  i s d e l i v e r e d t o the h o s p i t a l  when the ambulance becomes a v a i l a b l e f o r another  one study, B e l l  ( 1 ) developed a queuing model f o r comput-  the s i z e o f an emergency ambulance f l e e t  specified  standards o f s e r v i c e .  r e q u i r e d to meet  He used the example of a system  with a uniform i n c i d e n t p a t t e r n with a s i n g l e ambulance By a n a l y z i n g a queuing system with u n l i m i t e d ambulance a b i l i t y , he provides approximate r e s u l t s c u l t i e s of computing steady s t a t e r e s u l t s queuing system.  call.  location. avail-  to overcome the d i f f i f o r a multi  server  He presented e a s i l y computed g u i d e l i n e s to a s s i s t  - 7 -  the  administrator  fleet  size.  o f an a m b u l a n c e s y s t e m i n d e t e r m i n i n g  Unfortunately,  uniform incident patterns of  h i s method c a n o n l y using  optimal  be a p p l i e d f o r  a s i n g l e ambulance l o c a t i o n , which  c o u r s e i s n o t t h e c a s e i n t h e G.V.R.D. M o r s e , h a s e x a m i n e d s i n g l e queue and m u l t i p l e  and  found t h a t  waiting  t h e s i n g l e queue s y s t e m e x h i b i t e d  time than t h e m u l t i p l e  queue s y s t e m .  queue s y s t e m s  a smaller  (6)  This  result  s u p p o r t s t h e common p r a c t i c e o f f o r m i n g a s i n g l e d i s p a t c h when a l l a m b u l a n c e s a r e b u s y and a s s i g n i n g  the f i r s t  a m b u l a n c e t o t h e i n c i d e n t w h i c h h a s been w a i t i n g This  policy i s often  its  current The  queue  available  the longest.  a l t e r e d s l i g h t l y by a s s i g n i n g  ambulance t o r e s p o n d t o a nearby t r a n s f e r c a l l  mean  a busy  after  completing  call.  d i s t r i b u t i o n of incident  arrival  rates  found i n the  G.V.R.D. was f o u n d t o f i t t h e f a m i l i a r P o i s s o n d i s t r i b u t i o n w i t h a time v a r i a b l e r a t e .  The d i s t r i b u t i o n o f s e r v i c e  was f o u n d n o t t o be e x p o n e n t i a l .  time however  M o r e o v e r , i t was h i g h l y  d e p e n d e n t on t h e p a r t i c u l a r a m b u l a n c e s b u s y a t t h e t i m e each was r e c e i v e d .  In addition, the service  the  same f o r e v e r y s e r v e r  the  ambulances a r e l o c a t e d This  any  call  time d i s t r i b u t i o n i s not  e x c e p t f o r t h e s p e c i a l c a s e when a l l a t t h e same s t a t i o n .  c h a r a c t e r i s t i c of servers  s u b s t a n t i a l l y complicates  a n a l y t i c a l e f f o r t t o model s u c h a q u e u i n g s y s t e m b e c a u s e t h e  location locations  of the servers influence  and s p a t i a l d i s t r i b u t i o n o f i n c i d e n t  t h e t r a v e l time which i s a s i g n i f i c a n t  component o f t h e s e r v i c e of queuing systems w i t h  time.  There i s i n i t i a l l y  mobile servers  no t r e a t m e n t  i n the l i t e r a t u r e .  (3).  1.2.2.  Simulation  Model  Many r e s e a r c h e r s s t u d y i n g ambulance simulation  as a t o o l .  Savas  (9) r e p o r t s t h e r e s u l t s  s i m u l a t i o n s t u d y o f t h e ambulance Hospital  District  simulation  system o f King  i n New Y o r k C i t y .  as t h e b a s i s  with a d i s t r i c t .  s y s t e m s have  He u t i l i z e s  used of a  County a GPSS  f o r a decision to allocate  ambulances  T h i s model was b a s e d upon t h e a s s u m p t i o n  of a Poisson d i s t r i b u t e d  r a t e o f emergency o c c u r r e n c e and a  stochastic  service process with  piece-wise  linear  a service  function of transit  t h a t t h e b e s t way t o u t i l i z e  (Fortran) d i g i t a l  distance.  ambulances  In another s t u d y , Swoveland  rate that He  is a discovered  i s to disperse  them.  e t . a l . (10) d e v e l o p e d a  s i m u l a t i o n w h i c h was u s e d f o r e s t i m a t i n g  i n f o r m a t i o n on s y s t e m c h a r a c t e r i s t i c s . s i m u l a t i o n was u s e d t o c o n s t r u c t  The o u t p u t o f t h e  an a n a l y t i c a l a p p r o x i m a t i o n  o f mean r e s p o n s e t i m e w h i c h i n t u r n was u s e d t o c o n s t r u c t t h e objective function study w i l l  f o r the optimal  l o c a t i o n problem.  be b a s e d on t h i s model and w i l l  t h e G.V.R.D.  This  a p p l y t h i s model t o  A d e t a i l e d d e s c r i p t i o n o f t h e s i m u l a t i o n model i s  p r o v i d e d i n C h a p t e r 3. 1.2.3.  O p t i m i z a t i o n Method t o L o c a t e  The  ambulance  Ambulances  l o c a t i o n p r o b l e m must be c o n s i d e r e d i n t h e  c o n t e x t of a p p r o p r i a t e system performance previously, ambulance  this  study w i l l  criteria.  judge t h e performance  As n o t e d  o f an  s y s t e m on t h e b a s i s o f i t s r e s p o n s e t i m e .  Because  t h e mean i s t h e most common measure u s e d , t h e e f f e c t i v e n e s s o f response time w i l l  be m e a s u r e d  i n t e r m s o f t h e mean.  - 9 The problem  of o p t i m a l l y  l o c a t i n g "N" ambulance i n a  s e r v i c e area can be s t a t e d e x p l i c i t l y  to be that o f s e l e c t i n g  a subset "w" o f ambulance l o c a t i o n s , from the set o f a l l feasible  l o c a t i o n s , so that the mean response time w i l l be  minimized. The problem  can be s t a t e d as:  Min R (w)  ffl]  weW where R(w) i s the system mean response time f o r the ambulance l o c a t i o n set w and W i s the c o l l e c t i o n o f a l l f e a s i b l e combina t i o n s of ambulance l o c a t i o n s . To solve  [1], simulation  can be a p p l i e d .  ( c a r d i n a l i t y of W) becomes l a r g e , s i m u l a t i o n effective.  But, i f (W) i s no longer  I t was f o r t h i s reason that Swoveland  e t . a l . (10)  developed an a n a l y t i c a l approximation of mean response time which was based on the s i m u l a t i o n . " p r o b a b i l i s t i c enumeration  From t h i s they used a  method" to solve [ l ] .  In t h i s study i t was found that good s o l u t i o n s could be obtained by i t e r a t i v e l y moving each ambulance to an adjacent location until  the mean response time could not be f u r t h e r  improved. This  "local  search A l g o r i t h m " was a p p l i e d to solve the  ambulance l o c a t i o n problem  i n the G.V.R.D.  - 10 -  CHAPTER 2 - EXISTING 2.1.  Existing Ambulance  AMBULANCE SERVICES IN G.V.R.D.  Ambulance  Services  services are c u r r e n t l y being  provided  to the  s e v e r a l m u n i c i p a l i t i e s w i t h i n t h e G.V.R.D. by t h e t e n a m b u l a n c e c o m p a n i e s and f i r e  departments l i s t e d  o f ambulance  a r e s e r v i c e d by M e t r o p o l i t a n  (76%  calls  of calls  service  they  Ambulance Co. the dispathing Ambulance  operation  ( a b o u t 2%  s e r v i c e ) i s a back-up s e r v i c e f o r c a l l s  originating outside gives,  The m a j o r i t y  and W h i t e Rock  A small part of Metropolitan's  of a l l c a l l s  1.  i n t h e G.V.R.D.), who a l s o p r o v i d e  f o r D e l t a , Richmond, S u r r e y  Companies.  i n Table  o f t h e i r primary  service region.  f o r each m u n i c i p a l i t y , t h e p e r c e n t a g e o f c a l l s  Table 2 serviced  by each o f t h e t e n ambulance s e r v i c e s . With the exception ambulance  o f M e t r o p o l i t a n Ambulance, a l l o f t h e  companies o p e r a t e  with  a constant  number o f c r e w s  o v e r each h o u r o f t h e day and o v e r e a c h day o f t h e week. politan  Ambulance  operates  with nine  c r e w s d a i l y b e t w e e n 8 a.m.  and 6 p.m. and e i g h t crews a t a l l o t h e r The  cost per c a l l  municipality  as shown i n T a b l e  compared w i t h  the current  M e t r o p o l i t a n Ambulance c h a r g e s $20.00 in for  t o the user  plus  calls  listed  v a r i e s by company and These c h a r g e s s h o u l d be  i s approximately  $53.00.  $l./mile for a l l calls  outside  for calls  which f o r Metropolitan  which they  and W h i t e Rock and a f l a t  service $53.00  o f B u r n a b y , V a n c o u v e r and New  W e s t m i n s t e r , West V a n c o u v e r F i r e than those  times.  actual cost per c a l l ,  D e l t a , Richmond, S u r r e y a l l other  1.  Metro-  Department has h i g h e r  originating  rates  i n Horseshoe Bay, c a l l s  o  Van  Bby  %  •  N W %  Rmd %  %  Sry %  N Vn %  W Vn. %  D'el /o  W Rk  A  Coquitlam F i r e Dept. Delta Amb. Metropolitan Amb.  .1 99.6  100.0  96.6  4.1  1.0  /a  P My  A  1.5  6.3  100.0 4.7  32.7  22.3  9 3 . 0 - 1 . 2  Port Coquitlam F i r e Dept.  . ?  Port Moody F i r e Dept.  Surrey Amb.  P Coq  /a 67.3  North Vancouver F i r e Dept.  Richmond Amb.  Coq  -  .3  1.1 '  2.3  94.1 76.0  West Vancouver F i r e Dept.  4.0 2.3  White Rock Amb.  98.8  16.7  TABLE  2  AMBULANCE SERVICE BY MUNICIPALITY • (Columns Sum To 100%)  96.0  7 , 7  6.5  Company  Primary Service Area  Coquitlam F i r e Dept.  D i s t r i c t of Coquitlam  Delta Amb.  Delta  Metropolitan Ambulance  Burnaby, Vancouver, New Westminster  North Vancouver F i r e Dept.  // Ambulances Leased or Owned  1 13  v Manned Ainbs. Per Shift  1  (f  Ave. Calls /Day  Cost/Call to User  1.6  no cnarge  1.4  $20 + $ 1/mi.  95.3  Burnaby: $20 Vancouver: $25 + $ 1/mi. New Westminster: $25 + $ 1/mi  North Vancouver, North Vancouver District  6.6  North Vancouver Residents $10 For a l l others $20.+ $ 1/mi.  Port Coquitlam F i r e Dept.  Port Coquitlam  1.2  no charge  Port Moody F i r e Dept.  Port Moody  1.0  no charge  Richmond Amb.  Richmond  3  2  4.5  $20 + $ 1/mi.  Surrey Ambulance  Surrey  2  1  .7.2  $20 -P $' 1/mi.  West Vancouver F i r e Dept.  Wes't Vancouver  3  2  3.0  $22.50  White Rock Ambulance  White Rock, Surrey  3.0  $20 +•$l/mi.  TOTAL FOR REGION  32  TABLE 1  3-9  22  125.0  AMBULANCE COMPANIES SERVING THE G.V.R.D.  - 13 g o i n g t o VGH,  and  c e r t a i n other unusually  the  fire  departments of the  and  Port  Moody do  not  District  to Metropolitan  each s u c h  Ambulance a r e  Delta,  is possible  a r e a s and For  type of  Institutional  the  are  $53.00  for  calls  W h i t e Rock  municipalities within  serviced  by  following  Billing  certain  their  other  Metropolitan  Ambulance  rough c l a s s i f i c a t i o n  per  of  assistance,  of the  47%  companies,  (ambulance not  18%  cent of a l l b i l l i n g  to i n d i v i d u a l s  (private  o l d age  billing  Approximately for  calls  billing:  Private b i l l i n g s  welfare,  the  by  t o some e x t e n t by  to p r o v i d e the  Type o f  No  Coquitlam  hospital)  charge a f l a t  R i c h m o n d , S u r r e y and  i  municipalities.  by  Although  Coquitlam, Port  b e t w e e n home and  Ambulance who  each s u b s i d i z e d  primary service  calls  calls.  call.  Metropolitan,  it  of  long  charge f o r ambulance s e r v i c e , r o u t i n e  (e.g., scheduled t r a n s f e r c a l l s directed  -  etc.)  33%  used, etc.)  20%  billings  to i n d i v i d u a l s are  written  off  non-payment.  2.2.  Demand f o r Ambulance  2.2.1.  Data C o l l e c t i o n  D a t a was during  Services  c o l l e c t e d from the  O c t o b e r and  November o f  ten  1973.  d i f f e r e n t ambulance I n f o r m a t i o n was  companies  recorded  for  - 14 -  all  calls  occurring  i n V a n c o u v e r , B u r n a b y , and New  o v e r a 14-day p e r i o d .  Information  was c o l l e c t e d o v e r p e r i o d s It  was f o u n d t h a t  on c a l l s  seasonal  C o n s e q u e n t l y , i t was n o t f e l t during For  other  parts  was  necessary  (a)).  to c o l l e c t a d d i t i o n a l  of the year. observed the f o l l o w i n g  infor-  received  location of c a l l destination  dispatched  information  type o f c a l l time  (scene)  from scene  those c a l l s  following  ( s e e s e c t i o n 2.2.3.  recorded:  time c a l l  For  elsewhere  e f f e c t s i n t h e demand f o r  each o f t h e 2,227 c a l l s  m a t i o n was  occurring  o f t h r e e , o r f o u r weeks.  ambulance s e r v i c e a r e n o t s i g n i f i c a n t  data  Westminster  (e.g.,  a hospital)  by M e t r o p o l i t a n  was r e c o r d e d  f o r each  Ambulance t h e  call:  ( r e g u l a r , c a n c e l l e d , ambulance not used)  ambulance  - left  base  - a r r i v e d at scene - left  scene f o r d e s t i n a t i o n  - a r r i v e d at d e s t i n a t i o n - cleared priority For  destination of call  ( s i r e n , normal or t r a n s f e r )  those areas not d i s p a t c h e d  (accounting  f o r only  distribution distributions extrapolated  by M e t r o p o l i t a n  11% o f t h e c a l l s  o f t y p e s and p r i o r i t i e s of the various  Ambulance  w i t h i n the region) the of c a l l s ,  and t h e i r  components o f s e r v i c e t i m e s were  from the e m p i r i c a l d i s t r i b u t i o n s o b t a i n e d  from t h e  - 15 -  sample o f c a l l s A travel pairs  time m a t r i x g i v i n g  of locations within  U.B.C. the  d i s p a t c h e d by M e t r o .  HPS  basis  transporation  of travel  the t r a v e l  t i m e s b e t w e e n 6642  t h e G.V.R.D., was o b t a i n e d f r o m t h e s t u d y and t h e n a d j u s t e d somewhat on  times observed  i n our sample o f ambulance  calls . 2.2.2.  Definitions  The t e r m s this  d e f i n e d below  are used  frequently  throughout  report:  ANU  (Ambulance Not U s e d ) :  the s i t u a t i o n  r e a c h e s t h e scene but i s not used  i n which  f o r transport  an a m b u l a n c e (first-aid  may o r may n o t be a d m i n i s t e r e d ) . Ambulance U t i l i z a t i o n : actually Cancelied  servicing Call:  t h e p e r c e n t o f t i m e an a m b u l a n c e i s calls.  a call  f o r an a m b u l a n c e w h i c h  i s cancelled  b e f o r e t h e ambulance r e a c h e s t h e scene. High P r i o r i t y used  (Code 3 ) :  Calls  i n which  the s i r e n i s  en r o u t e t o t h e s c e n e .  L o a d i n g Time: spent  Calls  t h e amount o f t i m e s p e n t a t t h e s c e n e  applying f i r s t  a i d , moving the p a t i e n t  (time  to the  ambulance, e t c . ) Non-Primary  Response:  the s i t u a t i o n  i n which  a call  by some a m b u l a n c e o t h e r t h a n t h e one whose d e p o t to  t h e scene  o f the c a l l  (because  the l a t t e r  i s serviced  i s closest  i s busy  and  therefore unavailable to respond). R e s p o n s e Time:  t h e e l a p s e d time between a c a l l  by t h e d i s p a t c h e r and t h e a r r i v a l  being  received  o f t h e ambulance at t h e scene.  _  - 16 -  S e r v i c e Time: elapsed  the t o t a l  time spent s e r v i c i n g a c a l l  t i m e b e t w e e n an a m b u l a n c e b e i n g  - the  dispatched  and t h e  ambulance l e a v i n g the d e s t i n a t i o n t o which the i n d i v i d u a l ( s ) was  transported.  Start-Up  Time:  dispatched location  the elapsed  and t h e a m b u l a n c e d e p a r t i n g  the elapsed  by t h e d i s p a t c h e r Call:  from i t s c u r r e n t  time between a c a l l  and t h e a m b u l a n c e b e i n g  a non-urgent  being  (often scheduled) c a l l  the elapsed  the p a t i e n t ( s ) i s b e i n g  (a)  Current  treatment.  transported  (generally, this  i s time  wards).  Demand  Temporal V a r i a t i o n s (i)  Seasonal V a r i a t i o n s  T h e r e a r e no p r o n o u n c e d s e a s o n a l examination  of monthly c a l l  removed  i t i s only  during  these  enough t o w a r r a n t (ii)  that a f t e r  i n m o n t h l y demand.  two months i s n o t g r e a t  a separate  An  the t r e n d e f f e c t i s  t h e months o f December and J a n u a r y  i s noticeable increase  demand d u r i n g  v a r i a t i o n s i n demand.  volumes f o r the p e r i o d between August  1965 and November 1973 s u g g e s t s  there  aid  time spent at the p o i n t t o which  s p e n t a d m i t t i n g p a t i e n t s t o emergency 2.2.3.  i n which  ( o f t e n between  home and h o s p i t a l ) and does n o t r e c e i v e f i r s t Time:  received  dispatched.  a p a t i e n t i s t r a n s p o r t e d b e t w e e n two p o i n t s  Unloading  being  to proceed to the scene.  Time i n Queue:  Transfer  t i m e b e t w e e n an a m b u l a n c e  that  The i n c r e a s e i n  and i s n o t l a r g e  a n a l y s i s f o r t h a t p a r t of the year.  Day o f Week V a r i a t i o n s  An e x a m i n a t i o n  o f the d i s t r i b u t i o n  of c a l l s  by day o f t h e  - 17  week i n d i c a t e d a maximum l o a d Saturday Sunday loads  (about  ( a b o u t 25%  on  The  there  l e s s t h a n on  1.  The  on  difference  Thursday i s not  t i m e o f day  i s given  From m i d n i g h t u n t i l  for  6  the  demand b e g i n s i n c r e a s i n g and  increases  steadily until  is a slight of nine  decline  calls  during  per  system.  the  lunch  h o u r a t 2 p.m.  except  for spurts  the  a.m.  demand on  to a high  in  significant,  i n the  b e g i n s t o d e c l i n e once a g a i n ,  At 6  a.m.  noon,  hour.  the  at  After  demand  a r o u n d 8 p.m.  and  p.m.  (b)  S p a t i a l D i s t r i b u t i o n of C a l l The  pality,  variation in call i s given  t o 6 p.m. night  i s the  until  i n Table busiest  8 a.m.  Of  exception  r a t e by 3.  period  Generally,  slowest.  m o r n i n g as  to the  Origin  t i m e o f day  i s the  e a r l y hours o f the  notable  A significant  cost  the p e r i o d  while  i n the  the  r e s t of the  the  industrial  activity,  municia.m.  from mid-  day,  is a  per  day  per  to the  municipality in  thousand p o p u l a t i o n . data) between the  i n d i v i d u a l f o r ambulance  a s s o c i a t i o n does e x i s t b e t w e e n t h e  c a p i t a and  by  from 8  period  v a r i a t i o n by  a s s o c i a t i o n e x i s t s ( i n our the  day,  rule.  a v e r a g e number o f c a l l s  c a p i t a and  of the  D e l t a , w h i c h i s as b u s y i n  p a r t i c u l a r i n t e r e s t i s the  significant per  and  a minimum l o a d  Weekdays).  r a t e by  a whole i n F i g u r e  i s a steady d e c l i n e  climbing  the  Friday  Variations  variations in call  which time there  the  s y s t e m on  above w e e k - d a y s ) and  Time o f Day  G.V.R.D. as  10  the  b e t w e e n T u e s d a y , Wednesday and (iii)  the  15%  -  degree of u r b a n i z a t i o n entertainment  ( d e n s i t y of  facilities,  call  No  call  rate  service.  rate  per  population,  etc.).  For  example,  FIG. 1 - Average G.V.R.D. C a l l Rate (Calls/Kovr)  By Time of Day  Average /' calls/hour 12 M-8 AM 8 AM-6 PM 6 PM-12 M  Average // calls/day  Average // calls/day/ thousand population  % of population over 60 years  13.9  .10  11.5  .13 •  2.4  .04  9.1  .05  .04  1.2  .02  6.5  . .14  .35  .35  6.7  .15  17.6  North Vancouver  .18  .38  .29  7.0  .07  *9.1  Port Coquitlam  .05  .08  .06  1.6  .06  5.7  Richmond  .07  .29  .16  4.5  .06  7.7  Surrey  .19  .44  .43  8.5  .08  11.0  1.70  4.23  3.02  74.2  . .17  18.7  West Vancouver  .08  .16  .12  3.0  .08  15.5  White Rock  .04  .11  .05  1.8  .15  37.4  Port Moody  .03  .06 .  .03  1.10  .08  5.3  .25  Coquitlam  .05 ,  J-2  Delta  .05  New Westminster  Vancouver  .76  . .73  Burnaby  TABLE 3  DAILY AMBULANCE DEMAND RATE BY TIME OF DAY AND MUNICIPALITY  - 20  V a n c o u v e r has Vancouver. the  age  twice  This  rate per  r e l a t i o n s h i p i s , however, m o d i f i e d  region.  as  explained  Spatial  see  Distribution  data  stand  i n T a b l e 4 where t h e (from  f o r Lion's  a r e o v e r 60  Surrey  left  focused  to r i g h t  per  highest  rate  per  its relatively  years  old  (See  Royal  Hospitals).  The  Royal  Columbian are  ment n e c e s s a r y )  to p r o v i d e (2).  The  W h i t e Rock t h a t go  Hospital,  i n White  Table 5 i s the  any  General,  Gate,  the only  both the  St. ones  Facilities staff  k i n d o f emergency  m a j o r i t y of the are  Mary's,  and  treat-  82%  of c a l l s  originating  admitted  to Peace  Arch  Rock. complement o f T a b l e 4,  of c a l l  o r i g i n s by  2.2.4.  Demand G r o w t h  Change i n t h e  virtually  to " o t h e r "  up  Richmond  as m a j o r Emergency  emergency rooms w h i c h have a t a l l t i m e s  facilities  demand.  Columbian, St.  emergency rooms o f L i o n ' s  classified  G.V.R.D. w h i c h a r e  of  after picking  Shaughnessy, Burnaby G e n e r a l ,  in  (i.e.,  the o r i g i n  the h o s p i t a l a b b r e v i a t i o n s  and  the  on  a m b u l a n c e s go  P a u l ' s , Vancouver General  in  White  rate  call  by  Destinations  Gate, St. P a u l ' s ,  Vancouver G e n e r a l ,  the  i t s call  i n l a r g e p a r t by  of C a l l  just discussed  their patients  and  somewhat  3).  The We  West  example, w h i l e  W h i t e Rock's e x c e p t i o n a l l y h i g h  l a r g e p r o p o r t i o n o f r e s i d e n t s who  (c)  For  and  l a r g e as V a n c o u v e r ' s , w h i c h i s t h e  capita i s apparently  Table  c a p i t a as N o r t h  more u r b a n t h a n i t s n e i g h b o u r s ,  capita i s nearly the  call  s t r u c t u r e of the p o p u l a t i o n .  Rock i s no  in  the  -  g i v i n g the  distribution  hospital. Patterns  level  and  spatial  distribution  o f demand f o r  Average # calls/day Burnaby  .6%  13.9  5.2%  Coquitlam  1.2  Delta  2.4  7.7  New Westminster  6.7  1.2  North Vancouver  7.0  81.6  Port Coquitlam  1.6  5.3  Port Moody  1.1  Richmond  4.5  Surrey  8.5  Vancouver West Vancouver White Rock G.V.R.D. Total  4.1  .  74.2  .7  21.2  '. 3.0  93.0  2.3  1.9%  80.3  3.8  VGH 26.5% 3.8  8.7%  13.2%  SHY . 4.5%  BGH  SUK  RGH  29.0%  .6%  53.0  12.0  4.8  8.4  84.2  5.3  93.8  6.2 . 18.5  21.8  2.3  4.6  2.0  .4  54.3  2.4  4.8  1.2 -  15.4 12.0 12.2 \  •  6.2  1.5  52.3  1.5  12.3  1.1 •  1.1  1.1  47.1  20.7  • 1.1  .1  5.2  15.2 2.3  2.3 4.5  1.5%  7.1%  5.3  1.5  11.6%  OTHER'  7.7  2.0  —  .6%  3.8 76.9 •  9.1  1.8  TABLE 4  SMH  23.9%  4.6  1.5  125.9  RCH  SPH  LGH  35.1%  4.5%  3.9% "  3.9% '  DISTRIBUTION OF AMBULANCE DESTINATIONS BY MUNICIPALITY (RCWS SUM TO 100%).  4.5  81.8  3.4%  14.2%  LGH Burnaby  .8%  SPH 4.1%  Coquitlam  RCH  SMH  21.6%  13.6% ; 7.9%  12.3  Delta  VGH  4.5  .2  SHY  BGH  10.6%  77.6%  RGH • 2.0  North Vancouver Port Coquitlam  .5 62.0 .8  .8  West Vancouver White Rock  TABLE 5  9.4  4.5  8.8  4.5  1.5  Surrey Vancouver .  45.5  .8  10.6  3.4  20.6 •  4.0  2.0  8.0  2.1  Port Moody Richmond  25.7  2.0%  1.5  .5  New Westminster  SDH  4.7  90.8  31.0  .5  is)  4.5  2.3  6.1  1.7  70.3  2.0  11.1  9.1  .8  1.5  1.7  2.0  82.0  9.9  13.6  87.7  66.7  15.5  2.1  .5 •  1.5  •1.2  (CoSl?^ S  1.5  F  0 R I G I N  B  Y  -  HOSPITAL)  2.0  - 23 -  ambulance s e r v i c e o v e r time i s e x t r e m e l y We a r e even u n c e r t a i n as t o w h i c h  difficult  to forecast.  f a c t o r s most i n f l u e n c e demand.  C e r t a i n l y p o p u l a t i o n , age s t r u c t u r e , income d i s t r i b u t i o n , of s e r v i c e to user, availability the  general  accessibility  o f emergency f a c i l i t i e s , t h e  o f p r i v a t e and p u b l i c t r a n s p o r t a t i o n f a c i l i t i e s , a w a r e n e s s and p e r c e p t i o n  f a c t o r s which a f f e c t individually Of  cost  demand.  o f t h e ambulance s e r v i c e a r e  However, t h e i r  and i n c o m b i n a t i o n  and  relative  importance  w i t h one a n o t h e r i s unknown.  one t h i n g we a r e s u r e :  i n the C i t y of Vancouver the  demand f o r a m b u l a n c e s e r v i c e i s i n c r e a s i n g a t a much f a s t e r r a t e than p o p u l a t i o n . in  Vancouver i n c r e a s e d  i n c r e a s e d by o n l y population in  Between 1966 and 1971 t h e a n n u a l volume o f c a l l s 2 1 % ; a t t h e same t i m e t h e p o p u l a t i o n  4%.  increased  demand f r o m y e a r  Hence, t h e c a l l by 17% d u r i n g  to year  67  0.3%  68  9.4%  69  6.2%  70  1.0%  71  2.2%  72  6.3%  service  long range trends  are d i f f i c u l t  arise  The  p e r 1000 increases  as shown b e l o w :  % i n c r e a s e i n number o f c a l l s from p r e v i o u s y e a r  Although  not  that period.  were q u i t e e r r a t i c ,  Year  that  r a t e per year  i n t h e demand f o r a m b u l a n c e  t o f o r e c a s t , the consequent  i n the planning  n e c e s s a r i l y severe.  difficulties  and management o f t h e s e r v i c e a r e  This  i s because ambulance systems a r e  - 24  highly  labour  i n t e n s i v e ; only  ment i s r e q u i r e d t o i n i t i a t e many o f t h e  capital  incrementally capital  -  a relatively and  resources  maintain  small the  service.  Moreover,  ( e . g . , a m b u l a n c e s ) can be  increased  i n r e s p o n s e t o c h a n g e s i n demand.  resource,  capital invest-  communications equipment  The  remaining  (assuming o f f i c e  is  l e a s e d ) , i s a v a i l a b l e i n d i s c r e t e " s i z e s " , where each  is  appropriate  For  for handling  a fairly  2.3.  current  PRODUCTION AND  2.3.1.  Production  level  d e l i v e r y s y s t e m and,  sub-system o f the t o t a l  as s u c h ,  transport.  care  The  focus  health be  of h e a l t h care which i t p r o v i d e s  The  of t h i s  components, r e s p o n s i v e n e s s ,  quality  of s e r v i c e provided  r e p o r t i s on which  s u b - s y s t e m s ) i s an i m p o r t a n t  the  by  treatment  first  of  ( u n l i k e most o t h e r  c o n s i d e r a t i o n i n both  the  these health design  o p e r a t i o n o f an a m b u l a n c e s e r v i c e . "Responsiveness"  t h a t we  i s an  imprecise  less  term, i n s p i t e  a l l know g e n e r a l l y what i t means.  a m b u l a n c e w h i c h r e s p o n d s t o two or  i n the  i t s e f f e c t i v e n e s s should  ambulance system i s a f u n c t i o n o f r e s p o n s i v e n e s s ,  three  and  ambulance c a l l s  Components  to the p o p u l a t i o n i t s e r v e s .  and  communi-  o f demand).  measured i n terms of the q u a l i t y  an  sufficient  EVALUATION  Ambulance S e r v i c e i s one care  has  c a p a c i t y to d i s p a t c h a l l of the  G.V.R.D. ( a t t h e  "size"  w i d e r a n g e o f demand r a t e s .  e x a m p l e , M e t r o p o l i t a n Ambulance now  cation  space  " r e s p o n s i v e " than  m i n u t e s and  to the o t h e r  one  calls  o f the  fact  F o r e x a m p l e , i s an  i n f o u r m i n u t e s each more  w h i c h r e s p o n d s t o one  i n s i x minutes?  call  in  two  - 25 -  In t h i s times  c h a p t e r we  shall  p r i m a r i l y be r e p o r t i n g  f o r t h e v a r i o u s p r o d u c t i o n components o f t h e  ambulance s e r v i c e s which  Delta,  Richmond, S u r r e y , Vancouver  and W h i t e  c o n s i d e r the e f f e c t s  ponsiveness The  duction"  (average)  In Chapter  o f v a r i o u s o t h e r measures o f  times r e q u i r e d  3 we res-  system.  each  call  f o r each  i s t h e sum of f i v e  of  "pro-  time  time to  time at  time at  scene  scene  transport  time  from  scene  hospital  «  service response  Call arrives, ambulance dispatched  time  ambulance leaves for scene  time  r-^  —^  t r a v e l time to scene  start-up time  time at I t r a v e l time scene ^\ . t o h o s p i t a l  ambulance arrives at scene  R e s p o n s e t i m e d a t a was  services  Westminster,  components:**  travel  *  Rock.*  (average) time spent s e r v i c i n g  start-up  ^  B u r n a b y , New  on t h e d e s i g n o f an a m b u l a n c e  the i n d i v i d u a l  existing  serve the g e o g r a p h i c a l area d i s p a t c h e d  by M e t r o p o l i t a n A m b u l a n c e :  shall  average  ambulance leaves for hospital  only a v a i l a b l e  ambulance arrives at hospital  from the  d i s p a t c h e d by M e t r o p o l i t a n Ambulance  time at hospital  ambulance leaves hospital  ambulance  (89.3% o f a l l c a l l s  i n t h e G.V.R.D.). **  We  shall  use t h e words " s c e n e " t o mean t h e l o c a t i o n  t h e a m b u l a n c e i s d i s p a t c h e d and to which  the p a t i e n t  "hospital"  t o denote  the  i s t r a n s p o r t e d (even i f i t i s n o t  a  to  which  location "hospital").  - 26 2.3.2.  Analysis  Recall  o f Components  that response time i s defined  between the a r r i v a l of  of a c a l l  the ambulance at t h e The  current  palities  t o t h e d i s p a t c h e r and  average  r e s p o n s e t i m e f o r each  a r e g i v e n i n T a b l e 6.  24 h o u r a v e r a g e .  The  column  calls.  calls  For example,  originating  Note t h a t  average  l a b e l e d "90th are exceeded  10% o f t h e c a l l s  h a v e a r e s p o n s e t i m e g r e a t e r t h a n 18.0  18.0  of the m u n i c i -  o f t h r e e p e r i o d s o f the day,  c o n t a i n s those response times which  the  arrival  scene.  t i m e s a r e g i v e n i n each  the  the  w i t h i n t h e b o u n d a r i e s o f M e t r o p o l i t a n Ambulance  patching service  overall  as t h e e l a p s e d t i m e  i n Burnaby  response  as w e l l  as  i n o n l y 10% in  of  Burnaby  ( c o n v e r s e l y 90%  have a r e s p o n s e  an  Fractile"  originating  minutes  dis-  time not  of  exceeding  minutes). With  the e x c e p t i o n o f Burnaby,  the response  times  display  a strong negative correlation with population density. New  Westminster  and W h i t e  and  low r e s p o n s e t i m e s .  Rock a l l h a v e f a i r l y  Vancouver,  dense p o p u l a t i o n s  D e l t a , R i c h m o n d and S u r r e y a r e more  s p a r s e l y p o p u l a t e d and h a v e l o n g e r r e s p o n s e t i m e s . The  long response  there i s currently  time i n Burnaby  i s due  ( i . e . , when t h e d a t a was  ambulance l o c a t e d i n Burnaby.  t o the f a c t  that  collected) only  T h i s ambulance, which  one  responds  - 27 -  to the m a j o r i t y o f the c a l l s average  response  the f a c t  that  graphical It with for  i n B u r n a b y , has an  t i m e o f 11.2 m i n u t e s , w h i c h  i n terms  of travel  i s attributable to  t i m e i t has a v e r y  large  i s interesting  the m u n i c i p a l i t i e s  stationed.  t o compare t h e a v e r a g e times. i n which  only a single  times are p r i m a r i l y  a m b u l a n c e i s busy  response  The d i f f e r e n c e s  For these m u n i c i p a l i t i e s  long response  the c a l l s  those which  until  the response  a r e most  with  especially  In t h i s  the closest  time.  ambulance,  6.7 c a l l s  Westminster  t o o c c u r when t h e o n l y a m b u l a n c e l o c a t e d  Westminster  i s busy.  p e r day i n New i n New  c a s e an a m b u l a n c e i s e i t h e r  or occasionally  which-  F o r example, i t i s  f o r one o f t h e a v e r a g e  Burnaby, Vancouver,  case t h e  ambulance  not unusual  In t h i s  dramatic  o c c u r when t h e  becomes f r e e o r e l s e d i s p a t c h e s a more d i s t a n t ever a c t i o n minimizes  time  ambulance i s  with another c a l l .  dispatcher e i t h e r holds the c a l l  from  geo-  area t o cover.  the 90th f r a c t i l e  closest  originating  sent  (3.4% of a l l c a l l s )  from S u r r e y o r Richmond. The  surprisingly  to the f a c t t h a t  low 9 0 t h f r a c t i l e  t h e New W e s t m i n s t e r  up i n t h e n o r t h e r n p a r t o f S u r r e y o t h e r day, r e s p r e s e n t i n g about White  t i m e f o r S u r r e y i s due  a m b u l a n c e p r o v i d e s a back  ( a b o u t one s u c h  call  6% o f a l l S u r r e y c a l l s ) and  Rock Ambulance s e r v e s s o u t h S u r r e y and p r o v i d e s  back-up s e r v i c e The  average  i n Vancouver Richmond.  ( r e s p o n d i n g t o 16.7% o f a l l S u r r e y service  one h o u r  additional  calls).  t i m e s v a r y f r o m a low o f 4.2  t o a h i g h o f about  every  minutes  i n D e l t a and i n  I t i s i m p o r t a n t t o keep i n mind t h a t s e r v i c e  times  - 28 Average Response Time ( i n minutes) Time o f Day Municipality*  12 M-8  Burnaby Delta  AM • 8 AM-6  PM  6  . Overall 24 PM-12 M hours)  11.6  12.3  11.3  11.9  9.8  9.7  10.5  10.0  90 Fractile t h  •  18.0 18.0  Average Service Time  49.3 61.6. O  New  Westminster  Richmond Surrey Vancouver White Rock  OVERALL  .  6.7  12.8  7.8 '  10.5  9.8  10.2  9.2  10.0  19.0  59.6  11.5  10.3  9.3  10.3  16.6  49.8  7.2  8.3  7.6  7.9  12.0  42.0  7.7  6.0  7.3  10.0  44.6  8.4  8.9  16.0  46.1  7.0  8.3  9.3  .  22.0  N/A  I n f o r m a t i o n not a v a i l a b l e f o r C o q u i t l a m , N o r t h Vancouver, P o r t C o q u i t l a m , P o r t Moody and West Vancouver.  TABLE 6  AVERAGE RESPONSE TIME AND TIME BY MUNICIPALITY  SERVICE  - 29 -  have a s i g n i f i c a n t  indirect  time spent s e r v i c i n g a call  calls  occurs the closest  distant The  ambulance w i l l overall  effect  on r e s p o n s e  t i m e s ; t h e more  the greater the l i k e l i h o o d ambulance w i l l  be busy  and a more  frequency d i s t r i b u t i o n  of response  i s g i v e n i n F i g u r e 2B d i s p l a y s  i n which  value.  The calls  the response  f o r emergency  o n l y a r e g i v e n i n F i g u r e s 3a and 3b. the v a r i a t i o n s  i n average  call  the c a l l s  priority  occurring  priority,  and by t i m e o f day a r e h i g h e s t  i n t h e wee h o u r s  t h a t on t h e a v e r a g e , s t a r t - u p  calls.  t i m e s by  s t a r t - u p t i m e s a r e , by  l o w e s t f o r emergency c a l l s ,  The  time  and by t i m e o f d a y .  As e x p e c t e d , a v e r a g e  response  response  t o e x a m i n e T a b l e 7, w h i c h  c o n t a i n s , by p r o d u c t i o n component, a v e r a g e  the  a specified  8% m i n u t e s .  f r e q u e n c y and c u m u l a t i v e d i s t r i b u t o r s  by t i m e o f d a y , i t i s i n s t r u c t i v e  for  The c u m u l a t i v e  f o r 60% o f t h e c a l l s t h e  t i m e was n o t more t h a n about  Before examining  of  (over  the percentage of  time d i d not exceed  F o r e x a m p l e , we s e e t h a t  response  time  days p e r week) f o r t h e a r e a d i s p a t c h e d  by M e t r o p o l i t a n Ambulance i s g i v e n i n F i g u r e 2A.  calls  when  have t o be d i s p a t c h e d .  24 h o u r s p e r d a y , s e v e n  distribution  that  o f the morning.  time accounts  for a full  Note  28% o f  time. average  time at t h e scene  i s greatest  for transfer  T h i s happens d u r i n g t h e d a y t i m e , when t h e m a j o r i t y o f  transfer  calls  occur.  Response times are g r e a t e s t on t h e s y s t e m  d u r i n g t h e day when t h e l o a d  i s t h e h e a v i e s t and when t h e t r a v e l  times are the  - 30  slowest. calls  As e x p e c t e d , t h e r e s p o n s e  (i.e.,  siren  i s p r o b a b l y due  generally originate  time.  at h o s p i t a l s , which  hospital  calls  are c e n t r a l l y  located.  and by  affect  at h i s o r h e r  priority  response destination  emergency c a l l s  service  ferred  f r o m one  hospital  R e t u r n i n g now  range  and S u r r e y  Westminster  times,  The  i s due  relatively  to a  a patient  variation  i n average  response  i s trans-  hospital.  except D e l t a  r e s p o n s e by  New  response  morning  t i m e o f day i n due  to the  there i s a g r e a t e r p r o p o r t i o n of c a l l s  o c c u r when t h e a m b u l a n c e l o c a t e d  i n New  time  (where i t  (where i t i s i n t h e e a r l y  i n average  signi-  time i s between  i s extremely l a r g e , undoubtedly  t h a t d u r i n g t h e day  priority,  see t h a t , e x c e p t f o r  l o n g e s t average  variation  calls  i n which  in a l l muncipalities  i n the evening)  times.  to another, o f t e n d i s t a n t  t o T a b l e 6, we  The  6 p.m.  The  calls  there i s l i t t l e  by t i m e o f day.  v a r i a t i o n by  service  time f o r t r a n s f e r  of t r a n s f e r  hours).  a significant  have t h e s h o r t e s t  fraction  and  " u n l o a d i n g " times  Because o f f a s t e r r e s p o n s e  ficant  8 a.m.  Average  vary  minutes.  b u t n o t by t i m e o f day.  Westminster,  low  c o n s i d e r a b l y , but to a l a r g e extent  to the n e x t .  S e r v i c e times e x h i b i t  long average  The  are r e l a t i v e l y  as t h e y i n d i r e c t l y  time spent w i t h the p a t i e n t  f r o m 12 t o 16  New  calls.  a f u n c t i o n o f emergency room a d m i t t i n g p r o c e d u r e s , w h i c h  f r o m one  is  calls  i n t i m e a t t h e s c e n e by t i m e o f day  ( n o t shown i n F i g u r e d ) v a r i e s is  transfer  to the f a c t t h a t t r a n s f e r  large, particularly The  and  time f o r t r a n s f e r  principally  Variations  time i s l o w e r f o r emergency  used) than f o r normal  f a c t t h a t the response  are not  -  Westminster  fact which  is either  FIG.  2  - D i s t r i b u t i o n of Response Time, Current Data, A l l C a l l s (Burnaby, Vancouver and New Westminster only)  FIG. 3)  1 2  3  FIG3jb 3,  4  a  Frequency  5  6  7  8  Distribution  9  10  11  12  13  14  15  16  17  18  19  20  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 o f Response Time, C u r r e n t D a t a , Emergency C a l l s Only (Burnaby, V a n c o u v e r , and New W e s t m i n s t e r o n l y )  Time of Day ( a l l priorities)  Priority Normal  Emergency  13.8%  63.8%  22.4%  100.0%  2.3  2.2  2.6  2.0  2.4  9.2  8.0  7.8  9.5  7.0  8.7  8.7  9.5  8.2  9.9  9.2  8.0  9.0  44.4  45/5  41.2  50.6  43.9  40.8.  44.0  12AM-8 AM  8 AM-6 PM  6 PM-12 M  17.8%  56.1%  26.2%  Average start-up times  2.6  2.4  Average response times  7.9  Average time at scene  -  % of calls  Average service time  •  TABLE  7  Transfer  AVERAGE OPERATIONS TIMES (in minutes) BY TYPE AND TIME OF CALL (Burnaby, New Westminster and Vancouver) only  A l l Priorities  - 34  busy w i t h  another c a l l  w i t h i n New  back-up s e r v i c e to Burnaby, P o r t 2.3.3.  Ambulance  an  C o q u i t l a m or  include  the  a f t e r " c l e a r i n g " the utilization 8.  per  providing  Surrey.  i s defined  as  the  f r a c t i o n of  ambulance i s a c t u a l l y engaged i n p r o v i d i n g  does n o t  Table  Westminster or i s  Utilization  Ambulance u t i l i z a t i o n that  -  time spent r e t u r n i n g d e s t i n a t i o n of the  a m b u l a n c e , by  to the  previous  t i m e o f day  by  time  service.  ambulance call.  This depot  Average  company i s g i v e n  in  0 manned ambulance  Average. Ambulance U t i l i z a t i o n Over12AM-8 AM 8 AM-6 PM 6 PM-12 AM a l l  Cbmpr.ny .or Firc.Df.pt.  Primary Servicing Area  Coquitlam Fire. Dept.  D i s t r i c t of Coquitlam  2,  N/A  Delta Arab.  Delta  1  5.2%  N/A 9.8%  N/A  3.3*  2.9%  5.8%  19.4%  54 .5  28.5  38.1  North Vancouver, N o r th Va n c ouv e r District  4.0  8.3  6.4  6.7  Port Coquitlam F i r e Dept.  Port Coquitlam  N/A  N/A  N/A  2.5 '  Port: Moody F i r e Dept.  Port Moody  1  N/A  N/A  N/A  4.2. '  Richmond  Richmond  i2  6.4  17.6  • . 1  12.2  35.6  20.2  22.6  2  2.7  5.8  4.3  4.4  5.4  18.7  5.4"  9.8  Metropolitan Ambulance  Burnaby, Vancouver, and New W c s tmins t e. r  North Vancouver F i r e Dept.  Amb.  Surrey A'.nb.  Surrey  West Vancouver F i r e Dept.  West Vancouver  White Rock Ambulance  White Rock, South Surrey  .*  .  8« 9  Approximate average u t i l i z a t i o n  TABLE  8  . AMBULANCE UTILIZATION BY TIME OF DAY  8.9  - 36 CHAPTER 3 - COMPUTER SIMULATION MODEL This  c h a p t e r d i s c u s s e s t h r e e main  simulation  i n system a n a l y s i s ;  s i m u l a t i o n models ambulance 3.1.  topics:  t h e use o f  t h e d e s c r i p t i o n o f computer  a n d ; t h e model v a l i d a t i o n  f o r t h e Vancouver  system.  Use o f S i m u l a t i o n i n S y s t e m Computer s i m u l a t i o n  Analysis  c a n be d e f i n e d  as t h e u s e o f a  n u m e r i c a l model t o s t u d y t h e b e h a v i o r o f a s y s t e m as i t operates over time. purely mathematical.  P a r t s o f t h e model may be s y m b o l i c , O t h e r p a r t s may be l o g i c a l ,  respresentation of operating p o l i c i e s . ally  s u c h as i n t h e  A s i m u l a t i o n model norm-  i s u s e d i n an e x p e r i m e n t a l manner t o i n d i c a t e  of a system t o a s e t o f given parameter  i.e.,  the response  settings.  O f t e n , i n t h e system under s t u d y , t h e t r a n s i e n t b e h a v i o r is  of interest  i n addition  I n t h e c a s e o f an ambulance know how a s y s t e m r e s p o n d s average performance. similar  to the steady state  performance.  s y s t e m i t may be more i m p o r t a n t t o t o a peak l o a d t h a n t o know i t s  F u r t h e r m o r e , two s y s t e m s h a v i n g a  average performance  c a n have v e r y d i f f e r e n t  transient  behavior, Simulation system dynamics.  i s one o f t h e few t o o l s Most a n a l y t i c a l  available  techniques are only able to  determine s t e a d y s t a t e performance measures. a n a l y s e dynamic how  b e h a v i o r must depend  a s y s t e m moves ahead  o f computer  simulation.  i n time.  for estimating  A model u s e d t o  on s t r u c t u r e s  This  feature  to explain  i s the essence  - 37 -  3.2.  General The *  Description  o f Computer S i m u l a t i o n Model  a m b u l a n c e s i m u l a t i o n model c o n s i s t s o f two an a m b u l a n c e c a l l s  g e n e r a t o r which  programs:  c r e a t e s an " i n p u t  stream" *  t h e main s i m u l a t o r w h i c h system  3.2.1.  and  c r e a t e s an " o u t p u t  Ambulance C a l l s  The  s i m u l a t e s the b e h a v i o r of the stream"  Generator  ambulance c a l l s  g e n e r a t o r p r o g r a m c r e a t e s an " i n p u t  s t r e a m " o f a l l ambulance c a l l s w i t h the f o l l o w i n g i n f o r m a t i o n for  each  call:  *  time of occurrence  *  l o c a t i o n o f the  *  priority  *  time at  *  time at h o s p i t a l  *  travel  time  is  distribution.  at  empirical 3.2.2.  and  o f a scene  to the  destination  with  a r e a f u n c t i o n o f t h e t i m e o f day.  selecting priority on  from a P o i s s o n d i s t r i b u t i o n  inter-arrival of calls  an e m p i r i c a l  (i.e.,  emergency,  distribution.  time at the h o s p i t a l  normal,  Similarly,  are a l s o generated  from  Simulator  main s i m u l a t o r c r e a t e s t h e " o u t p u t s t r e a m " w h i c h  to-  gether w i t h the " i n p u t stream" p r o v i d e s d e t a i l e d i n f o r m a t i o n about  each  call  p r o c e s s e d by  the  This  t i m e f r o m an e x p o n e n t i a l  distribution.  Main  The  The  are based  the scene  location  i s sampled  r a t e s which  a c c o m p l i s h e d by  transfer)  from  a hospital)  time of a c a l l  mean a r r i v a l  call  scene  (usually The  of  incident  simulation.  time an  - 38 -  The  output stream provides  f o r each  call:  *  the dispatch  *  t h e ambulance d i s p a t c h e d  *  t h e l o c a t i o n o f t h e a m b u l a n c e when  *  the response  The typical  structure  to the c a l l dispatched  time.  of the simulation  sequence o f e v e n t s .  notification returns  delay  program f o l l o w s the  The a m b u l a n c e s e r v i c e b e g i n s when  o f an i n c i d e n t o c c u r s  and ends when t h e a m b u l a n c e  to i t s s t a t i o n .  Notification The  input  incident  s t r e a m t o t h e model i s a s i m u l a t e d  occurrences  as t h e y a r e r e p o r t e d  (ambulance d i s p a t c h e r ) . is provided  t o t h e agency  With t h e n o t i f i c a t i o n ,  about t h e i n c i d e n t  series of  information  ( i . e . , l o c a t i o n , type o f i n c i d e n t ,  etc.) . Ambulance After  Availability an i n c i d e n t h a s been r e p o r t e d ,  ambulance i s d i s p a t c h e d , availability  the dispatcher  of i t s vehicles.  free  *  on t h e way t o a c a l l  *  busy w i t h  *  f r e e and r e t u r n i n g  a t any p o i n t i n  states:  a t i t s home b a s e  With t h i s  a patient  information,  t o home b a s e a set o f immediately a v a i l a b l e or  soon t o be a v a i l a b l e v e h i c l e s of a v e h i c l e  must c h e c k t h e c u r r e n t  Each v e h i c l e  t i m e i s i n one o f t h e f o l l o w i n g *  and b e f o r e an  c a n be i d e n t i f i e d  t o respond t o the i n c i d e n t .  for selection  -  Vehicle  Selection  A decision  -  and D i s p a t c h  i s n e x t made t o s e l e c t  able ambulances. is  39  The a m b u l a n c e t o be d i s p a t c h e d t o t h e s c e n e  d i s p a t c h e d by one o f t h e f o l l o w i n g  (a)  the closest This rule  from t h e s e t o f a v a i l -  available  ambulance  i s called closest  rules: (closest  i n time)  responds.  a m b u l a n c e r e s p o n s e o r CAR  or (b)  t h e ambulance a s s i g n e d t o a d i s t r i c t first  even  currently  i f i t isstill  outside the d i s t r i c t .  regionalized Arrival  arrival  rule  i s called  r e s p o n s e o r RR.  t i m e o f an a m b u l a n c e a t t h e s c e n e  l o c a t i o n o f t h e ambulance t o t h e i n c i d e n t  gether with  by  Hence, t h i s  and i s  o f an  incident  s c h e d u l e d i n s i m u l a t e d t i m e by a d d i n g t h e t r a v e l t i m e f r o m t h e  current  For  from a c a l l  a t t h e Scene  The is  returning  s e r v e s i t s own d i s t r i c t  t h e time t h e ambulance t a k e s l e a v i n g  emergency c a l l s a given f r a c t i o n  On t h e Scene  which (<CL)  Care  t o account  forfirst  at the scene, a f u r t h e r  a i d assistance  i f necessary.  calls  o r c a s e s where a m b u l a n c e s a r e n o t r e q u i r e d of calls  cancellation  i s randomly  data.  cancelled.  at a l l , a c e r t a i n  The i n d i c a t i o n o f  o f t h e number o f c a n c e l l e d  I f the c a n c e l l a t i o n  time, the c a l l  extra-  f o r t h e cases o f c a n c e l l a t i o n o f  i s done on t h e b a s i s  from e m p i r i c a l response  To a c c o u n t  delay i s  and p o s s i b l e  ction  proportion  f r o m home b a s e .  use a s i r e n t h e t r a v e l time i s m u l t i p l i e d  Once t h e a m b u l a n c e a r r i v e s incurred  location to-  i s classified  time i s l a r g e r  as ANU ( a m b u l a n c e  calls  than not used)  - 40 -  call;  otherwise the c a l l  is classified  as c a n c e l l e d .  The  ambulance turns back to the s t a t i o n a f t e r the a p p r o p r i a t e simulated time and at that moment i s freed to respond to other  calls.  Destination  from t h e Scene  For those cases that r e q u i r e t r a n s p o r a t i o n o f the i n j u r e d person to a medical select  arises.  facility,  the question o f which h o s p i t a l to  The s e l e c t i o n  i s done on the b a s i s o f e m p i r i c a l  probabilities of destination the ambulance's a r r i v a l  at h o s p i t a l  by adding to the time of c a l l at scene  and t r a v e l  Ambulance Return The  f o r each source area.  The time of  i s computed i n the s i m u l a t i o n  to the sum of response  time from the scene  time,  time  to the h o s p i t a l .  to the S t a t i o n  ambulance t r a v e l s along the s h o r t e s t path to i t s home  base a f t e r completing v a r i o u s a c t i v i t i e s  i n the h o s p i t a l  as admitting the p a t i e n t , p r o c e s s i n g r e c o r d s , e t c . can be dispatched f o r another  assignment  such  The ambulance  while at a h o s p i t a l or  on the way home. 3.3.  Model V a l i d a t i o n  f o r the Vancouver Ambulance System  To v a l i d a t e any kind o f model, i t i s necessary  to demonstrate  that the model r e p r e s e n t s a true a b s t r a c t i o n of r e a l i t y . not enough that a model gives r e s u l t s  It i s  observable i n the r e a l  world.  The model should a c t u a l l y behave l i k e the r e a l w o r 1 d , p a r t i c u l a r l y i n i t s dynamic o p e r a t i o n i n time; otherwise one cannot that the r e s u l t s obtained under s l i g h t l y be  different  be c e r t a i n  conditions w i l l  useful. An approach  suggested  i n an a r t i c l e by Naylor and Finger (7)  - 41 (1966)  called  "Multi-Stage V e r i f i c a t i o n "  s i m u l a t i o n model.  i s used t o v a l i d a t e t h e  T h i s method o f v e r i f i c a t i o n  consists of the  following stages: *  the f i r s t  stage c a l l s  postulates  f o r the f o r m u l a t i o n of a s e tof  o r hypotheses  describing  the behaviour of  the system under s t u d y . *  the second stage c a l l s of these p o s t u l a t e s ical  *  stage consists  to p r e d i c t  statist-  of testing  t h e model's  ability  t h e b e h a v i o r o f t h e system under s t u d y .  General V a l i d i t y  The  as one c a n u s i n g a v a i l a b l e  as many  tests.  the f i n a l  3.3.1.  f o r an a t t e m p t t o v e r i f y  o f t h e Model  most i m p o r t a n t a s s u m p t i o n made f r o m t h e model i s t h a t  the d i s t r i b u t i o n distribution.  of "calls  arriving"  i s a typical Poisson  O t h e r a s s u m p t i o n s , s u c h as t h o s e made a b o u t . l o a d -  i n g and u n l o a d i n g t i m e and c a n c e l l a t i o n s ,  a r e b a s e d on e m p i r i c a l  dis t r i b u t i o n s . 3.3.2.  Statistical  To t e s t  Test f o r P o i s s o n A r r i v a l s  that the a r r i v i n g  distribution,  the following  distribution  theorem  follows  (8) w i l l  a Poisson  be a p p l i e d .  Suppose one h a s o b s e r v e d t h e p r o c e s s o v e r a p e r i o d  of length  T, d u r i n g w h i c h n e v e n t s h a v e o c c u r r e d .  F o r j = l , . . ., n , l e t V.  denote  of the period  the time  at which  the j  (measured  from the s t a r t  event o c c u r r e d .  of observation)  I f t h e event has o c c u r r e d i n  accord with  a P o i s s o n P r o c e s s , t h e random v a r i a b l e s  U^, . .  independent  and u n i f o r m l y d i s t r i b u t e d o v e r i n t e r v a l  0 t o T.  C o n s e q u e n t l y one method o f t e s t i n g w h e t h e r type i s t o t e s t whether  . , u" a r e n  the events are of Poisson  t h e o b s e r v a t i o n s U , . . ., U  are independ-  - 42 e n t and u n i f o r m l y d i s t r i b u t e d The  t e s t was  conducted  over 0 to  f o r t h r e e p e r i o d s o f t h e day  ponding  to t h r e e ambulance s h i f t s :  6 p.m.;  6 p.m.  .  .  Von  .,  U  Mises The  - 12 m i d n i g h t .  are independent  n  t e s t was  To  based  t i m e were t e s t e d .  thirteen  The  that Uj  o f 12.6  level  tests  day  Cramer  level. from  the t h r e e p e r i o d s - 6 p.m.  arid  12 a.m.  6  p.m.  - 8  a.m.  f o r a true d i s t r i b u t i o n (uniform),  are expected.  i s not  D e t e r m i n i n g the Length problem  -  accepted.  i s a Uniform d i s t r i b u t i o n  The one  F o r each  r e s u l t b e t w e e n 8 a.m.  a Poisson d i s t r i b u t i o n ) 3.3.3.  significance  the  on a s a m p l e o f f o u r t e e n days  At 10% s i g n i f i c a n c e acceptance  8 a.m.  t h a t the o b s e r v a t i o n U j ,  test  a l l f o u r t e e n t e s t s were a c c e p t e d and  t e s t s were  corres-  - 8 a.m.;  and u n i f o r m l y d i s t r i b u t e d ,  M e t r o p o l i t a n Ambulance Company,  - 12 m i d n i g h t  12 m i d n i g h t  e m p l o y e d a t a 10%  t e s t was  T.  Hence, the  assumption  (and h e n c e t h a t a r r i v a l s  follow  rejected. of the S i m u l a t o r  of d e t e r m i n i n g the l e n g t h of the s i m u l a t i o n i s  o f s e l e c t i n g a sample s i z e o f s u f f i c i e n t magnitude t o p r o v i d e  t h e d e s i r e d degree o f a c c u r a c y i n t h e mean r e s p o n s e  time.  different  1500)  totals  generated.  of c a l l s  E a c h number was  random number s e e d s . response  ( 5 0 0 , 750,  t i m e s i n each  The  1000,  generated  five  1250  and  times w i t h  s t a n d a r d d e v i a t i o n between  number o f c a l l s was  Five were  different average  calculated.  Figure 5  shows t h e v a l u e o f s t a n d a r d d e v i a t i o n .  N o t e t h a t as t h e number o f  calls  decreases.  increases,  3.3.4. One  the s t a n d a r d d e v i a t i o n  Correspondence  of Real World  o f t h e most i m p o r t a n t t e s t s  and  Simulated  of v a l i d i t y  Data  i s the  ability  - 43 o f t h e model t o p r e d i c t response the  times from  response  time a c c u r a t e l y  t h e d a t a were n o t u s e d  (empirical  i n the creation  model). A h i s t o r i c a l v a l i d a t i o n was p e r f o r m e d  by c o m p a r i n g  t i m e d a t a f r o m t h e r e a l w o r l d w i t h t h e model r e s u l t s time p e r i o d . similarity The  Chi-square test for testing  distribution observed  t h e degree  t h e degree o f  method  which  o f s i m i l a r i t y between a  c a t e g o r i e s and t h e  i n r e l a t i v e f r e q u e n c i e s f o u n d i n each  at t h e extreme t a i l s  category are  S i n c e a c a t e g o r y must h a v e a t l e a s t i s not u s e f u l ,  to test observations  of a 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  Company o f V a n c o u v e r  t i m e f o r M e t r o p o l i t a n Ambulance  i s compared t o t h e s i m u l a t i o n r e s u l t s i n  From t h e d a t a i n T a b l e 9, t h e C h i - S q u a r e  a t a .05 s i g n i f i c a n c e 26.22.  f o r t h e same  time.  The d a t a a r e s u m m a r i z e d i n t o  f i v e o b s e r v a t i o n s , the t e s t  F i g u r e 4.  to test  i s a classical statistical  to derive a s t a t i s t i c .  The  were u s e d  response  g e n e r a t e d by a model and f r e q u e n c y d i s t r i b u t i o n o f  data.  difference used  Chi-square tests  on t h e d i s t r i b u t i o n o f r e s p o n s e  can be u s e d  to  of  l e v e l w i t h 16 d e g r e e s  statistic  o f freedom,  T h u s , t h e h y p o t h e s i s t h a t t h e two s a m p l e s  s i m u l a t e d ) came f r o m t h e same p o p u l a t i o n i s a c c e p t e d .  i s equal  ( a c t u a l and  - 46 -  Actual^ Freq.(f)  Simulated Freq.(f)  1- 2  4.32  4  .32  0.02  2- 3  12.48  7  5.48  2.40  3- 4  26.88  28  1.12  0.04  4- 5  34.56  39  4.44  0.57  5- 6  47.04  55  7.-96  •:ii;-34  6- 7  50.40  47  3.40  0.22  7- 8  32.64  48  15.36  7.22  8- 9  34.56  45  10.44  3.15  9-10  30.72  40  9.28  2.80  10-11  33.60  26  7.60  1.71  11-12  38.88  30  8.88  2.02  12-13,  27.84  19  8.84  2.80  13-14  15.36  13  2.36  0.36  14-15  19.20  16  3.20  0.53  15-16  .11.52  12  0.48  0.01  16-17  11.04  9  2.04  0.37  17>  48.96 .  42  16.96  0.98  A.  f - f  f  25.20  Table 9 " : ~ CHI Square Goodness of F i t Test of Response Time P r o b a b i l i t y D i s t r i b u t i o n  - 48 -  CHAPTER 4 - THE AMBULANCE LOCATION PROBLEM In t h i s chapter the problem of minimizing the mean response time of the ambulance system as a f u n c t i o n of the l o c a t i o n of the  ambulance depots i s considered.  closest 4.1.  ambulance d i s p a t c h  We s h a l l  r u l e i s used.  E s s e n t i a l Features i n the Location The f o l l o w i n g features  during  of Ambulances  of ambulance systems were noted  the computer s i m u l a t i o n  studies.  ambulances are not always awaiting s t a t i o n when a c a l l  assume that the  a call  at t h e i r  for their service i s received,  the p r o b a b i l i t y that an ambulance i s at i t s depot depends upon the i n c i d e n t r a t e . the  response time f o r p a r t i c u l a r c a l l  depends upon  the number of ambulances which are busy when the c a l l is  received.  since during  peak periods  departure point the  f o r ambulances responding to c a l l s ,  l o c a t i o n s of h o s p i t a l s a f f e c t the mean response time.  These features considered  the h o s p i t a l becomes a  suggest that the l o c a t i o n of ambulances could be  as a s t o c h a s t i c l o c a t i o n problem i n that the a s s i g n -  ment o f c a l l s  to servers  i s a dynamic process and a f u n c t i o n o f  the number of busy ambulances at the time c a l l s 4.2.  are r e c e i v e d .  An A n a l y t i c a l Approximation to Mean Response Time Let N be a c o l l e c t i o n o f nodes  number of ambulances locations.  (i.e.,  An assignment p  Hence, f o r any JL e ( l .  ( d i s t r i c t s ) and K be the  ambulance depots) to assign i s a mapping from (1 . . . the  to node K) to N.  l o c a t i o n of  - 49 ambulance  A,  Let T d e n o t e  the c o l l e c t i o n  o f a l l assignments, o f which  K t h e r e a r e |T|=(N) where jT| i s t h e c a r d i n a l i t y  of the setT .  V (^) as t h e mean r e s p o n s e t i m e i n t h e a b s t r a c t a m b u l a n c e  Define location  model. The p r o b l e m o f o p t i m i z i n g t h e a m b u l a n c e l o c a t i o n s c a n be s t a t e d as f i n d i n g an a s s i g n m e n t peT s u c h t h a t V (f>) = V (p) f o r p"eT s u c h t h a t V (^) = V (^ all^eT.  T h e r e f o r e , an a n a l y t i c a l  a p p r o x i m a t i o n i s t h e mean  r e s p o n s e t i m e f u n c t i o n V w o u l d be d e s i r a b l e . e t . a l . (10)  Swoveland which  i s based  on s i m u l a t i o n  v (p) * Z \  h a v e made t h e f o l l o w i n g a p p r o x i m a t i o n results:  o  K  w  i e N q=l  c ^) 1  d  (>(i»q).i) • • - t i l '  where N - t h e number o f nodes K - t h e number o f  ambulances  "^=> ( i , q ) - t h e l o c a t i o n o f q t h c l o s e s t under  assignment  w (i,q) = the f r a c t i o n s e r v i c e d by t h e q t h c l o s e s t A  a m b u l a n c e t o node i  ^ •  o f c a l l s which  o c c u r a t node i and  ambulance.  m a t r i x (w ( i , q ) ) was o b t a i n e d f r o m a number o f s i m u l a t i o n  r u n s w i t h a w i d e mix o f a s s i g n m e n t s .  Because  t h e v a l u e w ( i , q ) p r o d u c e d by one a s s i g n m e n t significantly was  i t was f o u n d d i d not d i f f e r  f r o m t h o s e p r o d u c e d by any o t h e r a s s i g n m e n t , i t  determined that the values o f w ( i , q ) are independent  A comparison  o f e x p r e s s i o n (1)  w i t h t h e mean r e s p o n s e  o b t a i n e d f r o m s i m u l a t i o n was made w i t h a v a r i e t y assignments.  that  The r e s u l t s  o b t a i n e d by S w o v e l a n d  of ^ .  times  o f ambulance e t a l (10)  show  - 50 t h a t t h e v a l u e from e x p r e s s i o n  (1)  was a r e a s o n a b l e a p p r o x i m a t i o n  o f mean r e s p o n s e t i m e . 4.3.  A Local Search  Algorithm  M i n i m i z i n g v over T with v defined with  complete enumeration  considered.  [1]  as i n e x p r e s s i o n  i s t o o e x p e n s i v e an a p p r o a c h  t o be  F o r e x a m p l e , w i t h N = 82 and K = 2 0 , t h e r e  would  20 be |T|= 82  assignments t o enumerate.  At each its  current  effects  s t e p o f t h e a l g o r i t h m , one a m b u l a n c e i s moved f r o m location  a reduction  expression[1].  t o an a d j a c e n t l o c a t i o n u n t i l  i n t h e mean r e s p o n s e t i m e , as computed by  The a l g o r i t h m  t e r m i n a t e s when a l o c a l  r e a c h e d ; i . e . , when no f u r t h e r r e d u c t i o n be  s u c h a movement  a c h i e v e d by m o v i n g a s i n g l e  minimum i s  i n mean r e s p o n s e t i m e c a n  ambulance from i t s c u r r e n t  location  t o any o f i t s a d j a c e n t l o c a t i o n s . Let A j C N denote t h a t  collection  o f nodes w h i c h a r e d e f i n e d  t o be " a d j a c e n t " node j . We s a y t h e a s s i g n m e n t p a s s i g n m e n t p i f f o r some J(> e  i s adjacent to  for a l l if t . The Step 0  algorithm  i s as f o l l o w s :  Calculate  t h e mean r e s p o n s e  f o r an  initial  S e t k = 0 and go t o S t e p 1 .  a s s i g n m e n t po. Step 1  time  S e a r c h f o r an a s s i g n m e n t  which  f o r w h i c h v (pV)  I f no s u c h a s s i g n m e n t  < v (PL.) .  i s adjacent to  and exists,  t e r m i n a t e o t h e r w i s e go t o S t e p 2. Step 2  one  Set  One may p r o c e e d f r o m S t e p  and go t o S t e p 1 .  1 t o S t e p 2 as s o o n as t h e f i r s t  found f o r which v  Alter-  - 51 n a t i v e l y , before proceeding to step 2 one may adjacent assignments f i n d the one  enumerate a l l  (or some minimal number of assignments)  f o r which  to  the marginal improvement i n the o b j e c t i v e  i s maximum. 4.4.  Experimental E v a l u a t i o n of the Algorithm R e c a l l that e x p r e s s i o n [ l ] determines  the system mean  response time by summing the mean response time f o r each node m u l t i p l i e d by the p r o b a b i l i t y of an i n c i d e n t  at that node.  Consequently, one would expects that the a l g o r i t h m would tend to s e l e c t the l o c a t i o n s c l o s e to the nodes with a high p r o b a b i l i t y of an i n c i d e n t .  Thus the nodes with low p r o b a b i l i t y of an  i n c i d e n t would tend to s u f f e r a high mean response time, and the d e s i r a b l e ambulance l o c a t i o n s depend on the s p a t i a l  distribution  of demand. I f the i n c i d e n t  rate were to i n c r e a s e one would expect  ambulances to be i n the i d l e s t a t e a c a l l ) less frequently.  (i.e.,  at t h e i r s t a t i o n awaiting  As shown i n f i g u r e 6 t h e p r o b a b i l i t y of 1  c a l l s being served by the c l o s e s t ambulance decreases as the r a t e of incidents increase.  However, the p r o b a b i l i t i e s that c a l l s  served by 2nd and 3rd c l o s e s t ambulances both i n c r e a s e d . observations lead one to expect that the d e s i r a b l e  are These  ambulance  l o c a t i o n s are a f u n c t i o n of the l e v e l o f demand w i t h i n the  system.  In the a l g o r i t h m we have d i s c o v e r e d that when o p t i m i z i n g ambulance l o c a t i o n , low demand areas g e n e r a l l y s u f f e r a high mean response time.  In an e f f o r t  to reduce the v a r i a n c e i n  average response times between high demand and low demand, the travel  time matrix was  each element  was  r e p l a c e d by a t r a v e l time matrix i n which  r a i s e d to the kth power (k = 2,3,4).  The  - 52  -  a m b u l a n c e s were t h e n l o c a t e d by response time. placed It  The  a greater  adjusted  more and 4.5.  one  input  may  ask  choice  starting  is a local  search  locations.  We  the  differences in configurations  was  not  times.  ambulances  Locations  l o c a t i o n s a f f e c t s the locations. two  Since  for finals  these  same  algorithm found  that  sets of l o c a t i o n s  locations (i.e., the  the  sets of d i f f e r e n t  s e t s o f l o c a t i o n s and  i f not  mean  the  same).  final  sets  In t h e s e  runs,  d i f f e r e n c e i n mean r e s p o n s e t i m e b e t w e e n d i f f e r e n t s t a r t i n g of  the  l o c a t i o n s i s b e t w e e n 1 and final  sets  d e p e n d e n t on t h e run  for starting  l o c a t i o n s are q u i t e s i m i l a r ,  sets in  response  to d i s p e r s e  experimented with  the  the  longer  n e c e s s a r i l y converge t o the  numerous d i f f e r e n t s t a r t i n g  of  final  algorithm,  for  as much as  adjusted  i s a set of s t a r t i n g l o c a t i o n s ,  of s t a r t i n g  l o c a t i o n s would not  set of f i n a l  having  to Choice of S t a r t i n g  algorithm  response time a s s o c i a t e d with algorithm  average  t i m e s were f o u n d t o h a v e  would tend  of Algorithm  the  the  increased.  for this  how  calls  algorithm  more as k i s  Sensitivity As  travel  e m p h a s i s on  appeared t h a t the  minimizing  of f i n a l initial  experiments s t a r t i n g  increase  one's l e v e l  of l o c a t i o n s .  sets of  locations.  2 minutes.  But  l o c a t i o n s are  the  still  difference fairly  Thus, i t i s n e c e s s a r y  f r o m a number o f s t a r t i n g p o i n t s  o f a s s u r a n c e t h a t one  has  to to  found the b e s t  set  JEff ect_ofwGrobabUity.of_.an, inciden£.cl is patch by. k-.th. closes t. .Ambulance, (k-l^).—.  .4  .3  Prob:"'4th'closest  Rfltp r a i l  r>A-r  hnnr  -  CHAPTER 5 - DESIGN OF THE  54  -  EXPERIMENT  Introduction • The e x p e r i m e n t s c o n d u c t e d *  r u n s i m u l a t i o n w i t h a number o f d i f f e r e n t to create  *  followed the f o l l o w i n g process: assignment  (W(i,q)) matrix.  u s e t h e ( W ( i , q ) ) m a t r i x and l o c a l  search  algorithm  to determine the o p t i m a l l o c a t i o n s . *  run the s i m u l a t i o n with derive the s t a t i s t i c a l  the optimal locations to output i . e . , average  response  time. If  t h e e x p e r i m e n t s w i t h t h e s i m u l a t i o n model a r e w e l l  d e s i g n e d , t h e y s h o u l d be u s e f u l an a m b u l a n c e s y s t e m . 1.  the behavior of  Two r e q u i r e m e n t s must be c o n s i d e r e d .  The e x p e r i m e n t s must be p e r f o r m e d u n d e r conditions  so t h a t t h e e f f e c t  system performance its  effect with  system 2.  i n explaining  o f one v a r i a b l e  s i m u l t a n e o u s changes  i n the other  variables.  abstraction  of r e a l i t y  f o r s t u d y s h o u l d be an  so t h a t o n l y t h e i m p o r t a n t  f e a t u r e s o f the system a r e modeled. t h e changes  ation with limit  on  c a n be s t u d i e d w i t h o u t c o n f o u n d i n g  The a m b u l a n c e s y s t e m s e l e c t e d  light  controlled  This w i l l  high-  i n b e h a v i o r c a u s e d by e x p e r i m e n t -  the system v a r i a b l e s .  t h e number o f s t o c h a s t i c  I t i s important to  features  i n t h e model  i n o r d e r t o s h a r p e n t h e s y s t e m r e s p o n s e t o changes i n parameter  or p o l i c i e s .  feature of s t a r t  F o r example,  up t i m e a t home b a s e  by u s i n g mean s t a r t  the s t o c h a s t i c can be  up t i m e w i t h o u t s e r i o u s l y  eliminated affecting  - 55 the  r e a l i s m o f the model.  the  features  directly,  Finally,  that are b e l i e v e d t o a f f e c t  despite the fact  and  training,  priority  5.2.  study  (i.e.,  interesting level  system  o f ambulance  equipment,„carried on b o a r d , s c r e e n i n g  calls  dispatching).  Experiment The  will  r e s p o n s e t i m e most  t h a t many o t h e r  v a r i a b l e s have n o t been c o n s i d e r e d attendant  experimentation  Design  p l a n was b a s e d on t h e s y s t e m a t i c  variation  of the  following: *  Number o f a m b u l a n c e  *  L o c a t i o n o f ambulance  *  Dispatching  *  Arrival  The local  optimal  search  the p r e v i o u s  Policy  r a t e o f ambulance  calls  l o c a t i o n o f t h e a m b u l a n c e was f o u n d by u s i n g t h e  algorithm. chapter  The s i m u l a t i o n was u s e d t o d e s c r i b e i n  t o c h e c k t h a t r e s u l t s were i n d e e d  locally  optimal. Because both t h e l e v e l vary  and s p a t i a l  by t i m e o f d a y , i t was n e c e s s a r y  experiments during arbitrarily  distribution  t o conduct  d i f f e r e n t p a r t s o f t h e day.  d i v i d e d i n t o three periods:  t o 12 m i d n i g h t ; was an a r b i t r a r y  and 12 m i d n i g h t  8 a.m.  t o 8 a.m.  The mining the  separate, The day was t o 6 p.m.;  Because t h i s  o n e , i t does n o t f o l l o w t h a t s h i f t  c h a n g e s i n t h e numbers o f a m b u l a n c e s , s h o u l d h o u r o f 8 a.m.,  6 p.m.,  and  only  6 p.m.  division  changes, o r  occur  at the  midnight.  l o c a t i o n o f ambulances p l a y  response time.  o f demand  For this  an i m p o r t a n t  reason,  part  i n deter-  i t was n e c e s s a r y  a m b u l a n c e s o p t i m a l l y i n each e x p e r i m e n t .  The o p t i m a l  to locate ambulance  -  l o c a t i o n was was  -  56  obtained using that  described  local  search algorithm  which  i n the previous chapter.  A l t h o u g h we  have recommended s p e c i f i c  geographical locations  of  ambulance depots  ( e . g . , 4 1 s t and G r a n v i l l e ) f o r v a r i o u s  of  a m b u l a n c e d e p o t s a t v a r i o u s t i m e s o f d a y , we w o u l d n o t  o u r recommended c o n d i g u r a t i o n s out c o n s i d e r a b l e a l t e r a t i o n are  t o be  adopted  and a d d i t i o n a l  and  numbers expect  implemented  with-  experimentation.  There  f i v e main r e a s o n s f o r t h i s : Small  adjustments i n i n d i v i d u a l  n e c e s s a r y t o s e c u r e adequate  locations  are  often  accommodation f o r the  ambulance d e p o t , t o a c c o u n t f o r l o c a l  traffic  conditions,  etc. C o n s i d e r a t i o n s o t h e r t h a n r e s p o n s e t i m e may the  locations  o f ambulance d e p o t s .  reasons of t r a i n i n g  and  liaison,  influence  For example,  i t may  be  for  desirable  to  l o c a t e a c e r t a i n number o f a m b u l a n c e d e p o t s a d j a c e n t  to  emergency  rooms.  Some o f a l l o f t h e d e p o t  locations  e v e n i n g and e a r l y m o r n i n g the  depot  locations  Our  objective  be d i s p u t e d .  s e l e c t e d f o r the  p e r i o d s may  selected  be r e s t r i c t e d  f o r the daytime  i t may  be f e l t  s p a r s e l y p o p u l a t e d r e g i o n s i s worth  of the outa  relatively  l a r g e r i n c r e a s e i n average response time f o r the as a w h o l e .  This i s c l e a r l y  a political  may  that a small  i m p r o v e m e n t i n a v e r a g e r e s p o n s e t i m e i n one lying,  period.  of m i n i m i z i n g average response time For example,  to  region  decision.  - 57 Significant hours  increase i n certain  may n e c e s s i t a t e  a re-deployment  For example, i n response to  t h e N o r t h Shore  cantly  5.3.  to the f a c t  times d u r i n g rush o f some a m b u l a n c e s .  that back-up  and t o R i c h m o n d d e t e r i o r a t e  service  signifi-  d u r i n g t h e a f t e r n o o n r u s h h o u r s , i t may be w i s e  to  t e m p o r a r i l y move a d d i t i o n a l  at  such  units  into  these  areas  times.  Simulation Statistics 1.  Incident S t a t i s t i c s  F o r each to h o s p i t a l are  travel  incident,  the response  are c o l l e c t e d .  t i m e , w a i t i n g t i m e , and t i m e  Then, t h e f o l l o w i n g  system  statistics  calculated: *  Mean  *  Standard Deviation  *  Means by M u n i c i p a l i t i e s  *  9 0 t h f r a c t i l e v a l u e by M u n i c i p a l i t i e s have v a l u e s l e s s  o r equal than 90th f r a c t i l e  2.  Ambulance  Statistics  The  following  s t a t i s t i c s were c o l l e c t e d  *  Percentage  (90% o f c a l l s  of c a l l s  t o the system  f o r each  value).  ambulance:  a n s w e r e d by t h e  ambulance *  Mean t i m e i n q u e u e s , r e s p o n s e service  *  Mean  time  Utilization  t i m e , time t o h o s p i t a l ,  - 58 CHAPTER 6 - EXPERIMENT RESULTS AND In  this  Chapter effect  c h a p t e r the r e s u l t s  5 are r e p o r t e d . of varying  THEIR IMPLICATIONS  o f the experiments  discussed i n  V a r y i n g t h e number o f a m b u l a n c e s has  the average  response  time o v e r a l l  and  the  i n each  Municipality.  T h e r e f o r e , t h e s e c t i o n d e a l i n g w i t h t h e number o f  a m b u l a n c e s and  locations  *  i s divided  optimal locations with in  *  as  follows:  d i f f e r e n t number o f a m b u l a n c e s  system  Municipal variation  due  t o v a r i a t i o n o f number o f  ambulances 6.1.  O p t i m a l Ambulance L o c a t i o n With r e s p e c t t o the o b j e c t i v e of m i n i m i z i n g average  t i m e , we using  have d e t e r m i n e d  (near) o p t i m a l ambulance depot  the a l g o r i t h m d e s c r i b e d i n Chapter 4 f o r twelve  c o m b i n a t i o n s o f t i m e o f day period and  8 a.m.  - 6 p.m.  we  located  27 a m b u l a n c e d e p o t s ; f o r t h e p e r i o d 6 a.m.  have l o c a t e d -•,.8 a.m. The  15,18  21 d e p o t s ; and  we h a v e l o c a t e d actual  Appendix.  different  and  18  For the  9,12,15,18,21,24  - 12 m i d n i g h t  f o r the p e r i o d  12  we  midnight  depots.  a r e l i s t e d i n T a b l e 14 w h i c h  i s i n the  o f t h e c u r r e n t and o p t i m a l d e p l o y m e n t  (8a.m. - 6 p.m.)  Distribution calls  12,15  locations  A comparison  21 a m b u l a n c e s  gency  and  locations  and number o f a m b u l a n c e s .  have o p t i m a l l y  response  of response  i s shown on Maps 1 and time f o r a l l c a l l s  2.  and f o r emer-  o n l y , f o r each o f t h e t h r e e p e r i o d s o f t h e d a y ,  g i v e n i n F i g u r e s 7, 8 and 9.  One  finds,  f o r example,  15 a m b u l a n c e s a r e d e p l o y e d d u r i n g t h e p e r i o d 40% o f a l l emergency c a l l s  have a r e s p o n s e  of  8 a.m.  are  t h a t when  - 6 p.m.  (Fig.7)  t i m e w h i c h does n o t  59 "  exceed  2.8  minutes.  a c h i e v e d by 54%, 12, 15,  62%,  73% and  The  i n which  start-up  start-up  minutes.  t i m e o f 1.9  Both the s t a r t - u p d e c r e a s e d by 40%  to  t i m e and  i n which  to the  average  time t o the scene the s i r e n  are  i s used.  The  are not reduced f o r  f e w e r t h a n 1% o f a l l c a l l s  C o n s i d e r i n g the e f f e c t it  the t r a v e l  times from the scene t o the h o s p i t a l  be used on t h e way  minutes  the ambulance i s d i s p a t c h e d  T h i s a v e r a g e s o u t t o an  f o r those c a l l s  since  t i m e o f 2.4  t i m e i s z e r o when t h e a m b u l a n c e i s  the road".  emergency c a l l s  response time i s  respectively.  d i s p a t c h e d w h i l e "on  travel  minute  previously, a basic start-up  charged f o r a l l c a l l s  from i t s depot.  a 4.0  8 1 % o f a l l emergency c a l l s , f o r  18 and 21 a m b u l a n c e s ,  As m e n t i o n e d is  Similarly,  require  the  siren  hospital. of these assumptions  i s c l e a r t h a t t h e r e are at l e a s t  on r e s p o n s e  two p o l i c i e s w h i c h  e s t a b l i s h e d w h i c h w o u l d have a d i r e c t , p r e d i c t a b l e  can  effect  time  be on  response time: *  reduce s t a r t - u p  *  use t h e s i r e n more o f t e n  I f t h e s i r e n were u s e d which  i t i s n o t now  would  d e c r e a s e by about  1 minute  overall.  times  and  f o r al1 of those n o n - t r a n s f e r c a l l s  used  There  (64% o f a l l c a l l s ) , 2 minutes  for calls  and  group  and  time about  considered i n est-  policy.  Average day  i n that  response  a r e , o f c o u r s e arguments a g a i n s t the i n -  d i s c r i m i n a t e use o f t h e s i r e n w h i c h must be ablishing  average  for  r e s p o n s e t i m e s f o r each o f t h e t h r e e p e r i o d s o f t h e  f o r v a r i o u s numbers o f a m b u l a n c e s a r e d i s p l a y e d  i n Figures  20  _!  J  J  10%  20%  30% Fig. 7 b  Fig.  7  I 40%  J 50%  L _ J 60%  70%  1 80%  1  • 90%  Emergency C a l l s Only  D i s t r i b u t i o n of Response Time f o r the e n t i r e O p t i m a l Placement o f Ambulances  (8 a.m.*  G.V.R.D. w i t h - 6  p.m.)  - 61 -  12 Ambulances  10%  20%  30%  40% F i g . 8a  50%  60%  70%  80%  90%  A l l Calls  10 12 Ambulances  4>  e  •H H CO OJ co u CO 3 C C O *H O. g CO ^  <u  OS  10%  20%  30% Fig.  Fig.  8  40% 8b  50%  60%  70%  80%  90%  Emergency C a l l s O n l y  D i s t r i b u t i o n o f Response Time f o r the e n t i r e G.V.R.D. w i t h O p t i m a l Placement o f Ambulances (6 p.m. - 12 mid.)  - 62 -  - J L _ J L _ J _ J . ^ ^ 10%  20%  30%  40% F i g .  I  J.  !  10%  20%  1__ 30% F i g -  Fig.  9  9t  50%  .60% . 70%  80%  90%  9fli A l l C a l l s  !  I  I  I  40%  50%  60%  70%  l 80%  l 90% .  Emergency C a l l s Only  D i s t r i b u t i o n o f Response Time f o r t h e e n t i r e G.V.R.D. w i t h O p t i m a l Placement o f Ambulances (12 mid. - 8 a.m.)  1. Current Placement of Ambulances  - 65 -  10 and 11. calls:  F i g u r e 10 c o n t a i n s a v e r a g e  F i g u r e 11 c o n t a i n s a v e r a g e  Although  response  times  for a l l  f o r emergency c a l l s  i t i s not our f u n c t i o n  (siren) only.  t o recommend t o t h e G.V.R.D.  what p o i n t t o c h o o s e on t h e s e c u r v e s , i t i s a p p a r e n t  t h a t one  s h o u l d p r o b a b l y h a v e b e t w e e n 15 and 24 a m b u l a n c e s d u r i n g t h e day (8 a.m.  - 6 p.m.)  (6 p.m.  - m i d n i g h t ) , and b e t w e e n 9 and 18 i n t h e e a r l y  (midnight Any  sees  fewer  than  15 a m b u l a n c e s d u r i n g t h e day l e a d s t o a s e r i o u s  i n average  range.  in  average  of  g o i n g from  response  sensitive  though  less  which  with extremely long  than 9 i n the e a r l y  The 9 0 t h  response  f o r each fractile  i n average  morning.  the r e l a t i o n s h i p  between  times, service  average  t i m e s and  number o f a m b u l a n c e s i n each curves give those response  a r e met o r b e t t e r e d by 90% o f a l l c a l l s . (which i s the f r a c t i o n  ance i s b u s y ) i s r e a d f r o m t h e v e r t i c a l graph.  improvement  t h a n 12 a m b u l a n c e s a r e d e p l o y e d  1 2 , 13 and 14 d i s p l a y  ambulance u t i l i z a t i o n  the  response  t o numbers o f a m b u l a n c e s i n t h e  dramatic, deterioration  t i m e s , 90th f r a c t i l e  t h e day.  from F i g u r e 4  24 t o 27 a m b u l a n c e s .  ambulance u t i l i z a t i o n , of  Moreover,  t i m e d u r i n g t h e day i s o b t a i n e d as a r e s u l t  d u r i n g the evening o r fewer  response  of calls  t i m e o c c u r s when f e w e r  Figures  time.  On t h e o t h e r h a n d , o n l y a v e r y s l i g h t  A similar, response  response  that the f r a c t i o n  times i s p a r t i c u l a r l y 12-15  morning  - 8 a.m.).  deterioration one  b e t w e e n 12 and 21 a m b u l a n c e s i n t h e e v e n i n g  The  period  times  (average)  o f t i m e each  ambul-  s c a l e on t h e r i g h t o f  - 66 -  8  18  © i  a.m. - 6 p.m.  6 p.m. - 12 mid. 12 mid.-  16  8  a.m.  14  12  at w CO  c  <V  t  10  O 3 D. C in . H  00 TO M  (!) >  <  4 t  Number of Ambulances  Fig.  1  0  Average Response Time by Number oj_Ambulances Day,  forA l lCalls  /  b J^me_of y  - 67 8  a.m.  6 p. ID .  6 p.m. 12  mid.  12  mid.  8  a.m.  e •t-i  H  <1>  «  W dl. C u O 3 O. C erf 60 CO  u  >  12  15  18  21  24  27  Number of Ambulances  F i g . 11 Average Response Time by N-• mber of Ambulances by Time of Day, Emergency C a l l s Only  - 68 s e r v i c e time 50  utilization' 90th  fractile  response time  AO  \ o CO  40%  30  •H 4-1 P> CU  u c 3  J 10%  20  10  12  F i g . 12  15  18  21  24  27  E f f e c t o f Number o f Ambulances -on Response Time, S e r v i c e Time and Ambulance U t i l i z a t i o n  (8 a.m'  - 6  p.m.)  Number o f Ambulances  -  69  -  40  30% c  o  •r-l •U 03 N  20%  30  H  •H *-!  o c 0}  service  01  utilization  3 C  90th  •H  X c  •i-t  10%  time  fractile  response  time  20  OJ  e  H C  <u  10  F i g . 13  Effect  21  18  15  of Number of Ambulances on Response Time, S e r v i c e Time  and Ambulance  Utilization  (6  p.m.  - 12 micl.) "  D 6 <  - 70 -  40  service  time  utilization 90th  fractile  response  time  30  c  20%  o  CO N •r-l r-H •H  (J  10%.  20  c  corn •g  10  12 Fig.  14  Effect  15  18  of Number of Ambulances on Response Time, S e r v i c e Time  and Ambulance  Utilization  (12 mid. - 8  a.m.)  - 71 -  6.2.  Variations Average  are  i n R e s p o n s e Time by M u n i c i p a l i t y  response  t i m e and 9 0 t h f r a c t i l e t i m e s by M u n i c i p a l i t y ,  g i v e n i n T a b l e s 10, 11 and 12 ( f o r a l l c a l l s ) , f o r v a r i o u s  numbers o f a m b u l a n c e s . 21 a m b u l a n c e s , the  We s e e i n T a b l e 9, f o r e x a m p l e ,  West V a n c o u v e r  day o f 10.0 m i n u t e s  Ninety percent o f c a l l s response w i t h i n  has an a v e r a g e  compared w i t h originating  15.8 m i n u t e s  response  a regional  that  time d u r i n g  a v e r a g e 6.6.  i n West V a n c o u v e r  receive  or less.  From t h e s e t a b l e s we d i s c o v e r e d t h a t t h e m u n i c i p a l i t y low demands s u f f e r e d  a h i g h average  were a r e a s q u i t e o f t e n example, couver  West V a n c o u v e r  calls.  Vancouver. distant  response  time although there For  a m b u l a n c e s a n s w e r o n l y 7 0 % o f West Van-  30% o f West V a n c o u v e r  way t o s o l v e t h i s  with  a r e d i s p a t c h e d t o h i g h demand a r e a s .  The r e s t o f t h e c a l l s  ambulances  with  i t answers  calls  North  a r e s e r v i c e d by more  ( i . e . , North Vancouver problem  a r e from  or Vancouver).  i s t o employ a " r e g i o n a l  One  dispatch"  rule  w h i c h w i l l be d i s c u s s e d i n S e c t i o n 6.3. Figure Municipal  15 g i v e s a c o m p a r i s o n  average  i n f o r m a t i o n used for  response  t i m e f o r each number o f a m b u l a n c e .  to construct t h i s  t h e c a s e o f 18 a m b u l a n c e s ,  average  graph  Vancouver  i s i n T a b l e 10. has t h e b e s t  r e s p o n s e t i m e f o r each number o f a m b u l a n c e s  b e t t e r t h a n t h e G.V.R.D. a v e r a g e ) . ambulances, time  b e t w e e n t h e b e s t and w o r s t  Except  The  Except  Municipal  ( a b o u t 18%  f o r t h e c a s e o f 12  P o r t C o q u i t l a m has t h e w o r s t M u n i c i p a l  average  response  ( a b o u t 9 0 % above t h e G.V.R.D. a v e r a g e ) . You w i l l r e c a l l  f r o m C h a p t e r 4 ( S e c t i o n 4.4.) t h a t t h e  v a r i a n c e b e t w e e n a h i g h demand a r e a and low demand a r e a c o u l d be  riuciDer  Municipality  Ave ir calls /hr.  ART  FT 90  ART  FT 90  iiiiiuuxauuets  18  15  12 •  9  01  FT 90  ART  FT 90  ART  ART  FT 90  ;  27  24  21 ART  90^  FT ART 90  Burnaby  .73  18.8 36.8  12.3 19.8  10.2 16.0  8.9 13.2  8.2 12.2  7.6 10.5  6.6  9.9  Coquitlam  .12  22.7 44.7  13.4 26.7  9.1 19.0  9.1 13.3  8.8 10.9  8.1  8.4  8.6  Delta  .05  26.9 30.6  18.4 18.7  12.1 15.0  10.7 12.6  11.1 18.3  New Westminster  .35  20.1 41.7  10.3 17.3  9.5 15.4  7.7 12.1  7.1  North Vancouver  .38  21.2 45.3  11.5 25.9  9.0 18.5  8.3 16.4  6.7 13.3  6.6 12.1  6.2 10.7  Port Coquitlam  .08  35.2 53.6  17.0 32.5  13.9 25.4  12.8 21.8  12.3 21.4  11.6 17.0  11.6 15.5  Port Moody  .06  22.5 39.1  18.7 26.5  6.6 13.3  5.7  Richmond  .29  21.7 52.9  12.5 21.2  9.7 18.2  Surrey  .44  25.8 46,8  14.5 30.0  4.23  13.9 32.2  Vancouver  8.9  6.8  8.9  5.5  5.3  5.5  5.3  7.1 15.0  7.1 11.0  7.1  9.7  6.9  7.0  12.1 18.7  11.4 17.8  11.2 18.0  8.3 12.8  6.6 13.2  5.9 10.1  5.5  5.2  7.9  5.0  5.0  7.6  8.0  7.4 18.5  5.5  5.0  5.5  5.0.  7.2 12.0  6.6 10.7  6.1 10.4  6.0  9.7  41.9  41.2  40.8  40.6  21%  18%  17%  10.3 17.8  10.0 15.8  White Rock  .11  33.8 53.3  18.7 39.3  7.4 17.6  7.2 17.4  17.4 '40.6  10.4 19.5  8.1 15.8  Average S e r v i c e . Time  52.3  •45.3  42.8  Average U t i l i z a t i o n  67%  41%  33%  Average and 90  9.1 12.0  9.2 13.5  11.1 18.0  Table  9.1 10.8  9.9 15.2  20.6 43.2 18.5 35.8  #  6.8  10.5 12.7  5.3  5.3  J.6  7.0  10.5 12.7  9.7  West Vancouver  Overall  9.6  ' 25% 11  F r a c t i l e Response Times by M u n i c i p a l i t y  and by "umber of Ambulances (8am - 6pm, a l l c a l l s )  - 73 Number of Ambulances -•  15  Ave // calls /nr.  ART  .76  Coquitlam  .13  Delta  Municipality Burnaby  •  18 FT 90  ART  9.2  13.9  9.9  .04 13.8  21 FT 90  ART  90  8.5  12.6  7.9  11.5  15.6  9.2  15.4  8.6  10.7  15.0  9.5  10.4  11.3  11.9  New Westminster  .35  6.5  8.9  ' 6.7  9.0  6.4  8.8  North Vancouver  .29  6.6  10.0  7.2  12.4  6.4  9.8  Port Coquitlam  .06  15.9  17.0  11.3  15.9  5.9  7.1  Port Moody  .03  16.9  19.0  5.7  5.3  11.5  12.7  Richmond .  .16  8.8 '"'15.5  S.7  15.1  6.7  10.1  Surrey  .43  6.8  6.9  6.8  6.8  6.8  6.8  3.02  6.0  10.2  5.7  9.8  5.2  8.7  West Vancouver  .12 10.6  17.4  10.0  15.2  10.6  16.1  White Rock  .05  4.7  4.8  3.8  4.0  3.8  4.0  7.1  12.0  6.7  11.3  6.0  10.3  Vancouver  Overall  5.4  ?  Ave. Service Time  40. 7  40.2  39. 7  Ave. Utilization  24%  20%  17%  Table 10 Average and 90th Fractile Response Times by Municipality and by Number of Ambulances  \  (6pm - midnight, a l l calls)  Number, of Ambulances 12  15  18  Ave // calls /hr.  ART  FT 90  ART  FT 90  ART  Burnaby  .25  9.9  14.5  .8.2 10.7  7.9  10.2  Coquitlam  .05  8.6  9 .4  11.3  15 .4  8.5  9.6  Delta  .05  15. 5  15 .0  9.6  10.4  11.8  12.0  New Westminster  .14  6.7  7.5  7.9  11 .9  7.7  9.7  North Vancouver  .18  7.2  10.5  6.8  9 .4  3 .' 6.  8.7  Port Coquitlam  .05  16. 6  17.5  11.6  11 .1  10. 8  11.1  Port Moody  .03  20. 2  20.5  7.8  15 .6  9-9  16.0-  Richmond  .07  9.0  18.0  8.5  15 .0  5. 6  7.5  Surrey  .19  11.6  12.2  11.3  12 .1  11.6  12.1  1.70  6.3  10.3  5.8  9.5  5.1  8.0  West Vancouver  .08  9.6  17.4  8.7  15 .0  8.7  16.0  White Rock  .04  3.8  4.5  4.7  4 .8  3. 8  4.0  7.3  12.0  6.8  12.0  6.0  10.0  Municipality  Vancouver  Overall  2.8  Ave. Service Time Ave. U t i l i z a tion  -  41.8 16%  40.9 - 12%  FT 90  40.5 10%  Table 12 Average and 90th Fractile Response Times by Municipality and by Number of Ambulances (midnight - 8 am, a l l calls)  - 75 maximum m u n i c i p a l average response time GVRD average response time minimum m u n i c i p a l average  response  <u E  •rH  H a) co CO CIJ C J-> O  2  a- c CO *H  Pi  c  . rt  u >  '12  Fig.15  15  18  21  24  M u n i c i p a l V a r i a t i o n i n Average Ambulances f o r A.11  Calls  27  Number of Ambulances  Response Time by Number o f  (8 a.m. - 6 p.m.)  - 76 -  r e d u c e d by a d j u s t i n g in  an e f f o r t  travel  to reduce  period.  case the t r a v e l  r e p l a c e d by a m a t r i x o f s q u a r e d travel  travel  i n s u c h a way as t o m i n i m i z e a v e r a g e  times.  The e f f e c t  The  a g r e a t e r emphasis  resultant  on c a l l s  t i m e m a t r i x was  and cubed  travel  i n Map 2.  municipality  6.3.  travel  times.  a r e shown i n Maps 3 and 4.  o f average  configuration  response  t i m e by  f o r t h e t h r e e 21 a m b u l a n c e c o n f i g u r a t i o n s  using the o r i g i n a l travel  A comparison  then  t i m e s was t o  having longer response  ambulance c o n f i g u r a t i o n s  case  adjusted response  These s h o u l d be compared w i t h t h e o r i g i n a l o p t i m a l displayed  during the  A m b u l a n c e s were  located  place  times  t i m e s ; i n the second  t i m e s was u s e d .  of the squared  performed  response  B o t h were f o r 21 a m b u l a n c e s ,  In the f i r s t  a m a t r i x o f cubed  Two e x p e r i m e n t s were  the v a r i a n c e i n average  between M u n i c i p a l i e s . daytime  time.  t i m e s , squared t r a v e l  produced  t i m e and cubed  t i m e s , i s g i v e n i n T a b l e 13. Dispatch Rules  The  dispatch rule  currently  m i n s t e r , and V a n c o u v e r , day,  i s the "regional  serving which  employed i n Burnaby,  i n a l l but the b u s i e s t p e r i o d s o f the  dispatch" rule.  these three M u n i c i p a l i t i e s  i t has p r i n c i p a l  Each o f e i g h t  responsib1ity.  Whenever a c a l l  ambulance a s s i g n e d t o t h e t e r r i t o r y o f t h e c a l l  (if  available),  terms  o f response  There  ambulances  i s assigned a t e r r i t o r y  the  even  New West-  over  occurs,  i s dispatched  i f t h a t ambulance i s n o t t h e " c l o s e s t " ( i n  t i m e ) one t o t h e c a l l .  a r e two r e a s o n s  f o r employing  this  dispatching decisions  dispatch  rule:  a.  i tsimplifies  f o r t h e d i s p a t c h e r s and,  b.  i t t e n d s t o e q u a l i z e t h e w o r k l o a d among t h e a m b u l a n c e  crews.  - 77 True Travel Times  Squared Travel Times  Cubed Travel Times  Burnaby  8.2  8.6  8.4  Coquitlam  8.8  8.7  8.7  11.1  13.9  12.5  New Westminster  7.1  8.1  7.9  North Vancouver  6.7  6.6  6.6  Port Coquitlam  12.3  7.6  7.6  Port Moody  5.5  11.3  11.3  Richmond  7.1  6.8  6.4  11.2  9.4  9.8  5.2  6.6  6.8  10.0  ,9.7  9.7  White Rock  7.4  6.4  10.6  Overall  6.6  7.3  7.4  Municipality  Delta  Surrey Vancouver West Vancouver  Table 13 Average Response Times by Municipality, with Optimal Placement of 21 Ambulances With True , Squared, and Cubed Travel Times -  (8 am - 6 pm)  /o -  MAP 3.  Optimal Placement of 21 Ambulances with Squared Travel Times (8 a.m. -  6 p.m.)  s  MAP 4.  Optimal Placement of 21 Ambulances with Cubed Travel Times (8 a.m. -  6 p.m.)  - 80 -  We have experimented  with one other d i s p a t c h r u l e , the  " c l o s e s t " d i s p a t c h r u l e , i n which ambulance i s always  dispatched.  the " c l o s e s t "  available  For the regions as a whole  the  " c l o s e s t " d i s p a t c h r u l e y i e l d s average response times  are  roughly 12% lower than average response times produced  the  " r e g i o n a l " dispatch rule  for  period  8 a.m.  - 6 p.m.  which under  (a decrease from 8.3 to 7.3 minutes Although the r e g i o n a l  average  response  time i s b e t t e r when the " c l o s e s t " d i s p a t c h r u l e i s used, the variance o f average response time between M u n i c i p a l i t i e s  i s greater.  T h e r e f o r e , the choice o f d i s p a t c h r u l e s depends on the o b j e c t i v e of  the a d m i n i s t r a t i o n .  6.4.  Sensitivity  of Response Times to Changes i n Demand  We have performed  a small number of experiments  a p p r e c i a t i o n f o r the a b i l i t y demand l e v e l s .  to gain some  o f the system to deal with i n c r e a s e d  Increased demand l e v e l s may occur i n the short run  or  i n the long run.  in  r e g i o n a l demand i f the s e r v i c e i s p r o v i d e d without charge, or  for  a nominal For  For example, we would expect some i n c r e a s e  charge.  a daytime  deployment  of 21 ambulance the e l a s t i c i t y of  response time, as a f u n c t i o n of c a l l means that i f the c a l l  r a t e per hour, i s .36.  This  rate goes up from 7.0 c a l l s / h r by 100% to  14 c a l l s / h r , the average response time goes up 36% (from 6.5 to 8.8 minutes). (for  R  percent.  S i m i l a r l y , i f the c a l l  r a t e goes up by R percent  200%) the response time would i n c r e a s e by about Hence, at the 21 ambulance l e v e l , the system  .36 x R  can handle  a c o n s i d e r a b l e i n c r e a s e i n demand with only a moderate d e t e r i o r a t i o n i n response time.  - 81  -  F r o m - a n o t h e r p o i n t o f v i e w , i t was r a t e were t o i n c r e a s e by a m b u l a n c e s w o u l d be t i m e as o b t a i n e d For  .36  with  (.36  Tradeoffs Estimates  for  various  Figure for  call  x 21  added t o m a i n t a i n 6.5.  21  ( 1 0 0 % ) = 36%  ambulances  13,  m  existing  response  call  rate.  ( i ; ; e . , R=100%) ,  ambulances) - would have t o  same l e v e l  of response  Between A n n u a l O p e r a t i n g of t o t a l  levels  x R additional  same a v e r a g e  r a t e were t o d o u b l e  = 7.6  be  C o s t a n d K R e s p o n s e Time  annual o p e r a t i n g  cost  ( i n 1974  dollars)  displayed in  f o r each a v e r a g e r e s p o n s e t i m e l e v e l o n l y ) , the  8  time.  of average response time are  (for a l l calls  annual o p e r a t i n g  c o s t was  or  computed  formula* = 621  + 125  (.416N, + a  .25N  + e  ) , when, . $621,000 i s t h e  estimated  o f management, d i s p a t c h e r s attendants  and  two  this  total  attendants,  attendants.  ambulance, the  e q u i p m e n t , and  (salaries  than  c o s t o f m a n n i n g one  24 h o u r s a day,  goes f o r d e p r e c i a t i o n and the  s t a f f other  365  $105,000 goes t o wages and  a m b u l a n c e d r i v e r s and  with  and  cost per year  ambulance  r e n t and  not  ambulances).  . $125,000 i s t h e e s t i m a t e d with  fixed  o t h e r management r e l a t e d c o s t s w h i c h do  v a r y w i t h t h e number o f  *  the  ambulances at the  Cost i n thousands of d o l l a r s 33N  (.36)  call  more a m b u l a n c e s - t h a t i s , r o u g h l y  the  emergency c a l l s  from the  then  r e q u i r e d to a c h i e v e  example, i f the  then  R percent,  found t h a t i f the  The  operating  utilities  days a y e a r .  Of  fringe benefits for remaining  expenses  cost of f i r s t  ambulance  $20,000  associated  aid supplies  f o r the  ambulance  A l l c o s t e s t i m a t e s were o b t a i n e d f r o m M e t r o p o l i t a n Company's a c t u a l and f o r e c a s t e d c o s t s .  and depot.  Ambulance  - 82 -  3.5  4.0  4.5  5.0  5.5  6.0  6.5  7.0  7.5  8.0  8.5  Average Regional Response Time ( i n minutes) F i g . T6  Tradeoff Between Average Response Times and Annual Operating Cost  - 83 t h e numbers fractions periods (6/24 NJ, °  .416,  .25, and  o f t h e 24 h o u r  8 a.m.  = .25)  - 6 p.m.  .333  are, respectively,  day w h i c h  and m i d n i g h t - 8 a.m.  (8/24  =  night  (6 p.m.  t i m e 24 h o u r s  a day  o n l y , o f 4.3  the c a l c u l a t i o n  response  average  14.2  16.5  w o u l d be r e q u i r e d  values s u f f i c e  e =  16.5  =  14.2  N  A  N  see  i n the e a r l y  deployed, f r a c t i o n a l  for this  We  from  19.2  w o u l d be n e e d e d i n  numbers o f a m b u l a n c e s c a n n o t  19.2  8).  time about  (although f r a c t i o n a l  =  average  time f o r  a day.  response  a m b u l a n c e s w o u l d be n e e d e d d u r i n g t h e d a y , about  of  (mid-  of the annual operat-  m i n u t e s , 24 h o u r s  8 t h a t to m a i n t a i n t h i s  t h e e v e n i n g , and  - 6 p.m.),  ( f r o m F i g u r e s 7 and  c o s t r e q u i r e d t o m a i n t a i n an a v e r a g e  emergency c a l l s  (8 a.m.  to m a i n t a i n the given l e v e l  C o n s i d e r , f o r example,  D  .333).  - 12 m i d n i g h t ) and e a r l y m o r n i n g  - 8 a.m.)  response  N  - midnight  N , and N a r e , r e s p e c t i v e l y , t h e numbers o f e m  evening  Figure  i n the t h r e e  (10/24 = . 4 1 6 ) , 6 p.m.  a m b u l a n c e s r e q u i r e d d u r i n g t h e day  ing  fill  the  actually  morning be  calculation).  Hence,  m Consequently, the annual c o s t i n thousands 621  + 125  o r r o u g h l y 2.73  (.416  million,  o f F i g u r e 13 w h i c h t i m e o f 4.3  (19.2)  minutes  of dollars  equals  + . 2 5 ( 1 6 . 5 ) + . 3 3 3 ( 1 4 . 2 ) = 2727,  which  i s t h e v a l u e on t h e v e r t i c a l  c o r r e s p o n d s t o an a v e r a g e  regional  on t h e c u r v e f o r emergency c a l l s  scale  response only.  - 84 -  We do not wish to convey the i m p l i c i t  assumption that i t i s  n e c e s s a r i l y d e s i r a b l e to have the same l e v e l time at a l l times of the day  (which was  determining the two curves i n Figure  of average response  the assumption made f o r  13).  In p a r t i c u l a r ,  we  should point out that i f one were to add one more ambulance  for  one hour per day, i t would have a much g r e a t e r impact on response times i f added during the daytime than i f added i n e i t h e r the evening or e a r l y morning hours. To i l l u s t r a t e t h i s p o i n t , c o n s i d e r the e f f e c t ambulance  of adding one  f o r one hour i n each of the three periods of the day, to  those numbers of ambulances  needed to provide an 8 minute  response time, 24 hours a day. a d d i t i o n of one ambulance  We  average  f i n d from Figure 7 that the  decreases average response time by  roughly 2/3 of 1 minute i n each of the three periods of the day. However, t h i s r e d u c t i o n i s a p p l i e d to more c a l l s per hour during the daytime than during the evening or e a r l y morning.  Specifically,  the t o t a l r e d u c t i o n i n response time per hour i s 4.7 minutes 8 a.m.  - 6 p.m.,  midnight  (2/3 x 7.0  (2/3 x 5.4  night  - 8 a.m.  6.6.  Summary and  c a l l s / h r ) 3.6 minutes during 6  c a l l s / h r ) and only  (2/3 x 2.8  1.9 minutes during  during p.m.  12 mid-  calls/hr).  Conclusions  The r e s u l t s of the s i m u l a t i o n experiments on the model of the Vancouver ambulance i n t o ambulance results *  systems have provided some i n t e r e s t i n g  system behavior.  can be b r i e f l y  The most noteworthy c o n c l u s i o n s and  summarized  $s f o l l o w s :  The long-range planning of ambulance ambulance  insights  s e r v i c e must regard  s e r v i c e as an i n t e g r a l part of the t o t a l  - 85 -  emergency h e a l t h c a r e  system.  I m p r o v e m e n t s s h o u l d be made i n t h e c o - o r d i n a t i o n o f community emergency  resources.  Ambulance s e r v i c e s h o u l d be p r o v i d e d on a r e g i o n a l b as i s . A m b u l a n c e s s h o u l d be l o c a t e d s t r a t e g i c a l l y response  time.  For a given d e s i r e d l e v e l and  location  o f response  t i m e , t h e number  o f a m b u l a n c e s s h o u l d be d i f f e r e n t i n  different periods Periodic  to minimize  review  o f t h e day.  of the level  and s p a t i a l  o f demand s h o u l d be made and a d j u s t m e n t s  distribution s h o u l d be  made i n t h e number and l o c a t i o n s o f a m b u l a n c e s . The  determination o f the proper  response  time  level  s h o u l d be b a s e d i n p a r t on an a n a l y s i s o f t h e t r a d e o f f b e t w e e n c o s t and r e s p o n s e  time.  86  Time o f Day Number of Ambulances  8am-6pm Marine D r / l l t h St  (WVan)  Capilano Rd/Marine Dr  (NVan)  3rd S t / L o n s d a l e  (NVan)  13th S t / L o n s d a l e  (NVan)  V  V  Burrard/W.Georgia  (Van)  V  v  Main/Hastings  (Van)  V V  41st/Nanaimo  (Van)  V  Knight/41st  (Van)  V V  Fraser/41st  (Van)  V  'GranvMle'/'Alst  (Van)  MacDonald/Broadway  (Van)  Burrard/Broadway  (Van)  Granville/Broadway  (Van)  V  Cambie/Broadway  (Van)  V V  Main/Kingsway  (Van)  Fraser/Kingsway  \  6pm-midnight I 5 _ 18" 2]  V v  \/  V  V .V  \ 6-  V  V  V V  V  V  V  V  V V V  \  V  V  V  V  V  V V V V V V,  V-  V  V  V \  V  V V V  V  (Van)  0ak/70th  (Van)  Granville/Georgia  (Van)  Hastings/Boundary  (Van)  Kingsway/Imperial  (Van/Bby)  Grandview Hgwy/fioundary  (Van)  Lougheed/Boundary  (Van/Bby)  Boundary/S.E. M a r i n e D r .  (Bby)  Barnett/Willingdon  (Bby)  6 t h Av./12 S t  (NWest)  Brunet/Columbia  (NWest)  Grant McConachleway/499 Hgwy  (Rich)  No 5 Rd/499 Hgwy  (Rich)  Barnett/Gatensbury  (PMdy)  Barnett/Woodland D r .  (PCoq)  Roper/Johnston Rd  (WRock)  S c o t t Rd/Ladner Trunk Rd  (Sry)  O l d . Y a l e Rd/King George Hgwy  (Sry)  Tsawassen/Ladner Trunk Rd  (Lad/Sry)  L,adner Trunk/K.G. Hgwy T a b l e 14  (Sry)  V  V  V V  V V  V  V  V  V  V  V  V  s. V  V V  \  V  \  V  V  V  V V  \  V  V V  V V  (Van)  Nanaimo/Broadway  V  V  (Van)  Clark/Broadway  mi^lnjlgji^^^m  V V V  V  V  V  V  V V  V  V V  V V V \  V  V  V  V V V  V V V  V V  V  V  V  \  V \  V V V  V  V \  V  V  \  V  V V  V  V  N  \  V  \,  V  V  V VV  \  V  V  \  -  V V V V  V  V  \  V V  V  V  \/  V V  Ny  V  V  V  V  V V \ \  V  V  \  V V V V V \  V \ 1 1  V  V  V V  V  \  V  V  \  V  V  V V V V  V  \ —  Optimal Placement o f Ambulance Depots by Time of Day and Number of Ambulances  1  - 87 -  REFERENCES  1.  B e l l , C o l i n E., " O p t i m a l P l a n n i n g o f an Emergency M e d i c a l S e r v i c e " , U n i v e r s i t y o f C a l i f o r n i a at I r v i n e ( u n p u b l i s h e d report).  2.  Emergency M e d i c a l S e r v i c e s , R e p o r t t o G.V.R.D. A d v i s o r y C o m m i t t e e by t h e Emergency M e d i c a l S u b c o m m i t t e e , Vancouver C a n a d a , A p r i l , 1970.  3.  F i t z s i m m o n s , J . A., "Emergency M e d i c a l S y s t e m s : A s i m u l a t i o n s t u d y and C o m p u t e r i z e d Method f o r D e p l o y m e n t o f A m b u l a n c e s " , U n i v e r s i t y o f C a l i f o r n i a , Ph.D. thesis, Los A n g e l e s , 1970.  4.  F o u l k e s , R. G. , " H e a l t h S e c u r i t y f o r B r i t i s h Columbian'.,', Queen's P r i n t e r , V i c t o r i a , C a n a d a , December, 1973.  5.  G i b s o n , Bugbee, A n d e r s o n and O d i n , "Emergency M e d i c a l S e r v i c e s i n the Chicago A r e a " , U n i v e r s i t y o f Chicago, C h i c a g o , 1971.  6.  M o r s e , P h i l l i p M., Queues, I n v e n t o r i e s W i l e y , New Y o r k , 1958.  7.  N a y l o r , T. H. and F i n g e r , J . M., " V e r i f i c a t i o n o f Computer M o d e l s " , 'Management S c i e n c e , V o l . 14, No. 2 ( O c t o b e r 1 9 6 7 ) , Page B-92 t o B-101.  8.  P a r z e n , Emanuel, S t o c h a s t i c F r a n c i s c o , 1962.  9.  S a v a s , E. S., " S i m u l a t i o n and C o s t - E f f e e t i v e n e s s A n a l y s i s o f New Y o r k ' s Emergency Ambulance S e r v i c e " , Management S c i e n c e , V o l . 15, No. 12, ( A u g u s t 1 9 6 9 ) , page B-608 t o B-627.  10.  and  Maintenance,  P r o c e s s e s , Holden  Day,  San  S w o v e l a n d , C , Uyeno D., V e r t i n s k y I . and V i c k s o n R., "Ambulance L o c a t i o n P r o b a b i l i s t i c E n u m e r a t i o n A p p r o a c h " , Management S c i e n c e , A p p l i c a t i o n P a r t 2, V o l . 20, (December 1 9 7 3 ) , page 686 t o 698.  

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