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Passenger distribution functions for small airports Geddes, Erica 1984-12-31

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PASSENGER DISTRIBUTION FUNCTIONS FOR SMALL AIRPORTS  by  ERICA GEDDES  B.Sc,  Queen's University, 1979  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in FACULTY OF APPLIED SCIENCE DEPARTMENT OF CIVIL ENGINEERING  We accept this thesis as conforming to the required standard >  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1984 © E r i c a Geddes, 1984  i  In p r e s e n t i n g  t h i s thesis i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I  further  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 copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be  department o r by h i s o r her  granted by  the head o f  representatives.  my  It i s  understood t h a t copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be  allowed without my  permission.  Department o f The U n i v e r s i t y o f B r i t i s h 1956 Main Mall Vancouver, Canada V6T 1Y3  DE-6  (3/81)  Columbia  written  ABSTRACT  This research looks at one input required for the design and planning of small a i r p o r t s .  It investigates the number of passengers  expected to use the terminal. Data describing passenger volumes was gathered from a i r l i n e records at eight airports i n B r i t i s h  Columbia.  flight  The volumes were formed  into frequency d i s t r i b u t i o n s and a theoretical model was found that would best describe the data.  The selection of the model was based on the  o v e r a l l f i t of the curve (as measured by the Chi-Squared s t a t i s t i c and by visual inspection) and the a b i l i t y of the model to predict the right hand t a i l of the observed curve (as measured by the 90th percentile values). Three model d i s t r i b u t i o n s were studied: the Lognormal.  the Normal, the Poisson and  According to the selection c r i t e r i a , the lognormal  d i s t r i b u t i o n was found to be the best model for use i n a i r terminal design.  iii TABLE OF CONTENTS  ABSTRACT  i i  LIST OF FIGURES  v  LIST OF TABLES  vi  ACKNOWLEDGEMENTS 1.  2.  3.  4.  vii  INTRODUCTION  1  1.1  Statement of Problem  1  1.2  Approach  2  LITERATURE REVIEW  6  2.1  A i r Terminal Sizing  6  2.2  Design Volume Determination  17  2.3  Passenger D i s t r i b u t i o n Functions  19  METHODOLOGY  21  3.1  Data Description  21  3.2  Features of the Distributions  23  3.3  Procedure  27  3.3.1  Goodness-of-Fit C r i t e r i o n  30  3.3.2  Design Volume C r i t e r i o n  31  3.3.3  V i s u a l Inspection C r i t e r i o n  34  ANALYSIS  35  4.1  C r i t e r i a f o r Acceptance or Rejection  35  4.1.1  Goodness-of-FIt  35  4.1.2  Design Volumes  46  4.1.3  V i s u a l Inspection  50  4.1.4  Ease of Use  53  4.1.5  Applicability  54  Selection of a Model  54  4.2  iv 5.  CONCLUSIONS  56  5.1  Assessment  56  5.2  F u r t h e r Research  58  REFERENCES  60  APPENDIX A  -  Computer Programs  63  APPENDIX B  -  D e t a i l e d Chi-Squared C a l c u l a t i o n s  69  APPENDIX C  -  A c t u a l D e c i l e s by F l i g h t Event  76  APPENDIX D  -  Histograms  79  V  LIST OF FIGURES  1.  Airport Terminal Passenger Flows  7  2.  Terminal Planning Process  8  3.  Terminal F a c i l i t i e s  4.  90th Percentile by F l i g h t Event and by Passenger Volume  10  33  vi LIST OF TABLES  I.  D i s t r i b u t i o n Models Used by A i r l i n e s and A i r c r a f t Manufacturers  5  II.  Quantity of Available Data  22  III.  Data Desception f o r F l i g h t s  24  IV.  Data Description for Airports  25  V.  Comparison of Calculated and C r i t i c a l Chi-Squared Values f o r F l i g h t s  VI.  37  Comparison of Calculated and C r i t i c a l Chi-Squared Values for Airports  40  VII.  Acceptance Rate by F l i g h t  43  VIII.  Acceptance Rate by Airport ( A l l Airports)  44  IX.  Acceptance Rate by Airport (Airports with Multiple Flights Only)  X.  Comparison of Actual and Predicted 90th Percentiles for F l i g h t s  XI.  47  Comparison of Actual and Predicted 90th Percentiles for Airports  XII.  45  48  Average Differences between Actual and Predicted 90th Percentiles  49  XIII.  V i s u a l Inspection of Histograms f o r F l i g h t s  51  XIV.  Visual Inspection of Histograms for Airports  52  ACKNOWLEDGEMENTS  I wish to express my thanks to Professor G.R. Brown for h i s guidance throughout this t h e s i s .  I would also l i k e to thank the Terminal Services s t a f f of Transport Canada's P a c i f i c Region Airports Branch who made the study possible.  1 1.  INTRODUCTION  1.1  Statement of the Problem Expenditure for the design and construction of airport terminals i s  considerable.  Even though regional airports are not as large as the  international and national airports they connect to, the amount of c a p i t a l and time involved can s t i l l be s i g n i f i c a n t . For example, the expansion of the a i r terminal complex at Castlegar, B r i t i s h Columbia i s expected to cost approximately  $6 m i l l i o n .  Of t h i s ,  $2.5 m i l l i o n w i l l be spent to enlarge and renovate the terminal building with Che remaining $3.5 m i l l i o n going to parking l o t reconstruction, relocation of services and design fees. in 1981  The planning of the project began  and completion i s expected to be i n 1987.  The fact that the design  and construction w i l l take s i x years i l l u s t r a t e s the magnitude of the e f f o r t involved. The purpose of t h i s study was processes of a i r terminal design.  to improve the input to the a n a l y t i c a l  The p a r t i c u l a r input looked at was  number of passengers expected to occupy small terminals. of passengers  the  A i r l i n e records  enplaning and deplaning for each f l i g h t were used to  determine the number of passengers  expected.  The study looked at the frequency d i s t r i b u t i o n curves of the f l i g h t volumes.  Knowledge of the shape of these d i s t r i b u t i o n s w i l l help the  terminal design process.  For example, a peak volume (such as the 90th  percentile) can be calculated and used as a design c r i t e r i o n . A l t e r n a t i v e l y , the f u l l d i s t r i b u t i o n can be used f o r simulation models which randomly sample from the expected values.  With this more accurate  representation of passenger occupancies, the terminal design w i l l be more efficient.  1.2  2  Approach Records of the number of passengers getting on and off of a i r c r a f t  were  collected from small regional airports.  frequency d i s t r i b u t i o n s .  They were compiled  into  A common s t a t i s t i c a l d i s t r i b u t i o n model was  then  found which would adequately describe the actual data so that i t could be used f o r the design of terminals. When passenger volume data i s used f o r terminal design, i t i s t y p i c a l l y i n one of the following forms:  (1)  design hour volume of passengers;  (2)  design f l i g h t load;  (3)  d i s t r i b u t i o n of expected  (4)  d i s t r i b u t i o n of expected f l i g h t loads;  (5)  design daily pattern of passenger volumes, or  (6)  design d a i l y f l i g h t  passengers;  schedule.  If the passenger volumes (and f l i g h t load volumes) are described by a model d i s t r i b u t i o n , the values to be used f o r the terminal design can be better  determined. In t h i s work, the data used to determine expected passenger volumes  at the terminal was  f l i g h t load data.  The individual observations are the  number of deplaned and enplaned passengers of one f l i g h t stop.  In other  words, each data point Is the sum of a l l of the passengers getting o f f of the airplane when i t arrives at the a i r p o r t , and a l l those boarding the airplane as i t departs. " f l i g h t event".  These two movements w i l l be designated as one  A l l airports i n the study have one a r r i v a l and  one  departure association with each event - that i s , the f l i g h t routes do not originate or terminate at these p a r t i c u l a r s i t e s .  3 These airports have only a few major f l i g h t events d a i l y , and f o r each, the a r r i v a l and departure occur within the space of a half-hour. For these reasons, the passenger volumes of a f l i g h t event are equivalent to half-hourly volumes.  This s i m p l i f i e s the analysis since f l i g h t event  volumes can be measured to d i r e c t l y determine design volumes f o r planning. The f l i g h t events are grouped together into years, such that a " f l i g h t " w i l l be defined as the t o t a l of a l l of the f l i g h t events that occur, at the same time of the day over the course of one year. there w i l l be 366 or less f l i g h t events i n one f l i g h t .  This means  Since the volumes  of passengers involved i n each f l i g h t event vary over the year, each f l i g h t w i l l have a certain d i s t r i b u t i o n of the frequency of occurrence of the f l i g h t volumes. To derive hourly planning volumes, however, a l l hours with a c t i v i t y must be compiled f o r the year.  Therefore, as a second step, a l l events of  a l l f l i g h t s at an airport w i l l be combined to form another frequency distribution. This, then, w i l l be the data under study - i n d i v i d u a l f l i g h t s and f l i g h t s compiled at each a i r p o r t .  Each d i s t r i b u t i o n w i l l be formed into a  histogram so that i t can be compared to t h e o r e t i c a l s t a t i s t i c a l models. O r i g i n a l l y , nine possible d i s t r i b u t i o n models were considered: (1)  Binomial  (2)  Polsson  (3)  Normal  (4)  Gamma or Erlang  (5)  Weibull  (6)  Lognormal  4 (7)  Negative Binomial  (8)  5th Degree Polynomial  (9)  Beta  Of these, three were selected for further study: Poisson and Lognormal. c a l i b r a t e , and to apply.  the Normal,  The three are r e l a t i v e l y simple to understand,  to  They also appeared to reasonably represent the  shape of the observed d i s t r i b u t i o n s .  Table I shows some of the  d i s t r i b u t i o n s used by a i r l i n e s and a i r c r a f t  manufacturers.  Both quantitative and q u a l i t a t i v e methods were used to select the d i s t r i b u t i o n which would best r e p l i c a t e the actual data.  A computer  performed the most of quantitative work by doing two things. Chi-squared  F i r s t , the  s t a t i s t i c was calculated for each d i s t r i b u t i o n model and  compared to the t h e o r e t i c a l Chi-squared values.  This comparison  determined  i f the model provided a s t a t i s t i c a l l y s i g n i f i c a n t f i t . The second application of the computer was to measure the a b i l i t y of each model to accurately predict the behaviour of the upper t a i l (the right hand end) of the d i s t r i b u t i o n .  This i s p a r t i c u l a r l y useful i n the  determination of peak design volumes.  Actual and predicted 90th percentile  volumes were calculated to measure the t a i l  behaviour.  The t h i r d c r i t e r i o n used to evaluate the three models was more subjective.  It involved v i s u a l l y inspecting each observed and  expected  histogram and ranking each model according to i t s a b i l i t y to reproduce observed  the  data.  F i n a l l y , the s e l e c t i o n of the best model was based on i t s a b i l i t y to be understood  and to be applied.  5  TABLE I  D i s t r i b u t i o n Models Used by A i r l i n e s and A i r c r a f t Manufacturers  Distribution  Users  Binomial  Quantas (business and 1st classes)  Polsson Normal  United A i r l i n e s , Boeing, Lockheed, KLM, Quantas (economy class) Pan American, A i r Canada  Gamma/Erlang  Swiss A i r  Weibull  American  Lognormal  McDonnell-Douglas  Negative Binomial  B r i t i s h Airways  5th Degree Polynomial  Lufthansa  (now switched to Rayleigh)  Beta (empirical model)  Source:  References  Cathay  - Lauehli *, 11  Pacific  V e l l a , et a l  2 2  ;  Wang ; 2<+  Soumis et a l  6  2.  LITERATURE REVIEW An airport terminal i s a transfer point between ground and a i r  transportation systems.  By most d e f i n i t i o n s , the a i r terminal includes the  building structure, the roadway curb, the station platform i f the a i r p o r t i s served by t r a n s i t , and the a i r c r a f t apron.  The flow between ground and  a i r i s shown schematically In Figure 1. The purpose of the a i r terminal i s to aid this transfer between ground and a i r and also, i n the case of connecting passengers, between a i r and air.  Although the system of pedestrian movement i s complex, the transfer  must be done as quickly, as comfortably and as e f f i c i e n t l y as possible. Planning an a i r terminal i s a complicated and usually lengthy process. Careful design w i l l be even more c r i t i c a l as c a p i t a l funds are reduced a premium i s placed on the space available. planning process i s given i n Figure 2.  and  A t y p i c a l framework f o r the  There i s , at present, no universal  procedure f o r the generation of terminal designs nor f o r the evaluation of proposed terminal concepts.  This i s not to say, of course,  methodologies do not e x i s t .  There are numerous ways to size f a c i l i t i e s and  to model the movement of pedestrians between them.  that  These w i l l be discussed  below.  2.1  A i r Terminal Sizing Planning of airport terminals incorporates the s i z i n g of t h e i r  f a c i l i t i e s and the arrangement of these f a c i l i t i e s within a building structure.  Some of these elements are mandatory stops f o r passengers;  others are optional.  Essential for processing are the t i c k e t i n g and bag  7 FIGURE 1  A i r p o r t Terminal Passenger Flows  Arriving  Departing  APRON AIRSIDE  Deplaning  Enplaning  TERMINAL BUILDING  Originating  Terminating  CURB  V  GROUNDSIDE  8 FIGURE 2  Terminal Planning Process  NEED IDENTIFIED  AVIATION FORECASTS  OPERATING POLICY  FACILITY SIZING  USER INPUT + FORECASTS OF COSTS AND REVENUES  LAYOUT CONCEPTS GENERATED  EVALUATION OF CONCEPTS  OPTIMIZATION AND SELECTION OF CONCEPT •  •  check-in counters, security checkpoints, holdrooms, gates and baggage claim devices.  Occasionally, some of these may be bypassed i f , f o r example, a  passenger has no checked luggage or i f t i c k e t i n g i s done on board the aircraft. Optional components vary from airport to a i r p o r t .  Some examples are  restaurants, washrooms, telephones, giftshops and banks.  Space i s also  provided f o r the o f f i c e s of a i r l i n e and airport employees as well as f o r e l e c t r i c a l and mechanical  utilities.  F a c i l i t i e s can be further divided into those used by enplaners ( t i c k e t i n g , holdroom) and those used by deplaners (baggage claim).  Figure  3 shows the basic passenger flow f o r a simple terminal layout. The function of terminal planners Is to balance the demands of passengers, a i r l i n e companies, government agencies, concessionaires and other airport users with the services to be supplied by the f a c i l i t i e s . Obviously, the objectives of these parties w i l l often c o n f l i c t .  There are,  however, three tenets that are geneally accepted as being fundamental to good design - that the terminal be f l e x i b l e , economic, and provide an acceptable l e v e l of service to the users. are:  ( 1 ) F l e x i b i l i t y to allow f o r : -  staged growth  -  new technology  -  unforeseen  circumstances  Some facets of each of these  10 FIGURE 3 Terminal F a c i l i t i e s  H0LDR00M  AIRLINE OFFICES/ CARGO AREA  SECURITY  GENERAL WAITING AREA  TICKETING/ CHECK-IN  CONCESSIONS/SERVICES  DEPLANING/ ARRIVING PASSENGERS  ENPLANING/ DEPARTING PASSENGERS  11 (2) Economic Optimization of: -  c a p i t a l costs  -  operations and maintenance costs  -  revenues  -  benefits to users (often intangible)  (3) Level of Service as Affected by: -  area per person  -  waiting times  -  walking distances (inside and outside;  -  temperature and  -  lighting  -  amenities  -  concessions  with and without bags)  humidity  (such as seating, no-smoking areas)  -  handling of disabled persons  -  information systems  In most terminal design methods, the space required for each function i s calculated on the basis of an expected peak occupancy.  The occupants  are each a l l o t t e d a certain area, the amount of which i s dependent upon the purpose of the area and upon some measure of personal comfort.  The  i s quantified into discrete categories known as Levels of Service.  latter For  example, at a given Level of Service each person i n the general waiting area may  be given 1.5 square metres of space but the occupants of the  holdroom would be deemed to need only 1.0 square metre.  For a reduced  Level of Service, these areas would be, say, 1.2 and 0.7  square metres  respectively.  12  The design occupancy i s either determined d i r e c t l y from a design volume or i s calculated by a model of the terminal flows.  In the former case,  the  number of passengers i n the area i s taken as a proportion of a design flight  volume, or of the airport's peak hourly design volume.  proportion i s based on h i s t o r i c a l patterns. are permitted  If greeters and  The well-wishers  i n the f a c i l i t y , the r a t i o of non-passengers to passengers i s  multiplied by the number of passengers to f i n d the t o t a l occupancy. This method of fixed proportions was Canada u n t i l a few years ago.  used extensively by  It i s the simplest way  f a c i l i t y space requirements, aside from using standard  Transport  of c a l c u l a t i n g terminal layouts.  For this reason i t i s s t i l l used, both i n Canada and the United States, when more advanced tools are unavailable or for preliminary There are d i f f i c u l t i e s , design volumes.  estimates.  however, with the use of t y p i c a l proportions of  De Neufville® explains this as being due to the method not  incorporating the stochastic features of the movements through the terminal. Models which incorporate pedestrian flows are better able to predict the dynamic nature.  They can also point out c r i t i c a l areas of  congestion  (often the t i c k e t i n g area and the bag claim area). Flow models are t y p i c a l l y used to evaluate proposed layouts.  They do  not generate layouts, which i s a largely subjective process, although attempts have been made to quantify i t . developed two indices to catalogue  For example, Braaksma and Ramsey  terminal layouts.  Braaksma also  developed a computerized method of creating preliminary layouts. 3  There are b a s i c a l l y four categories of a n a l y t i c a l methods f o r analyzing terminal flows (based on H o r o n j e f f ) : 12  5  13  (1) Network Models Network models i l l u s t r a t e the airport functions and describe t h e i r Interrelationship i n the processing system.  Once the processing times  of each l i n k and the passengers' paths through the network are known, the t o t a l t r i p time can be estimated.  Analysis of the network can  i d e n t i f y c r i t i c a l links that a f f e c t the entire system.  Braaksma  applied a CPM network model to evaluate passenger delay (Simulating the Turnaround Operation of Passenger A i r f r a c t using the C r i t i c a l Path Method, University of Waterloo, 1970).  This approach does not consider  the volume of passengers t r a v e l l i n g on any l i n k or path.  It does not  assign passengers to paths, predict the effects of queue building nor model random behaviour. (2) Queueing Models Entrance and exit queueing models can be developed f o r each f a c i l i t y . Standard formulae can not be used because the demand i s not steady, but builds up and dissipates with each f l i g h t .  The f a c i l i t i e s have to be  analyzed i n the order i n which passengers go through them.  For  example, an analysis of the t i c k e t counter could use a cumulative d i s t r i b u t i o n curve of passenger a r r i v a l times and the average service rate of the t i c k e t i n g agents.  Both would be plotted.  The queue length  and waiting times would then be determined graphically from the differences i n the curve. Horonjeff*  2  (Queueing models are well-explained by  and de N e u f v l l l e ) . 8  Ashford and Wright  1  describe the  d i f f i c u l t y with these models when several f a c i l i t i e s are linked together i n chains:  the mathematics may become lntactable when random  a r r i v a l s and exponential service times are incorporated.  ( 3 ) Simulation Models These aire computer models which can provide very detailed information, but can be expensive to run.  By d e f i n i t i o n their inner workings cannot  be explained by simple equations and so can be d i f f i c u l t to validate. An example i s the Vancouver Airport Simulation Model models operate on a projected f l i g h t schedule.  2 1  .  Simulation  Passenger a r r i v a l  r a t i o , processing rates, walking speeds and passenger routes are also input the variables may be fixed, or the model may randomly select them from a d i s t r i b u t i o n .  By i t e r a t i o n , the movement of a l l persons  throughout the day are found producing computations of delays, t r a n s i t time, and occupancies. ( 4 ) Hydraullc/Hydrologic Models This i s a r e l a t i v e l y new type of model f o r terminals which assumes pedestrians behave i n a manner similar to f l u i d flow.  Ramsey and  H u t c h i s o n ^ used a flood flow analogy and found i t less expensive than the Vancouver Airport Simulation Model.  Their model routes passengers  through the system i n the way i n which a storm proceeds through the various reaches of a r i v e r .  As input, a daily schedule i s required  which i n i t i a t e s the "storms" of passengers and determines the volume of passengers flowing through the terminal.  Resistance c h a r a c t e r i s t i c s of  the processors and links as w e l l as the desired l e v e l of service are also required model inputs. There are obvious benefits to the use of these models.  Once set-up,  they can be repeated i n order to evaluate proposed layouts and to examine t h e i r s e n s i t i v i t y to variations i n input. or only a part of i t .  They can model the entire system  15  Like a l l a n a l y t i c a l methods, terminal models are only as useful as the information input into them, which t y p i c a l l y includes: ( 1 ) c h a r a c t e r i s t i c s of passengers, non-passengers and baggage; (2)  a i r c r a f t types and c h a r a c t e r i s t i c s ;  ( 3 ) a c t i v i t y l e v e l s of passengers and  aircraft;  ( 4 ) rates of a r r i v a l , usually i n r e l a t i o n to f l i g h t  times;  ( 5 ) processing and flow rates; and ( 6 ) the variations of a l l of the above factors over the course of the This information may  be d i f f i c u l t , i f not impossible to obtain.  day. Survey  information such as found by the extensive surveys done i n the Canadian Airports System Evaluations , can be used for model input. A l t e r n a t i v e l y , 4  a survey can be used d i r e c t l y to determine f a c i l i t y occupancy but since a survey can only be done for a few days, the results may  not be  representative. These are the usual methods of airport terminal s i z i n g . above, peak occupancies  As explained  are determined from design volumes or from models.  The areas are calculated by multiplying the number of occupants by a given unit area.  Some i t e r a t i o n may  be necessary since the size of an area w i l l  a f f e c t the t r a v e l times through i t and, therefore, the flows. In an e f f o r t to simplify design Transport Canada i s now layouts f o r a l l new  terminals.  using  standard  The process i s called the Systemized  Terminal Expansion Program, or STEP . 20  The purpose of the program i s to  avoid r e p e t i t i o n of the design process since the requirements of small terminals tend to be similar.  It also speeds the selection, review, and  approval processes, as well as the preparation of the contract drawings. Furthermore, by incorporating a pre-planned expansion c a p a b i l i t y ,  16  terminals are able to adjust to changing t r a f f i c conditions, which are often d i f f i c u l t to forecast at small s i t e s . The design year f o r STEP buildings i s the year of opening, although the chosen size must s u f f i c e for three years.  By minimizing the time to the  design year, there i s more certainty i n forecasting the requirements.  The  lifespan of three years was chosen to balance the added cost of expansion with the savings made by delaying the construction. O r i g i n a l l y , the selection of a STEP terminal was based upon s i x criteria:  (1) Total Annual Passengers This i s an e a s i l y obtained s t a t i s t i c which gives a general Indication of the airport size.  However, i t i s too broad to be of use i n f a c i l i t y  sizing.  (2) Planning Volume This hourly volume would more accurately r e f l e c t the demand made on the facilities.  I t i s not yet o f f i c i a l l y defined for small a i r p o r t s , but  the 90th percentile (of a l l hours with t r a f f i c ) has been used. Complete data i s d i f f i c u l t to c o l l e c t , however, for small a i r p o r t s .  (3) C r i t i c a l  Aircraft  The largest scheduled a i r c r a f t also gives a reasonable idea of demand on the terminal. usually the Boeing  (In B r i t i s h Columbia, the c r i t i c a l a i r c r a f t i s 737).  (A) Daily Movements of C r i t i c a l  Aircraft  This also provides an e f f e c t i v e demand measure.  17 (5) Involvement R a t i o The  involvement r a t i o s i s defined  as the r a t i o of the  passenger volume to the a i r c r a f t ' s a v a i l a b l e s e a t s . w e l l measured - e s p e c i a l l y f o r m u l t i - s t o p  flight  airport's It i s also  not  routes.  (6) Maximum Passenger Loads T h i s i s the l a r g e s t l o a d of e i t h e r e n p l a n i n g o r d e p l a n i n g p a s s e n g e r s . It i s neither  The  commonly used nor measured.  problem w i t h the use  of m u l t i p l e  c r i t e r i a was  t h a t one c r i t e r i o n  might i n d i c a t e a d i f f e r e n t STEP s i z e t h a n the o t h e r s d i d .  T h i s o f t e n made  s e l e c t i o n of a s i z e a m a t t e r of judgement. To  s i m p l i f y the p r o c e s s o f s e l e c t i o n , the l a t e s t d r a f t (1983) of  STEP P l a n n i n g and  Design M a n u a l  based on a h a l f - h o u r l y  proposes t h a t the e n t i r e s e l e c t i o n  2 0  d e s i g n volume o f p a s s e n g e r s .  v a l u e o r i n i t s f o r e c a s t i n g can  by  T h i s approach p l a c e s a g r e a t d e a l  emphasis on a s i n g l e d e s i g n v a l u e .  be  A g a i n , t h e r e i s no  o f f i c i a l d e f i n i t i o n of t h i s volume, a l t h o u g h the 90th p e r c e n t i l e passenger volume i s o f t e n used.  the  An e r r o r i n the measurement of  of the  l e a d t o an erroneous STEP s e l e c t i o n .  example, an e r r o r of the o r d e r of magnitude of ten passengers above  For the  a c t u a l h a l f - h o u r l y volume would cause s e l e c t i o n of a STEP 6 t e r m i n a l , when a STEP 5 would have been s u f f i c i e n t . More r e s e a r c h i n t o the b e h a v i o u r of small terminal  f l i g h t l o a d s s h o u l d improve the a c c u r a c y of d e s i g n volume  c a l c u l a t i o n s and,  2.2  therefore,  the s e l e c t i o n of a p p r o p r i a t e b u i l d i n g s i z e s .  D e s i g n Volume D e t e r m i n a t i o n There are a m u l t i t u d e of d e s i g n volumes f o r p a s s e n g e r s .  Statistics  18  can describe annual, d a i l y or hourly volumes.  They can be c l a s s i f i e d by  o r i g i n and destination or by enplanement and deplanement.  These can be  further broken down into major c a r r i e r , charter, domestic, transborder or international categories. Terminal design i s usually based on a peak hourly design volume.  Half-  hourly and six-hourly periods are also used. Definitions of what constitutes the peak hour abound. suggests that a planner simply select a reasonable volume. Federal Aviation A u t h o r i t y of a t y p i c a l week.  1 3  Horonjeff  11  The American  suggests the busiest hour of the busiest day  Although American airports are not guided by a single  body, many seem to favour the use of a percentage of either the annual total  8  or the average day of the busiest month . 19  Other d e f i n i t i o n s  proposed include the peak hour of the average weekday i n the busiest quarter and the nth highest hour of a l l hours of the year. U n t i l recently Transport Canada percentile d e f i n i t i o n .  17  has used an hour or half-hour  For larger a i r p o r t s , the accepted planning volume  was the 90th percentile of the annual d i s t r i b u t i o n of passengers.  This  more s t a t i s t i c a l approach r e l i e s on the prediction of the upper t a i l of a d i s t r i b u t i o n curve.  In the absence of complete data, some assumptions must  be made as to the form of this curve. Some terminal design procedures r e l y heavily on the hourly (or h a l f hourly) design volume.  For example Transport Canada's STEP method uses i t .  Simulation models may or may not make use of i t .  Most of them simulate  a c t i v i t y over the course of eighteen or twenty-four hours, and so require d a i l y input instead (such as a f l i g h t schedule or the passenger/nonpassenger r a t i o for each hour of the day).  19 Some o f t h e i n h e r e n t f e a t u r e s o f b a s i n g t e r m i n a l d e s i g n on t h e h o u r l y d e s i g n volume a r e l i s t e d below.  T h i s c o m p i l a t i o n i s based on t h e comments  of B r a a k s m a , de N e u f v i l l e , H o r o n j e f f , and H a m z a w i . 3  8  1 2  19  (1) no commonly agreed upon d e f i n i t i o n ; (2) v e r y dependent upon a i r c r a f t s i z e , s c h e d u l e and r o u t i n g ; (3) s t a t i s t i c does not i n c o r p o r a t e s t o c h a s t i c v a r i a b i l i t y o f t h e queueing process; (4) does n o t r e f l e c t i n d i v i d u a l a i r p o r t c h a r a c t e r i s t i c s such as t y p e o f t r a v e l l e r (commuter, v a c a t i o n e r ) o r catchment a r e a s i z e ;  and  ( 5 ) n o t d i r e c t l y u s e f u l f o r many computer s i m u l a t i o n s .  2.3  Passenger D i s t r i b u t i o n  Functions  T r a n s p o r t Canada has h i s t o r i c a l l y assumed t h a t f l i g h t l o a d s a t s m a l l airports are normally d i s t r i b u t e d . convenience  T h i s s e l e c t i o n has been made f o r  o n l y , s i n c e i t has a l s o determined  b e s t model f o r a l l cases.  t h a t t h e Normal i s n o t t h e  T r a n s p o r t Canada i s o f t h e o p i n i o n t h a t each  airport follows a different d i s t r i b u t i o n . A i r l i n e s (and t h e manufacturers  who s e l l a i r c r a f t t o them) have a  d i f f e r e n t approach t o t h e s t u d y o f passenger l o a d s . interested  They a r e more  i n t h e number o f o c c u p i e d s e a t s i n t h e a i r c r a f t than i n t h e  passenger volumes a t t h e a i r p o r t s . A i r l i n e s use a d i f f e r e n t c o m b i n a t i o n o f t h e volumes. Canadian P a c i f i c ' s V a n c o u v e r - T e r r a c e - P r i n c e a i r l i n e might be i n t e r e s t e d  F o r example, i n  Rupert-Vancouver f l i g h t , t h e  i n knowing t h e p r o b a b i l i t y o f f i l l i n g t h e s e a t s  on t h e second l e g - between T e r r a c e and P r i n c e Rupert.  Since there i s  v i r t u a l l y no T e r r a c e t o P r i n c e R u p e r t t r a f f i c , t h i s would be t h e t o t a l o f  20 those going from Vancouver to Prince Rupert (Prince Rupert's deplaners) and those going from Terrace to Vancouver (Terrace's enplaners).  Therefore,  the number of seats occupied  two  i s the r e s u l t of th summation of  independent randomly distributed variables.  It Is desirable, therefore for  an a i r l i n e to use a d i s t r i b u t i o n form which i s additive - that i s , the summation takes the same d i s t r i b u t i o n form as the parts. Of course, this would be only one reason f o r an a i r l i n e to select a p a r t i c u l a r d i s t r i b u t i o n , since i t i s only one use for the d i s t r i b u t i o n . Lauchli  1 4  selected the Erlang function during research for Swiss A i r to  determine optimal seating configurations of a i r c r a f t . Whale  22  continued  V e l l a , Martin  and  this work f o r Quantas A i r l i n e s but decided that the  normal and binomial d i s t r i b u t i o n s produced better r e s u l t s .  Wang  24  used an  empirical d i s t r i b u t i o n function to determine booking levels f o r Cathay P a c i f i c ' s long haul f l i g h t s . The behaviour aboard the a i r c r a f t , which interests the a i r l i n e s , i s obviously related to a c t i v i t y at the a i r p o r t s , which i s of interest i n this work.  For example, the a v a i l a b i l i t y of seats l i m i t s the number of  passengers that may  board the a i r c r a f t .  Also, a second f l i g h t may  be  warranted at a c e r t a i n point, even though the increase i n demand i s occurring at another stop i n the f l i g h t  route.  Because of this close i n t e r a c t i o n , the frequency d i s t r i b u t i o n s that the a i r l i n e s and the a i r c r a f t manufacturers have selected for use are of interest for airport terminal s i z i n g .  3.  METHODOLOGY  3.1  Data Description The f l i g h t load volumes came from eight airports i n B r i t i s h  Columbia.  They were o r i g i n a l l y released by the a i r l i n e c a r r i e r s to Transport Canada i n order to a s s i s t i n the planning of airport terminal buildings.  Although  the carriers are not obliged to release this Information, they did so to ensure reasonable s i z i n g of the f a c i l i t i e s which they w i l l be leasing and to promote co-operation with the government.  The data was not, however,  meant to be used p u b l i c l y so the airports have been designated by l e t t e r s (A through H). A l l of the f l i g h t s occurred between 1978 and 1982 at airports with three j e t stops or less each day. A l l f l i g h t s were served with Boeing 737 jets. The l i s t of airports i n Table I I i l l u s t r a t e s the years and f l i g h t s of the available data. As described e a r l i e r , the term " f l i g h t event" w i l l be used f o r the sum of the deplaned and enplaned passengers during a single v i s i t of an aircraft.  A " f l i g h t " w i l l be the t o t a l of a l l f l i g h t events that occur  over the course of one year at the same time of day. Therefore, each f l i g h t w i l l contain 366 f l i g h t events or l e s s . F l i g h t events cancelled due to poor weather (a very common occurrence) were excluded.  Also not considered were f l i g h t s which ran f o r  only a portion of the year.  This meant that a d i s t r i b u t i o n of a l l airport  a c t i v i t y could not be assembled  f o r Airport H since i t had several f l i g h t s  which ran In the summer only. The c h a r a c t e r i s t i c s of f l i g h t events at small airports have simplified the analysis.  Volumes of deplaned and enplaned passengers are  22  TABLE I I  Quantity of Available Data  Airport Designation  Number of Years of Data  Flights  Total Number  per Year  of F l i g h t s  A  1981  2  2  B  1978 to 1982  3  15  C  1980, 1981  2  4  D  1979, 1980  1  2  E  1979, 1980, 1982  1  3  F  1980, 1981  1  2  G  1981, 1982  3  6  H  1980 to 1982  1  3  37 F l i g h t s  equivalent to half-hourly volumes because the f l i g h t turnarounds are less than t h i r t y minutes and because the f l i g h t s are separated from each other. Furthermore, there are no connecting or t r a n s i t i n g passengers to account for. The prevalence of triangular routing has been mentioned.  A l l of the  airports i n this study are part of such routes - most of which originate or terminate i n Vancouver.  The routes with both stops included i n t h i s study  are:  and  Vancouver  -  A  -  C  -  Vancouver;  Vancouver  -  F  -  G  -  Vancouver (or reverse);  Vancouver  -  H  -  D  -  Vancouver.  The raw data was assembled  and entered into APL computer language,  such that each f l i g h t was a vector. 361 elements.  The f l i g h t vectors have from 137 to  Each element i s a f l i g h t event.  To analyze d i s t r i b u t i o n s f o r airports with more than one f l i g h t , the f l i g h t vectors for that year were concatenated. The descriptive d e t a i l s of these variables are given i n Tables I I I and IV. When arranged into frequency classes, the histograms had a right skew.  3.2  A good model should reproduce this  tendency.  Features of the Distributions Three model d i s t r i b u t i o n s w i l l be compared to the observed data.  A  more informed selection can be made i f the c h a r a c t e r i s t i c s of each one are understood. The Normal or Gaussian i s the most widely used of a l l frequency distributions.  Its formula i s :  24 TABLE I I I Data Description f o r F l i g h t s Airport  Flight  Number of F l i g h t Events  A  Al A2  292 358  18,957 32,694  1981 1981  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 Bl4 B15  137 247 258 287 222 259 291 274 279 167 339 291 273 294 291  12,629 28,167 32,201 30,809 21,059 17,813 24,884 26,074 25,726 16,154 39,195 34,316 34,359 16,519 30,682  1978 1979 1980 1981 1982 1978 1979 1980 1981 1982 1978 1979 1980 1981 1982  C  CI C'2 C3 C4  332 196 317 357  15,388 12,010 13,225 19,816  1980 1980 1981 1981  D  DI D2  328 352  23,857  1979 1980  E  El E2 E3  361 360 354  36,607 42,031 29,899  1979 1980 1982  F  Fl F2  344 358  36,941 40,427  1980 1981  G  Gl G2 G3 G4 G5 G6  344 352 313 328 343 329  13,995 28,758 44,647 13,964 27,324 43,684  1981 1981 1981 1982 1982 1982  H  HI H2 H3  355 328 331  30,790 28,664 24,705  1980 1981 1982  Total Number of Passengers  Year  25 TABLE IV Data Description for Airports Airport  Year  A  1981  B  1978 1979 1980 1981 1982  C  1980 1981  D  Combination of F l i g h t s  Total Number of Passengers  650  51,651  735 829 548 860 680  69,637 87,367 60,455 73,054 67,895  CI + C2 C3 + C4  528 674  27,398 33,041  1979 1980  Dl D2  328 352  23,857  E  1979 1980 1982  El E2 E3  361 360 354  36,607 42,031 29,899  F  1980 1981  Fl F2  344 358  36,941 40,427  G  1981 1982  1009 1000  87,400 84,972  H  Al + A2  Number of F l i g h t Events  Bl B2 B3 B4 B5  + + + + +  B6 B7 B8 B9 B10  + + + + +  Bll B12 B13 B14 B15  Gl + G2 + G3 G4 + G5 + G6  26  f  (  x  )  = _ J  e  x  [_  p  I  (11H)2]  0" / 2 TT  i U = mean - parameter approximated by E — where n = number of data X  points.  ( i -x) a = variance - parameter approximated by E — X  2  x = variable value.  The normal i s a continuous d i s t r i b u t i o n function that i s symmetrical about i t s mean. measurements.  It i s commonly used to describe variations i n physical  The sum of two normally distributed variables i s also  normally distributed.  This term f o r this feature i s additive regenerative.  The formula for the Poisson d i s t r i b u t i o n i s :  P(r, -  ^  r = discrete variable value X  i  u = mean = variance - parameter approximated by E —— approximated. It i s used for such things as determining the number of accidents i n a given time i n t e r v a l . parameter (u) increases. regenerative.  It has a right skew, but this decreases as the The Poisson d i s t r i b u t i o n i s also additive  27 The lognormal d i s t r i b u t i o n has the logarithm of i t s variable values distributed normally. i s possible.  Natural logarithms are usually used but another base  The function f o r a base ten lognormal d i s t r i b u t i o n i s :  X  f(x) =  X  .4343  "727 exp xa., log  r  1  [- j  /  l  o  g  i o  (  (  x  /  t  log  l  x  )  )J Z  The lognormal i s a highly f l e x i b l e d i s t r i b u t i o n which skews to the r i g h t . It i s not regenerative by addition, however, but by m u l t i p l i c a t i o n .  That  i s , the m u l t i p l i c a t i o n of lognorraally distributed variables i s also lognormal but the addition of them i s not.  3.3  Procedure After the data was assembled, an APL computer program (owned by I.P.  Sharp Associates) formed each vector into a frequency d i s t r i b u t i o n .  The  parameters of each of the three model d i s t r i b u t i o n s were calculated from the data, and the program compared the expected, curves to those of the observed data.  The three quantitative methods used to make the comparison  were:  i)  the "goodness-of-fit", as measured by the Chi-Squared  li)  the a b i l i t y of the model to predict the t a i l of the d i s t r i b u t i o n , as measured by the 90th percentile;  ill)  ranking of the models by v i s u a l Inspection.  statistics;  28 The quantitative procedures used are outlined i n this chapter. Discussion of the two q u a l i t a t i v e selection c r i t e r i a - the a b i l i t y of the models to be e a s i l y understood and t h e i r a p p l i c a b i l i t y - has been deferred u n t i l the next chapter. Three sources of uncertainty inherent i n any c u r v e - f i t t i n g are:  i)  the natural v a r i a t i o n of the data due to i t s randomness (due to unknown factors);  ii)  the s t a t i s t i c a l f a i l u r e to e f f e c t i v e l y estimate the parameters  from  the data; ill)  the fact that a given model Is poor f o r describing the curve.  Only the l a t t e r two sources can be minimized with a larger sample. The data had to be grouped into intervals and the expected and observed frequencies of each i n t e r v a l studied.  A cumulative d i s t r i b u t i o n form would  have eliminated the need to use i n t e r v a l s , but the APL program used was not able to construct i t . One inherent feature of histograms i s that each i n d i v i d u a l i n t e r v a l has a certain probability of matching the frequency that the model has predicted f o r i t .  Even i f the model i s a good one, a perfect f i t over a l l  i n t e r v a l s , while being the most l i k e l y event, i s s t i l l not very l i k e l y . the number of i n t e r v a l s increases, a perfect f i t becomes more rare.  As  If  fewer intervals are used, f i t t i n g the data to the model i s more l i k e l y . However, i f several models are under consideration, more of them w i l l f i t . This makes a selection d i f f i c u l t . needed.  Therefore, some sort of trade-off i s  29  Secondly, histogram class d i v i s i o n s should t h e o r e t i c a l l y be made so that the number of data points i s the same i n each.  For example, the  region of higher frequency w i l l have narrower i n t e r v a l s .  Even though this  i s s t a t i s t i c a l l y preferable, variable Interval widths are not commonly used. In any case, the APL program used had limited f l e x i b i l i t y .  It was a  standard s t a t i s t i c a l program and could only accept equal band widths. band width of ten was selected f o r a l l d i s t r i b u t i o n s .  A  This meant that the  number of divisions ranged from 10 to 27, according to the spread i n data values. The APL program used f o r the Normal and Poisson d i s t r i b u t i o n s i s shown i n Appendix A.  It i s an Interactive program which requests end  points and the class width from the user.  It then requires a s e l e c t i o n as  to whether the Normal or Poisson d i s t r i b u t i o n i s to be f i t to the data. O r i g i n a l l y , the lognormal curve f i t t i n g was done by taking the logarithm of each data point and then running the standard program with the Normal option. was  This approach proved to be unsatisfactory since the scale  the data logarithm.  The histogram intervals could not be compared to  those of the Normal and Poisson. A new program was written f o r the lognormal i n order to permit d i r e c t comparison.  It Is similar to the standard program (although less refined)  and i s l i s t e d i n Appendix A.  The body was written by the author (LN  program) but the histogram p l o t t i n g function (HISTO and CLASSIFY) were written by I.P. Sharp Associates. The three quantitative c r i t e r i a used were: model;  the s t a t i s t i c a l f i t of the  the a b i l i t y of the model to predict a design volume;  o v e r a l l f i t of the model as judged by a v i s u a l inspection.  and the  30 3.3.1-  Goodness-of-Fit C r i t e r i o n The Chl-Squared  s t a t i s t i c i s produced by the program as a measure of  the "goodness-of-fit" of the model.  I t i s used to decide whether or not a  d i s t r i b u t i o n should be retained or rejected.  The Chi-Squared  statistic i s  not meant to be used to choose among models. The d e f i n i t i o n i s :  k  (o, - e . )  x =I  \  2  1=1  where  6  2  1  i  o^ = observed  frequency  e^ = expected  frequency  i  = index of i n t e r v a l  The calculation should only be performed when the expected frequency of each i n t e r v a l i s at least f i v e , otherwise distortions can occur. For frequencies less than f i v e , intervals should be combined.  The programs d i d  not do t h i s , so the Chi-Squared value was hand-corrected by the author. Original and corrected values are i n Appendix B. A few of the f l i g h t s could not have t h e i r Chi-Squared  values  corrected because the program did not display enough s i g n i f i c a n t figures. These f i v e f l i g h t s were omitted from further calculations. Use of the Chi-Squared values w i l l be discussed i n the next chapter. It should be noted, however, that several pieces of information have been obtained from the data.  As described i n Section 3.2, the Normal and  lognormal have two parameters (the mean and variance) and the Poisson has one (the mean).  These have been estimated by the average or the standard  31  deviation of the data (or i t s logarithm).  In addition, the t o t a l number of  f l i g h t events has been used to determine the expected frequencies.  The  degrees of freedom of each d i s t r i b u t i o n w i l l depend upon this information.  3.3.2  Design Volume C r i t e r i o n As previously mentioned, there are many d e f i n i t i o n s of the planning  design volume.  Knowledge of this d i s t r i b u t i o n w i l l allow for a more  informed decision as to which d e f i n i t i o n should be used. This study w i l l look at the 90th percentile of the f l i g h t events as a representation of the upper t a i l of the d i s t r i b i t i o n . percentiles were calculated from the observed data. written to derive the expected figures.  The actual 90th Short programs were  The Normal and lognormal were  written i n APL but the Polsson was written i n FORTRAN.  They are l i s t e d i n  Appendix A. The other percentile d e f i n i t i o n used f o r large Canadian a i r p o r t s .  It  i s the 90th percentile by passenger volume - that i s , 10 percent of the passengers w i l l experience congestion.  This i s i n contrast to the above  percentile d e f i n i t i o n which would allow 10 percent of the f l i g h t s to be above i t and thus experience congestion.  The second d e f i n i t i o n could have  been used to measure the upper t a i l p r e d i c t a b i l i t y , but i t i s d i f f i c u l t to calculate and i s usually only s l i g h t l y higher from the 90th percentile by passenger event.  Figure 3 i l l u s t r a t e s the 90th percentiles by passenger  volume load were calculated f o r comparison purposes. One other d e f i n i t i o n of the planning design volume Is also included. This i s based on the average load factor and i s calculated by adding f i f t e e n percent to the mean load factor and multiplying this by the t o t a l number of a r r i v i n g and departing seats available:  32 [mean  l o a d  f a c t o r  +  the  l o a d  f a c t o r  Is  Because  f o r  a  B o e i n g  [(mean L  =  (mean  737  w i t h  117  d e p l a n e d  +  15%]  the  x  [//arrival  p r o p o r t i o n  s e a t s  t h i s  e n p l a n e d  2  x  117  d e p l a n e d  +  e n p l a n e d  and  of  d e p a r t u r e  a v a i l a b l e  e x p r e s s i o n  p a s s e n g e r s )  s e a t s  +  1  5  j  x J  p a s s e n g e r s )  s e a t s  r e d u c e s  >  + 3 5 .  s e a t s ]  [ L  2  that  are  t o :  x  117  s e a t s ] J  u s e d ,  33 FIGURE 3  90th Percentile by F l i g h t Event and by Passenger Volume  "x A  x  l  x  2  Deplaned + Enplaned Passenger Loads  90th percentile by f l i g h t event  x = 2  90th percentile* by passenger volume 00  10 percent of f l i g h t s  [ / X  00  f(x)dx = .10 x / f(x)dx]  l 00  00  10 percent of passengers [ / x f(x)dx = .10 x J xf(x)dx]  34 3.3.3  Visual Inspection C r i t e r i o n  This somewhat judgemental method of histogram selection was included to ensure that there was some measure of the reasonableness of each model. It also allowed for detection of any unexpected deviations i n the data or any trends i n the c u r v e - f i t t i n g . Since a l l histograms have equal Interval width, a v i s u a l comparison was given a ranking from best to worst and the results t o t a l l e d .  The  rating was made on the basis of how the model matched the o v e r a l l shape of the curve without trying to duplicate the Chi-Squared or 90th percentile measurements.  35 4.  ANALYSIS  4.1  C r i t e r i a for Acceptance or Rejection  4.1.1  Goodness-of-Fit The Chi-Squared value was used to accept or reject a model  d i s t r i b u t i o n for each set of observed data.  The number of acceptances  among a l l of the f l i g h t s or a l l of the airports was then calculated as a percentage.  The s t a t i s t i c was not used d i r e c t l y to decide which of the  three model d i s t r i b u t i o n s best f i t one p a r t i c u l a r f l i g h t or a i r p o r t , since such comparisons are not i t s purpose. Acceptance of a model i s the " n u l l hypothesis".  This hypothesis  states that there i s no difference between the expected and observed curves that cannot be attributed to randomness.  It i s assumed that the n u l l  hypothesis i s true u n t i l i t has been proven otherwise.  The onus i s ,  therefore, to prove that a model should be rejected. To generate the proof, the c r i t i c a l value of Chi-Squared i s found from the theoretical Chi-Squared d i s t r i b u t i o n :  X  where  2 a, v  v = the degree of freedom (number of intervals less the number of parameters estimated from the data) a = the l e v e l of significance (area under the Chi-Squared curve, above c r i t i c a l value).  If the Chi-Squared value calculated from the observed and expected frequencies i s less than the c r i t i c a l Chi-Squared, the f i t i s a good one  36  and  the n u l l hypothesis i s true.  The specified l e v e l of significance (a) 2  i s equal to the p r o b a b i l i t y that the calculated Chi-Squared (x 2 exceed the c r i t i c a l value (x  a  y  ) will  ) even though the f i t i s a good one.  Therefore, there i s a p r o b a b i l i t y , a, of r e j e c t i n g a model that was, i n f a c t , a good f i t . In this study, the comparison was made at three d i f f e r e n t significance l e v e l s :  .05, .01, and .001.  As the l e v e l of significance  decreases, there i s more p r o b a b i l i t y of the model being accepted. due  This i s  to the reduction of the probability of rejecting the model, even though  i t f i t s the data.  This i s c a l l e d a Type I error.  But by lowering t h i s  probability, the chances of accepting a model that i s actually a poor one are increased - a Type I I error.  Therefore, a balance i s needed since  minimizing one type of error increases the probability of the other. types can be reduced, however, by increasing  Both  the sample s i z e .  In this analysis, the Chi-Squared i s not the only c r i t e r i o n for selection.  Therefore, the t o t a l number of acceptances can be compared at  the three significance levels without forcing a conclusive decision on t h i s c r i t e r i o n alone. The  calculated and c r i t i c a l Chi-Squared values are shown In Table V  for f l i g h t s and Table VI for a i r p o r t s . Table VII and VIII show the percentage of acceptance for each model at each s i g n i f i cance l e v e l .  The results of Table VII for the thirty—seven  i n d i v i d u a l f l i g h t s show that the lognormal model was a s t a t i s t i c a l l y good f i t to the data more often than the Normal or Poisson. When the f l i g h t s were combined to get yearly d i s t r i b u t i o n s by a i r p o r t , a l l three models f i t less often, although the lognormal was s t i l l s l i g h t l y more successful.  37  TABLE V (a) Comparison of Calculated  and C r i t i c a l Chi-Squared Values f o r F l i g h t s NORMAL  Airport  Flight  x (d • o.f)  X .05  x .oi  A  Al A2  19.6 ( 7) 29.5 (10)  14.1 18.3  18.5 23.2  20.3* 25.2  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  48.6 23.0 22.3 28.1 12.9 64.0 68.9 49.5 56.4 15.6 38.7 46.1 45.6 213.3 32.8  (11) (11) (12) ( 9) ( 8) (11) (12) (13) (11) (11) (14) (13) (15) ( 9) (12)  19.7 19.7 21.0 16.9 15.5* 19.7 21.0 22.4 19.7 19.7* 23.7 22.4 25.0 16.9 21.0  24.7 24.7* 26.2* 21.7 20.1* 24.7 26.2 27.7 24.7 24.7* 29.1 27.7 30.6 21.7 26.2  26.8 26.8* 28.3* 23.6 22.0* 26.8 28.3 29.8 26.8 26.8* 31.3 29.8 32.8 23.6 28.3  C  CI C2 C3 C4  21.8 12.7 10.2 53.0  ( ( ( (  9.5 11.1 7.8 11.1  13.3 15.1* 11.3* 15.1  14.9 16.8* 12.8* 16.8  D  Dl D2  5.1 ( 6) 13.3 ( 7)  12.6* 14.1*  16.8* 18.5*  18.5* 20.3*  E  El E2 E3  21.8 ( 8) 16.4 (13) t  15.5 22.4*  20.1 27.7*  22.0* 29.8*  F  Fl F2  4.7 (11) 41.0 (12)  19.7* 21.0  24.7* 26.2  26.8* 28.3  G  Gl G2 G3 G4 G5 G6  t t 20.1 12.7 9.9 21.8  (14) ( 5) ( 9) (14)  23.7* 11.1 21.0* 23.7*  26.1* 15.1* 26.2* 29.1*  31.3* 16.8* 28.3* 31.3*  HI H2 H3  7.0 ( 9) 9.1 ( 8) 21.5 ( 8)  16.9* 15.5* 15.5  21.7* 20.1* 20.1  23.6* 22.0* 22.0*  H  2  Number of Acceptances  4) 5) 3) 5)  2  2  11  16  X .005 2  19  *Acceptance at this Level of Significance ( x < X ^, M) 2  2  t S i g n i f i c a n t figures of program do not allow Ch-Squared c a l c u l a t i o n s . Source:  Freund and Williams'*.  38 TABLE V (b) Comparison of Calculated  and C r i t i c a l Chi-Squared Values f o r F l i g h t s  POISSON Airport  Flight  x (d. o.f)  X .05  x .oi  X .005  A  Al A2  39.2 ( 9) 29.3 (12)  16.9 21.0  21.7 26.2  23.6 28.3  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  43.3 22.2 22.0 40.8 29.6 57.1 97.7 72.0 89.5 19.6 48.7 43.5 69.6 t 30.4  (12) (13) (13) (12) (11) (10) (11) (11) (12) (11) (14) (13) (14)  21.0 22.4* 22.4* 21.0 19.7 18.3 19.7 19.7 21.0 19.7* 23.7 22.4 23.7  26.2 27.7* 27.7* 26.2 24.7 23.2 24.7 24.7 26.2 24.7* 29.1 27.7 29.1  28.3 29.8* 29.8* 28.3 26.8 25.2 26.8 26.8 28.3 26.8* 31.3 29.8 31.3  (12)  21.0  26.2  28.3  C  CI C2 C3 C4  76.9 50.4 88.8 92.1  ( ( ( (  8) 8) 6) 7)  15.5 15.5 12.6 14.1  20.1 20.1 16.8 18.5  22.0 22.0 18.6 20.3  D  DI D2  27.3 ( 9) 34.1 ( 9)  16.9 16.9  21.7 21.7  23.6 23.6  E  El E2 E3  37.1 (11) 14.7 (14) 24.6 (11)  19.7 23.7* 19.7  24.7 29.1* 24.7*  26.8 31.3* 26.8*  F  Fl F2  20.3 (13) 27.2 (13)  22.4* 22.4  27.7* 27.7*  29.8* 29.8*  G  Gl G2 G3 G4 G5 G6  t 55.2 18.1 24.1 29.0 36.6  19.7 23.7* 14.1 21.0 25.0  24.7 29.1* 18.5 26.2 30.6  26.8 31.3* 20.3 28.3* 32.8  HI H2 H3  27.7 (12) 39.2 (12) 45.9 (10)  21.0 21.0 18.3  26.2 26.2 23.2  28.3 28.3 25.2  H  2  Number of Acceptances  (11) (14) ( 7) (10) (15)  2  2  6  8  9  *Acceptance of this Level of Significance (x < X ) t S i g n i f i c a n t figures of program do not allow Chi-squared c a l c u l a t i o n . Source: Freund and W i l l i a m s a  4  v  39  TABLE V (c) Comparison of Calculated and C r i t i c a l Chi-Squared Values f o r F l i g h t s  LOGNORMAL Airport  Flight  A  x (d. o.f)  X .05  x .oi  X .005  Al A2  14.5 ( 7) 19.7 ( 9)  14.1 16.9  18.5* 21.7*  20.3* 23.6*  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  22.3 3.4 7.7 19.6 4.1 16.5 21.5 16.7 18.0 9.2 52.9 34.0 43.1 53.4 23.9  ( 9) (11) (12) ( 9) ( 8) (U) (12) (12) (12) ( 9) (13) (12) (14) ( 9) ( 9)  16.9 19.7* 21.0* 16.9 15.5* 19.7* 21.0 21.0* 21.0* 16.9* 22.4 21.0 23.7 16.9 16.9  21.7 24.7* 26.2* 21.7* 20.1* 24.7* 26.2* 26.2* 26.2* 21.7* 27.7 26.2 29.1 21.7 21.7  23.6* 26.8* 28.3* 23.6* 22.0* 26.8* 28.3* 28.3* 28.3* 23.6* 29.8 28.3 31.3 23.6 23.6  C  CI C2 C3 C4  6.9 14.1 3.7 9.1  ( ( ( (  6) 5) 3) 6)  12.6* 11.1 7.8* 12.6*  16.8* 15.1* 11.3* 16.8*  18.5* 16.8* 12.8* 18.5*  D  Dl D2  11.2 ( 8) 36.8 ( 8)  15.5* 15.5  20.1* 20.1  22.0* 22.0  E  El E2 E3  18.2 (13) 14.9 (12) 2.8 (10)  22.4* 21.0* 18.3*  27.7* 26.2* 23.2*  29.8* 28.3* 25.2*  F  Fl F2  34.6 (11) 41.1 (12)  19.7 21.0  24.7 26.2  26.8 28.3  G  Gl G2 G3 G4 G5 G6  14.4 31.4 16.1 16.4 64.3 35.8  12.6 15.5 22.4* 12.6 21.0 23.7  16.8* 20.1 27.7* 16.8* 26.2 29.1  18.5* 22.0 29.8* 18.5* 28.3 31.3  H  HI H2 H3  26.0 ( 9) 24.2 ( 8) 28.1 ( 8)  16.9 15.5 15.5  21.7 20.1 20.1  23.6 22.0 22.0  2  ( 6) ( 8) (13) ( 6) (10) (14)  Number of Acceptances Accepted at this Level of Significance (x Source:  Freund and Williams'*  2  2  15  2  < x  2  a  22  v  )  2  23  TABLE VI (a)  Comparison of Calculated and C r i t i c a l Chi-Squared Values f o r Airports  NORMAL No. of Flights  Airport  Year  X (d. o.f)  X .05  x .oi  X .005  A  1981  2  75.8 (10)  18.3  23.2  25.2  B  1978 1979 1980 1981 1982  3 3 3 3 3  27.6 26.3 27.6 25.0 22.4  33.4 32.0 33.4 30.6 27.7  35.7 34.3 35.7 32.8 29.8  C  1980 1981  2 2  34.7 ( 6) 52.8 ( 5)  12.6 11.1  16.8 15.1 .  18.5 16.8  D  1979 1980  1  5.1 ( 6) 13.3 ( 7)  12.6* 14.1*  16.8* 18.5*  18.5* 20.3*  E  1979 1980 1982  }  21.8 ( 8) 16.4 (13) T  15.5 22.4*  20.1 27.7*  22.0* 29.8*  F  1980 1981  }  4.7 (11) 41.0 (12)  19.7* 21.0  24.7* 26.2  26.8* 28.3  G  1981 1982  3 3  270.7 (19) 194.1 (18)  30.1 28.9  36.2 34.8  38.6 37.2  2  92.6 53.9 82.0 132.6 55.4  (17) (16) (17) (15) (13)  2  2  2  H  Number of Acceptances  4  4  5  *Acceptance at this Level of Significance ( x < X ) t S i g n i f i c a n t figures of program do not allow Chi-Squared calculations Source: Freund and Williams (Reference 3) a  v  41 TABLE VI (b) Comparison of Calculated and C r i t i c a l Chi-Squared Values f o r Airports  POISSON No. of Flights  2(d. o.f)  X .05  x .oi  22.4  27.7  29.8  23.7 25.0 25.0 23.7 23.7  29.1 30.6 30.6 29.1 29.1  31.3 32.8 32.8 31.3 31.3  78.2 ( 9) 131.3 ( 8)  16.9 16.9  21.7 20.1  23.6 22.0  27.3 ( 9) 34.1 ( 9)  16.9 16.9  21.7 21.7  23.6 23.6  37.1 (11) 14.7 (14) 24.6 (11)  19.7 23.7* 19.7  24.7 29.1* 24.7*  26.8 31.3* 26.8*  \  20.3 (13) 27.2 (13)  22.4* 22.4  27.7* 27.7*  29.8* 29.8*  3 3  2230.0 (14) 1490.0 (14)  23.7 23.7  29.1 29.1  31.3 31.3  Airport  Year  A  1981  2  B  1978 1979 1980 1981 1982  3 3 3 3 3  240.4 120.3 210.2 528.5 46.6  C  1980 1981  2 2  D  1979 1980  1  E  1979 1980 1982  F  1980 1981  G  1981 1982  x  58.5 (13) (14) (15) (15) (14) (14)  2  2  X .005 2  H  Number of Acceptances  *Acceptance at this Level of Significance (x Source:  Freund and Williams'*  2  < X  4  a  v  )  4  42 TABLE VI (c) Comparison of Calculated and C r i t i c a l Chi-Squared Values f o r Airports  Year  LOGNORMAL  Nr> r»f Flights  X ( d .o.f)  X .05  x .oi  28.5 (11)  19.7  24.7  26.8  26.3 27.6 27.6 26.3 22.4  32.0 33.4 33.4 32.0 27.7  34.3 35.7 35.7 34.3 29.8*  2  2  2  X .005 2  A  1981  2  B  1978 1979 1980 1981 1982  3 3 3 3 3  1980 1981  2 2  9.2 ( 7) 9.3 ( 6)  14.1* 12.6*  18.5* 16.8*  20.3* 18.5*  1979 1980  1 1  11.2 ( 8) 36.8 ( 8)  15.5* 15.5  20.1* 20.1  22.0* 22.0  1979 1980 1982  1 1 1  18.2 (13) 14.9 (12) 2.8 (10)  22.4* 21.0* 18.3*  27.7* 26.2* 23.2*  29.8* 28.3* 25.2*  1980 1981  1 1  34.6 (11) 41.1 (12)  19.7 21.0  24.7 26.2  26.8 28.3  1981 1982  3 3  99.0 (19) 75.9 (20)  30.1 31.4  36.2 37.6  38.6 40.0  71.5 59.1 52.7 109.4 28.2  (16) (17) (17) (16) (13)  H  Acceptances  6  •Acceptance at this Level of Significance ( x Source:  Freund and  Williams  4  2  < X  6  2  ,,)  7  43  TABLE VII  Acceptance Rate By F l i g h t  Level of S i gni f1cance ( a)  Normal  Polsson  Lognormal  .05  33%  17%  41%  .01  47%  23%  59%  .005  56%  26%  62%  44  TABLE VIII  Acceptance Rate By Airport ( A l l Airports)  Level of Significance (a)  Normal  Polsson  Lognormal  .05  25%  12%  35%  .01  25%  24%  35%  .005  31%  24%  41%  45  TABLE IX  Acceptance Rate By Airport (Airports with Multiple F l i g h t s Only)  Level of Significance (a)  Normal  Poisson  Lognormal  .05  0%  0%  20%  .01  0%  0%  20%  .005  0%  0%  30%  46  These results are somewhat misleading, however, since they include airports with only one f l i g h t , which are also included as single f l i g h t s i n Table VII.  The airports which had multiple f l i g h t s had a much poorer  acceptance rate. f i t even once.  In fact, the Normal and Poisson did not provide a good These results are shown by Table IX.  It i s s i g n i f i c a n t that the t h e o r e t i c a l distributions f i t more poorly as more f l i g h t s were included.  This was  to be expected as the f l i g h t s at  one airport can be d i s t i n c t i n their c h a r a c t e r i s t i c s (average loads, days of the week, et cetera).  The f i n a l outcome may be that these t h e o r e t i c a l  models should be used only to describe individual f l i g h t s .  4.1.2  Design Volumes Tables X and XI l i s t the 90th percentiles by f l i g h t event f o r  f l i g h t s and airports respectively.  The predicted values for Normal,  Poisson and lognormal functions were calculated from the estimated parameters.  Short APL programs were used for the Normal and  lognormal.  The Poisson d i s t r i b u t i o n required a separate program because of the rounding errors involved.  The APL functions could not handle such high  means, so a FORTRAN program was written.  A l l are l i s t e d i n Appendix A.  The 90th percentile by passenger volume and the "mean load factor plus 15 percent" volume are attached f o r i n t e r e s t .  Both are alternative  d e f i n i t i o n s of the peak design volume and have been calculated d i r e c t l y from the data. Inspection of Tables X and XI reveals that both the Normal and lognormal provide reasonable predictions of the 90th percentile values. The Poisson d i s t r i b u t i o n i s consistently low i n i t s estimate.  The  average  47  • TABLE X Comparison  of Actual and Predicted  90th Percentiles by F l i g h t  90th P e r c e n t i l e by Event 90th Percentile by Pax Volume  Mean Load Factor + 15%  Airport  Flight  Actual  Predicted by Normal  A  Al A2  89 132  91 127  76 104  93 130  98 138  100 126  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  141 157 168 141 129 119 143 151 146 144 163 169 188 106 151  133 155 166 141 126 107 133 144 140 142 162 162 179 101 145  106 128 140 121 108 80 98 108 106 110 130 132 141 66 119  132 156 169 144 128 110 135 148 143 147 170 166 186 94 149  161 170 180 147 135 130 159 165 162 156 169 177 201 150 159  127 149 160 142 130 104 121 130 127 132 151 153 161 91 141  C  CI C2 C3 C4  66 83 58 78  65 83 58 76  56 72 51 66  67 85 59 77  74 90 61 86  81 96 77 91  D  DI D2  91 95  89 94  73 79  92 99  101 103  97 103  E  El E2 E3  136 163 122  137 159 121  115 131 97  142 164 122  145 170 132  137 152 120  F  Fl F2  144 154  144 155  121 127  152 164  150 168  143 148  G  Gl G2 G3 G4 G5 G6  61 109 198 65 110 190  63 111 192 64 112 183  50 94 158 52 92 148  66 115 197 69 123 191  75 115 206 72 114 199  76 117 178 78 115 168  H  HI H2 H3  116 115 102  118 116 102  99 100 86  122 120 105  125 124 112  122 123 110  Predicted by Poisson  Predicted by Lognormal  48 TABLE XI Comparison of Actual and Predicted 90th Percentiles by Airports  90th Percentile by Event AirPredicted No. of by port Year F l i g h t s Actual Normal  Predicted by Poisson  Predicted by Lognormal  90th Percentile by Pax Volume  Mean Load Factor + 15%  A  1981  2  119  115  92  115  132  145  B  1978 1979 1980 1981 1982  3 3 3 3 3  155 160 174 139 141  145 154 165 136 139  108 119 124 97 113  157 161 174 149 144  165 171 190 155 153  130 141 145 120 135  C  1980 1981  2 2  74 70  74 70  62 58  76 71  82 79  87 84  D  1979  1  91 95  89 94  73 79  92 99  101 103  97 103  136 163 122  137 159 121  115 131 97  142 164 122  145 170 132  137 152 120  144 154  144 155  121 127  152 164  150 168  143 148  162 156  150 145  99 97  165 161  189 179  122 120  1  E  F G H  1979 1980 1982  1 1  1980 1981  1  1981 1982  3 3  1  1  49 TABLE  XII  Average D i f f e r e n c e s Between A c t u a l and P r e d i c t e d 90th  Normal  For  Flights  Poisson  Percentiles  Lognormal  3.3%  24.9%  4.1%  4.4%  31.9%  4.0%  = E | p r e d i c t e d - a c t u a l | x 100% 37  For A i r p o r t s = E1 p r e d i c t e d - a c t u a l | x 100% 17  *  50  difference between actual and predicted values are shown i n Table XII f o r both f l i g h t s and airports.  The Poisson i s c l e a r l y  unacceptable.  A good model should predict the design volume within ten passengers i f i t i s to be used i n the Canadian STEP method.  For individual f l i g h t s  the Normal f a i l e d to do this twice (Flights B6 and B7) while the lognormal exceeded ten three times (Flights B14, F2 and G5).  The Poisson, however,  could only predict the 90th percentile within ten three times (Flights C3, G4 and G6).  Similarly, for the airport values the Normal missed four times  and the lognormal twice, but the Poisson was never within ten passengers of the actual value. The other two planning values show that the 90th percentile by passenger volume i s s l i g h t l y higher, but very close to the 90th percentile by event.  The second d e f i n i t i o n (mean plus 15 percent) i s much more  variable.  4.1.3  V i s u a l Inspection The subjective ranking of the o v e r a l l c u r v e - f i t i s shown i n Tables  XIII and XIV.  The lognormal was the most e f f e c t i v e , followed by the  Normal. The inspection also pointed out some of the trends i n the data and in the models.  The high peak and the right skew common i n most of the  histograms were not well reproduced by the Poisson and Normal distributions.  Also, many histograms had at least one other secondary peak  to the right of the highest peak.  This second mode may be due to the upper  l i m i t of the a i r c r a f t capacity, but proof of this conjecture would be beyond the scope of this study.  TABLE XIII V i s u a l Inspection of Histograms for F l i g h t s RANKING (1=BEST FIT, 3=W0RST FIT) Flight  Normal  Poisson  Lognormal  A  Al A2  3 2  2 3  1 1  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  3 2 2 2 2 3 2 2 3 3 2 3 2 3 2  2 3 3 3 3 2 3 3 2 2 1 2 3 2 3  1 1 1 1 1 1 1 1 1 1 3 1 1 1 1  C  CI C2 C3 C4  1 1 2 2  3 3 3 3  2 2 1 1  D  Dl D2  1 1  3 3  2 2  E  El E2 E3  1 1 3  2 2 2  3 3 1  F  Fl F2  1 1  3 2  2 3  G  Gl G2 G3 G4 G5 G6  2 2 2 1 1 2  3 3 3 3 2 1  1 1 1 2 3 3  H  HI H2 H3  1 1 1  3 3 3  2 2 2  69  95  58  Airport  TOTAL  52  TABLE XIV  V i s u a l Inspection of Histograms f o r Airports  Year  Mr. r\f INO* or Flights  A  1981  B  RANKING (1=BEST FIT, 3=W0RST FIT) Normal  Polsson  Lognormal  2  2  3.  1  1978 1979 1980 1981 1982  3 3 3 3 3  2 3 2 2 2  3  3  1 2 1 1 1  C  1980 1981  2 2  2 2  3 3  1 1  D  1980 1981  1  1  3  1  1  3  2 2  1979 1980 1982  1 1  1 1  2 2 2  3 3 1  1980 1981  1  1  1  1  3 2  2 3  1981 1982  3 3  3 3  2 2  1 1  32  43  27  Airport  E  F G H  1  1 3 3  (incomplet e) TOTAL  53 One other note should be made about the models.  The Normal  d i s t r i b u t i o n i s able to handle negative values, which cannot occur i n the r e a l data.  This causes a d i s t o r t i o n of the expected frequencies i n the  f i r s t left-hand i n t e r v a l .  Since the Poisson and lognormal can handle  p o s i t i v e values only, they are more representative of the lower frequency classes. Visual inspection can only indicate preferences among the models and any gross tendencies of the data.  I t cannot be used as an independent  c r i t e r i o n f o r acceptance or r e j e c t i o n .  4.1.4  Ease of Use The Normal d i s t r i b u t i o n i s the most prevalent of the three  distributions.  I t i s a common assumption  made by analysts that the data  they are dealing with f i t s a Normal pattern.  Because of the f a m i l i a r i t y  and general understanding, the Normal i s easy to use. The Poisson and lognormal are less common but are s t i l l known and understood by most engineers.  A l l three d i s t r i b u t i o n s have parameters  which are simple to determine and are tabulated i n most texts, although the Poisson i s not usually calculated for parameters greater than twenty. If standard s t a t i s t i c s computer programs are to be used, the Normal d i s t r i b u t i o n i s easier to find c u r v e - f i t t i n g routines f o r .  In this study,  the data had to be scaled down by a factor of ten to use the Poisson program and a separate program had to be written for the lognormal.  I f an  extensive program l i b r a r y Is available, of course, this problem w i l l not arise.  54 4.1.5  Applicability In terms of a p p l i c a b i l i t y to small airport design, the prediction of  the planning volume i s the most important feature of any d i s t r i b u t i o n .  The  normal and lognormal did this acceptably well f o r simple d i s t r i b u t i o n s . More complicated calculations may need to be done to determine the design volume under changing conditions.  For example, as t r a f f i c  increases, the upper t a i l of the d i s t r i b u t i o n w i l l be limited by the a i r c r a f t capacity.  A truncated curve w i l l then have to be used.  If the  f l i g h t route has several stops, the passenger volumes of a l l the a i r c r a f t s w i l l have to be added, and then this d i s t r i b u t i o n truncated. A d i s t r i b u t i o n that was additive regenerative would simplify this calculation. Also, i f the function were additive (the Normal and Poisson are), i t could be assumed that i f the t o t a l of the deplaned and enplaned passengers followed the d i s t r i b u t i o n , that both each separately would be d i s t r i b u t e d according to the same function.  Deplaned passenger d i s t r i b u t i o n s and  enplaned passenger d i s t r i b u t i o n s could be determined.  4.2  Selection of a Model Of the three d i s t r i b u t i o n s considered, none describes the data i n  a l l situations.  The lognormal i s , however, the preferred model - followed  by the Normal. As measured by the Chi-Squared s t a t i s t i c , the lognormal provided a good f i t more often. with multiple f l i g h t s .  None of the models were good at describing airports The percentages of acceptance do not indicate  whether a model should be taken for use i n a l l cases.  The lognormal was a  good f i t f o r 41 percent of the f l i g h t s and 33 percent of the airports (at a  55 .005  l e v e l of s i g n i f i c a n c e ) , but no deduction can be made as to whether or  not these percentages are s u f f i c i e n t to unconditionally use the lognormal model.  The decision remains judgemental. With reference to t a i l p r e d i c t a b i l i t y , both the Normal and lognormal  perform reasonably well.  Use of the Poisson would lead to serious e r r o r s .  Visual inspection suggests that the lognormal i s the better model, followed again by the Normal. The fourth c r i t e r i o n - that the model be easy to use - would lead to the s e l e c t i o n of the Normal. with the use of the other  There are no serious complications, however,  two.  F i n a l l y , the c r i t e r i o n that the model be applicable would indicate that i t be additive regenerative.  Only the Normal and Poisson  The o r i g i n a l hypothesis of this work was  are.  that a s t a t i s t i c a l model  could be found that would approximate the data well enough for use i n the s i z i n g of small a i r p o r t s .  If a model i s to be selected, i t would be the  lognormal, although i f an additive quality was have to be used.  required, the normal would  The Poisson d i s t r i b u t i o n can be discarded according  to  most of the c r i t e r i a . Although a s e l e c t i o n was  made, there i s some doubt as to whether or  not any of the three d i s t r i b u t i o n s i s s a t i s f a c t o r y .  If only  planning  design volumes are to be determined from collected data, either the lognormal or the normal i s adequate.  However, any analysis that requires  use of the entire d i s t r i b u t i o n should consider other models - perhaps one of the s i x l i s t e d In the beginning of this study.  This i s e s p e c i a l l y true  i f airports with multiple f l i g h t s are under analysis.  56 5.  CONCLUSIONS  5.1  Assessment The f i n a l decision to use a s t a t i s t i c a l model has to ultimately  depend upon professional judgement.  The study i l l u s t r a t e s that using  d i s t r i b u t i o n s f o r d i f f e r e n t purposes can r e s u l t i n the s e l e c t i o n of d i f f e r e n t models for each purpose. The lognormal provided the best model o v e r a l l , although i t had drawbacks.  Some f l i g h t s were better described by other d i s t r i b u t i o n s .  Also, the lognormal did not have the additive feature of the Normal and Poisson.  Nonetheless, the study had revealed some of the strengths and  weaknesses of the three. The scope of the study can be categorized i n three areas: number of models considered;  the data i t s e l f ;  the  and the computer programs  used. Three d i s t r i b u t i o n models were studied.  The Chi-squared  test  measured overall "goodness-of-fit" and the 90th percentile test measured t a i l predictability. The inherent assumption i n the entire approach was that the s t a t i s t i c a l models assumed that the data was random, when a c t u a l l y the number of passengers choosing a p a r t i c u l a r f l i g h t depends on the complex interaction of many variables.  The models incorporate these unknown forces  as randomness. The data i t s e l f has p a r t i c u l a r features which simplify the study. F i r s t a l l of the airports were i n B r i t i s h Columbia.  A i r transportation i n  this province has certain unique and consistent features.  For example,  there are r e l a t i v e l y few towns and these are t y p i c a l l y separated by mountain highways or waterways.  Therefore, a i r travel i s more common than  in other provinces. Calgary/Edmonton. these c i t i e s .  Also, most a i r t r a f f i c funnels through Vancouver or The majority of f l i g h t routes originate and terminate at  For example, a Canadian P a c i f i c f l i g h t follows a triangular  Vancouver-Terrace-Prince  Rupert-Vancouver route since neither Terrace nor  Prince Rupert can generate s u f f i c i e n t demand to warrant a single stop. Since there i s v i r t u a l l y no demand between Prince Rupert and Terrace, i t can be safely assumed that a l l enplaners at Terrace are bound f o r Vancouver, and that a l l of the deplaners at Prince Rupert came from Vancouver. Another feature of these f l i g h t s i s that they are a l l served by Boeing 737 a i r c r a f t which have a capacity of 117 seats.  This s i t u a t i o n has  evolved because the c a r r i e r s have found the Boeing 737 to be the most suitable a i r c r a f t f o r the region, although this may change i n the future. Furthermore, at these a i r p o r t s , f l i g h t events are isolated throughout the day.  This means that there i s no overlapping i n the use of the f a c i l i t i e s . L a s t l y , the scope of the research was defined by the computer  programs used.  A s t a t i s t i c a l packaged program was used to calculate the  Chi-squared values and to plot the histograms distributions.  f o r the Normal annd Poisson  It was found to be too r e s t r i c t i v e f o r the Lognormal,  however, and a separate program had to be written.  Budgetary  considerations limited the extent of the analysis In this regard. The scope - as defined by the models, the nature of the data, and the computer programs - did not seriously hinder the process.  There Is no  evidence that the use of a cumulative d i s t r i b u t i o n form or a d i f f e r e n t s t a t i s t i c a l measure (such as the Kolmogorov-Smirnov) would have s i g n i f i c a n t l y changed the r e s u l t s .  58 The results of the design volume analysis were consistent enough to allow the conclusion that the Normal and Lognormal are s a t i s f a c t o r y models. The purpose of this study was airport f a c i l i t i e s .  to further the planning of small  Once the correct d i s t r i b u t i o n i s known, i t can be used  d i r e c t l y i n , say, a Monte Carlo simulation where passenger loads are randomly sampled from the d i s t r i b u t i o n . expected occupancies  for f a c i l i t y sizing.  The simulation would then produce The d i s t r i b u t i o n can also  produce s p e c i f i c planning volumes (hourly or half-hourly).  F a c i l i t i e s are  then sized from a method of proportions or from a selection process such as Transport Canada's STEP. A frequency model would also be needed to determine more complicated effects on the airport passenger volumes.  It can quantify the effects of  route changes and a i r c r a f t capacity.  5.2  Further Research The p o s s i b i l i t i e s f o r further work are numerous.  L i t t l e research  has been done i n the f i e l d of smalll airports for several reasons:  (1)  Carriers are not required to submit data by f l i g h t or by day to the government;  (2)  detailed study was never considered necessary since a i r c r a f t were small, and f a c i l i t i e s  (3)  a i r c a r r i e r s are reluctant to release detailed information to competitors;  (4)  could be incrementally adjusted;  and  small airports have not been deemed as important as larger ones when research was  to be done.  59  Increased reliance on a single design volume, as well as less the reduced a v a i l a b i l i t y of construction c a p i t a l , may  change t h i s s i t u a t i o n .  Further research might include: (1)  Consideration  of other s t a t i s t i c a l models (Gamma, Weibull, Rayleigh,  Negative Binomial, Beta, et cetera); (2)  c a l c u l a t i o n and comparison of the 90th percentile by passenger volume as a design volume;  (3)  categorization of airports by parameters or by d i s t r i b u t i o n type;  (4)  calculations of the e f f e c t s of multi-stop to a i r c r a f t  f l i g h t routes with respect  capacity;  (5)  c a l c u l a t i o n and comparison of other percentiles (75th, 80th, 85th);  (6)  using a cumulative d i s t r i b u t i o n form and a Kolmogorov-Smirnov goodness-of-fit  (7)  measure;  consideration of the e f f e c t s of a trend to smaller  aircraft,  especially the Dash 7 i n B r i t i s h Columbia; (8)  derivation of demand d i s t r i b u t i o n s from the measured load distributions;  (9)  analysis of the costs of errors i n forecasting the design volumes on all facilities;  (10)  and  a network analysis f o r B r i t i s h Columbia a i r t r a f f i c .  60  REFERENCES  1.  Ashford, Norman and Wright, Paul H.  Airport Engineering.  John Wiley  & Sons, U.S.A., 1979. 2.  Benjamin, Jack, R. and Cornell, C. A l l i n . Decision for C i v i l Engineers.  3.  Braaksma, John P.  P r o b a b i l i t y , S t a t i s t i c s and  McGraw-Hill Book Co., U.S.A. 1970.  A Computerized Design Method f o r Preliminary Airport  Space Planning.  Technical Report, Department of C i v i l Engineering,  University of Waterloo, Waterloo, Ontario. 4.  Braaksma, John P.  Time Stamping:  t r a f f i c i n airports. Number 5, May 5.  1976,  a new way  to survey pedestrian  pp. 204-206.  Braaksma, John P, and Ramsay, W. Alex.  A i r Terminal  Design:  Transportation Engineering Journal,  ASCE, Volume 105, TE6, November 1979, Bury, Karl V.  1973.  T r a f f i c Engineering and Control, Volume 17,  Decentralization and Shape.  6.  October  pp. 669-714.  S t a t i s t i c a l Models i n Applied Science.  John Wiley  and  Sons, Inc., U.S.A., 1975. 7.  Chatfield, Christopher. Limited, London,  8.  S t a t i s t i c s f o r Technology.  1976.  de N e u f v i l l e , Richard and G r i l l o t , Michel. in Airport Terminals.  Design of Pedestrian Space  Transportation Engineering Journal, ASCE,  Volume 108, T E l , January 1982, 9.  Chapman and H a l l  pp. 87-101.  de Neufville, Richard and Rusconi-Clerici Ignazio. Terminals for Transfer Passengers.  Designing Airport  Transportation Engineering  Journal, ASCE, Volume 104, TE6, November 1978, pp. 775-787. 10.  Dunlay, William, J . , J r . applications. TE4, J u l y 1981,  Simulation Model V a l i d a t i o n :  airport  Transportation Engineering Journal, ASCE, Volume 107, pp. 401-412.  61  11.  Freund, John E. and Williams, Frank, J. Statistics:  the modern approach.  Elementary Business  Prentice-Hall, Inc., New  Jersey,  U.S.A., 1972. 12.  Horonjeff, Robert.  Planning and Design of Airports, Second E d i t i o n .  McGraw-Hill Book Company, U.S.A., 1975. 13.  International A i r Transport Association.  Airport Terminals Reference  Manual, Sixth E d i t i o n . 14.  Lauchli, U.  Matching Transportation Capacity to a Stochastic  Transportation Demand. Symposium, F l o r i d a , 15.  Ramsey, G.R.  Proceedings of Sixteenth Annual AGIFORS  1976.  Stuart and Hutchinson, B.G.  Flow Model.  An Airport Terminal Pasenger  Paper Presented at 63rd Annual Meeting of the  Transportation Research Board, Washington, D.C, 16.  January 1984.  Soumls, Francois, Ferland, Jacques-A. and Rousseau, Jean-Marc. Model f o r Assigning Passengers to a F l i g h t Schedule.  MAPUM A  University de  Montreal, Centre de recherche sur les transports - #142,  August  1979. 17.  Transport Canada, A i r . Airport T r a f f i c A l l o c a t i o n Model, Manual. Document AK 41-02-300, Airports Branch.  18.  Transport Canada, A i r . CATA's National Aviation Forecasting Models and Other Forecasting Methods.  TP #2046.  Policy, Planning and  Programming, March 1979. 19.  Transport Canada, A i r . Study of the A i r Terminal Building Planning Standard.  TP 4771E. (Salah G. Hamzawi).  Programming, July 20.  Policy, Planning and  1983.  Transport Canada, A i r . Systemized Terminal Expansion Program (STEP), Draft.  Document AK 62-08-000, Airports Branch, September 1983.  62 21.  Transport Canada, A i r . Vancouver Airport Simulation Model User's Manual. (E.J.M. Greco and G.R.  Haverty), Airports Branch, September  1974. 22.  V e l l a John, Jaul Martin and Whale Les. Seat Configuration.  Proceedings of Twenty-First Annual AGIFORS  Symposium, C a l i f o r n i a , 23.  Determining the Best A i r c r a f t  1981.  Walpole, Ronald E. and Myers, Raymond H.  Probability and S t a t i s t i c s  for Engineers and S c i e n t i s t s , 2nd Edition. Co., Inc., New York, 24.  Wang, Ken.  MacMillan Publishing  1978.  Modelling the Interaction between Payload R e s t r i c t i o n ,  Passenger Demand and Reservation Booking Levels. Twenty-Second Annual AGIFORS Symposium, Greece,  Proceedings of 1982.  APPENDIX A  COMPUTER PROGRAMS  64  APL  PACKAGE  PROGRAM  DISTRIBUTIONS  TO  COMPARE  ( I . P . SHARP  DATA  TO  NORMAL  S ASSOCIATES  AND  POISSON  LTD.)  FREQ 41981 ENTER THE FOLLOWING DATA. LEFT HAND END OF THE FIRST FREQUENCY CLASS ;YOUR DATA MI 11=26 30  CLASS WIDTH AND THE NUMBER OF CLASSES;YCUR DATA MAX=16H •: 10 13  DO YOU WISH A FIT DONE ON YOUR DATA? Y OR N Y NORMAL OR POISSON ? N OR P N (1)  DATA MEAN = 79.46307692 AND STANDARD DEV. - 27.90987073  DO YOU WISH A HISTOGRAM ? Y OR N Y DO YOU WISH TABULAR OUTPUT ? Y OR N Y  -ENDPOINTSR MID L OBS 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160  30 40 50 60 70 80 90 100 110 120 130 140 150 160 17 0  25 .0 35.0 45.0 55.0 65.0 75.0 85.0 95.0 105.0 115.0 125 .0 135.0 145.0 155.0 165.0  6 18 63 76 101 106 84 51 39 42 20 23 15 4 2  o/o  0.9 2.8 9.7 11.7 15.5 16 .3 12.9 7 .8 6.0 6.5 3.1 3.5 2.3 0.6 0.3  TOTAL OBSERVATIONS CHI-SQUARE  EXP 24.666 26.48 5 43.617 62.998 80.890 91.276 90.802 79 .188 60.912 41.614 24.895 12.9 38 5.893 2.408 1.420  o/o  3.8 4.1 6.7 9.7 12.4 14 .0 14 .0 12.2 9.4 6.4 3.8 2.0 0.9 0.4 0.2  650 78.0976  OBSERVED- o : EXPECTED- e : VARIABLE (COLUMN NO'. ) 1 150|  100  50  O O o e o o e o e « e » e• o ee o » e I 50  e o o o o o I 100  o o e e a e  150  200  65  APL  PROGRAM  TO  COMPARE DATA TO  LOGNORMAL  DISTRIBUTION  V LN w;LOGMEAN;LOGSD;LH;RH;RHO;START;END;FRQ;PROB LOGMEAN+-MEAN (1 0®GJ ) [2] LOGSD+STDDEV{l{»u) [3] MS+LOGMEAN,LOGSD ' LEFT HAND END ' [4] LH+Q C5] [6] ' RIGHT HAND END ' RH+Q [7] L8] VECTOR+LH ,LH+(10*i((.RH-LH)*10)) [9] LOGVECTOR+10W ECTOR c i o : ) PROBHL(0.5+(MS NORMALPROB LOGVECTOR)*10QQ))*\QM d i : ] RHO+pPROB L 12:1 STARTSLH-10),VECTOR C13: 1 END+-V ECTOR, (RH+10) d u : 1 FRQ<-PROB*pu> [ 1 5 : ] EXP+-LOGV ECTOR CLASSIFY (1 0®CJ )  [1]  [ie: ]  DELH (FRQ-EXP) * 2 ) ) Z>£X-KL(0.5+££7:xlOOO))*1000 [18.1 ' ' ' LH RH PROB EXP OBS X* [19: ] * ' [20 1 [ 2 1 . ] SC+-v(.(RHO,l)pSTART) [22.} EC*-l((RHO,l)pEND) [23.] PC*-f((RHO,l)pPROB) [2U ] FC<-v((RHO,l)pFRQ) [25 ] ECHAR+l((RHO,1)pEXP) [26 ] DCo-i({RH0.1)pDEL) [27 ) SC,' '.EC,' ',PC,' ',FC,' ',ECHAR,' ',DC [28 ] ' ' 0 ' ' [29 ] CS-r+IDEL [30 ] 'CHI-SQUARED = \T(C5) [31 ] ' ' 0 'TOTAL OBSERVATIONS - ',T(paO [32 ] • • 0 • ' [33 ] EXP HISTO FRQ ., [3U 1 * V [17;  9  .Subroutines  HISTO  and CLASSIFY  on n e x t  page.  SUBROUTINES  'HISTO'  AND  'CLASSIFY'  USED  IN  APL  PROGRAM  VHISTOIOH V Ri-EXP HISTO Cl] *FOR EXPECTED  [2]  AND  0BS\UI0\H\HH\TEST\B001\B002ILBL OBSERVED VALUES  DTCn-0  L3j [4]  H-[/EXP.OBS 0 £C2>10*Ll0®ff 0 HH-SCL* 1 1.5 2 3 4 5 6 8 H+-L/(HHZH)/HH TEST*-(\20)xH*20 0 B001+-TEST* .<EXP 0 B002*-TEST° .<0BS  [7]  7M(4xi  [5] [6]  R+e'  [8]  o*9'LB001+2*B002] + ptf)p 0 0 0 1)V? nSPACE IT OUT A iW?,[0]  [9] [10]  LBL+1 3 1 p#x LBL+-'EXPECTED:  BIT  l 0.5 0 0 LBL+(21plO*l)\LBL * OBSERVED: o'  [11] ' ' O ' * 0 ' ' 0 ' ' [12] W--(pLBL)[UpR 0 R*-(W*LBL),lOl((l+pR),W)+R 7  VC£ASSIJFY[[]] V R*-a CLASSIFY CJ  [1] [2] [3]  if^i«.<u / ? - ( l , [ l ] ff)-i?,[l] 0 R++/R V  [4]  V  0  R+LBL.R  10  'LN'  66  67  APL  PROGRAM AND  TO C A L C U L A T E  LOGNORMAL  EXPECTED  DECILES  FOR  DISTRIBUTIONS  vTfflVL[]]V V R+-TEN u\M\S\Z [:] M+-MEAN OJ [2] S+STDDEV u [3] Z--GAUSS 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 U3 V  (Line  4 without  '10*' f o r Normal  Distribution)  NORMAL  68 FORTRAN.PROGRAM  Listing  o f P0I  1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 1G 17 18 19 20 21 22 22.2 22.4 23 24 25 26 27 28 29 29 .05 29. 1 29 . 14 29 . 15 29 . 16 29 . 2 29.4 30 31 31.2 31.4 32 33 34 35 36 37 38  OUTPUT (Sample)  at  TO  CALCULATE  13:34:50 o n MAR  EXPECTED  2.  POISSON  90TH  1984 f o r CC1d=FCE6  C C234567 REAL M,PROBRR,RR DIMENSION R ( 2 0 ) , P ( 2 0 ) REAL Z.ZZ.F.D.DD RR=100.0 M=64.9 C R(1)=RR C DO 100 1=2.20.1 R(I )=R(1-1)+1.0 100 CONTINUE C F=0.0 PR0BRR=1.0 C DO 2 0 0 d=1.200,1 IF (d.GE.RR) GO TO 210 F = F+ALOG10(FLOAT ( d ) ) PROBRR=PROBRR+10**(FLOAT(d)*ALOG10(M)-F) 200 CONTINUE CONTINUE 210 PR0BRR=PR0BRR*EXP(-1.0*M) C P(1)=PROBRR DO 3 0 0 K=2,20 F=F+ALOG10((RR+FL0AT(K)-2.0)) P(K)=P(K-1)+EXP(-1.*M)*10**(R(K-1)*AL0G10(M)-F) CONTINUE 300 C WRITE(6,15)U 15 F0RMAT('U WAS :',14) C WRITE(6, 18)PR0BRR 18 FORMAT('PROBRR WAS :',F9.7) WRITE(6,13)M 13 FORMAT('PARAMETER :',F6.2) WRITE ( 6 , 1 0 ) FORMAT(' X +/PROB') 10 WRITE(6,12) FORMAT (' ) 12 DO 4 0 0 1 = 1 ,20, 1 WRITE(6, 1 1 ) R ( I ) ,P( I ) 1 1 FORMAT(1X,F4.0,3X,F5.3) CONTINUE 400 C STOP END  1 2 3 4 5  6 7 8  9 10 1 1 12 13  14 15  16 17 18 19  20 21 22 23 24  PROBRR WAS :0.5653268 PARAMETER :117.90 4/PROB X 120. 121 . 122. 123. 124. 125. 126. 127. 128. 129. 130. 131 . 132. 133. 134. 135. 136.  137. 138. 139.  0. 565 0. 601 0. 636 0. 670 0. 702 0. 733 0. 762 0. 789 0. 814 0. 837 0. 858 0 877 0 895 0 910 0 924 0 936 0 946 0 956 0 963 0 970  PERCENTILE  APPENDIX B  DETAILED CHI-SQUARED CALCULATIONS  70 APPENDIX B TABLE BI X CALCULATON FOR THE NORMAL DISTRIBUTION BY FLIGHT 2  PARAMETERS Airport  Flight  A  Al A2  B  u  a  INITIAL NUMBER OF DIVISIONS  CORRECTED X  2  NUMBER OF DIVISIONS  X  2  64.9 91.3  20.4 27.6  13 14  78.8 29.6  10 13  19.6 29.5  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  92.2 114.0 124.8 107.3 94.9 68.8 85.5 95.2 92.2 96.7 115.6 117.9 125.9 56.2 105.4  32.0 32.1 32.3 26.6 24.5 30.0 36.7 37.9 37.0 35.0 36.1 34.5 41.5 34.6 31.1  20 20 20 14 16 18 18 21 18 20 19 16 19 19 19  80.0 47.5 26.9 30.3 25.5 70.1 83.5 61.7 59.7 24.7 41.8 46.1 46.8 363.8 38.7  14 14 15 12 11 14 15 16 14 14 17 16 18 12 15  48.6 23.0 22.3 28.1 12.9 64.0 68.9 49.5 56.4 15.6 38.7 46.1 45.6 213.3 32.8  C  CI C2 C3 C4  46.3 61.3 41.7 55.5  14.9 17.0 12.4 16.1  10 11 8 9  46.7 29.4 17.7 53.3  7 8 6 8  21.8 12.7 10.2 53.0  D  Dl D2  62.3 67.8  21.1 20.7  11 12  29.7 15.8  9 10  5.1 13.3  E  El E2 E3  101.4 116.8 84.8  27.7 33.3 28.7  20 18 20  51.4 17.4 305.7  11 16  21.8 16.4  F  Fl F2  107.4 112.9  28.8 33.0  20 27  42.5 310.7  14 15  4.9 41.0  G  Gl G2 G3 G4 G5 G6  40.7 81.7 142.6 42.6 79.9 132.8  17.6 22.5 38.3 17.0 25.1 39.4  12 18 17 10 20 22  658.8 378.8 20.1 21.6 121.6 25.4  17 8 12 17  20.1 12.7 9.9 21.8  HI H2 H3  86.7 87.4 74.6  24.3 22.7 21.1  17 14 12  21.2 10.7 21.5  12 11 11  7.0 9.1 21.5  H  *  * *  * S i g n i f i c a n t figures of the program do not allow calculatons of Chi-squared.  71 APPENDIX B TABLE BII X CALCULATON FOR THE POISSON DISTRIBUTION BY FLIGHT 2  INITIAL Airport  Flight  A  Al A2  B  PARAMETER y  NUMBER OF DIVISIONS  CORRECTED X  2  NUMBER OF DIVISIONS  X  2  64.9 91.3  13 14  40.1 29.3  11 14  39.2 29.3  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  92.2 114.0 124.8 107.3 94.9 68.8 85.5 95.2 92.2 96.7 115.6 117.9 125.9 56.2 105.4  20 20 20 14 16 18 18 21 18 20 19 16 19 19 19  56.0 25.1 21.1 40.8 29.8 62.8 124.0 93.0 93.9 26.2 61.6 43.5 73.1 1636.6 31.3  14 15 15 14 13 12 13 13 14 13 16 15 16  43.3 22.2 22.0 40.8 29.6 57.1 97.7 72.0 89.5 19.6 48.7 43.5 69.6  14  30.4  C  CI C2 C3 C4  46.3 61.3 41.7 55.5  10 11 8 9  76.9 50.5 88.8 92.0  10 10 8 9  76.9 50.4 88.8 92.1  D  Dl D2  62.3 67.8  11 12  27.3 35.5  11 11  27.3 34.1  E  El E2 E3  101.4 116.8 84.8  20 18 20  39.5 15.6 72.7  13 16 13  37.1 14.7 24.6  F  Fl F2  107.4 112.9  20 27  29.7 117.6  15 15  20.3 27.2  G  Gl G2 G3 G4 G5 G6  40.7 81.7 142.6 42.6 79.9 132.8  12 18 17 10 20 22  61.9 60.6 19.0 24.4 43.6 56.8  13 16 9 12 17  55.2 18.1 24.1 29.0 36.6  HI H2 H3  86.7 87.4 74.6  17 14 12  28.3 39.2 45.9  14 14 12  27.7 39.2 45.9  H  *  *  Significant figures of the program do not allow calculatons of Chi-squared.  72 APPENDIX B TABLE B i l l X CALCULATON FOR THE LOGNORMAL DISTRIBUTION BY FLIGHT 2  PARAMETERS Airport  Flight  P LOG  a LOG  INIT:[AL NUMBER OF DIVISIONS  CORRECTED X  2  NUMBER OF DIVISIONS  X  2  A  Al A2  1.79 1.94  .14 .14  13 14  15.6 20.7  10 12  14.5 19.7  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  1.94 2.04 2.08 2.02 1.96 1.80 1.89 1.94 1.93 1.96 2.04 2.05 2.07 1.69 2.00  .14 .12 .11 .11 .11 .19 .19 .18 .18 .16 .15 .13 .15 .22 .13  18 20 20 14 16 17 18 21 18 20 18 16 19 19 18  31.8 10.1 9.4 20.4 9.1 18.3 23.6 24.1 23.4 14.7 56.0 34.3 45.9 77.7 26.4  12 14 15 12 11 14 15 15 15 12 16 15 17 12 12  22.3 3.4 7.7 19.6 4.1 16.5 21.5 16.7 18.0 9.2 52.9 34.0 43.1 53.4 23.8  C  CI C2 C3 C4  1.64 1.77 1.60 1.73  .14 .12 .13 .12  10 11 8 9  6.9 15.2 4.1 9.1  9 8 6 9  6.9 14.1 3.7 9.1  D  DI D2  1.77 1.81  .15 .15  11 12  11.2 43.9  11 11  11.2 36.8  E  El E2 E3  1.99 2.05 1.90  .13 .13 .14  20 18 20  67900. 19.0 11.3  16 15 13  18.2 14.9 2.8  F  Fl F2  2.01 2.03  .13 .14  20 27  486. 21300.  14 15  34.6 41.1  G  Gl G2 G3 G4 G5 G6  1.57 1.89 2.14 1.59 1.88 2.10  .20 .13 .12 .20 .15 .14  14 18 17 10 20 22  26.5 1110. 16.1 32.7 34300. 809.  9 11 16 9 13 17  14.4 31.4 16.1 16.4 64.3 35.8  H  HI H2 H3  1.92 1.93 1.85  .13 .12 .13  17 14 12  32.6 24.6 28.1  12 11 11  26.0 24.2 28.1  73  APPENDIX B  TABLE BIV  X CALCULATON FOR THE NORMAL DISTRIBUTION BY AIRPORT 2  (AIRPORTS WITH MULTIPLE FLIGHTS)  INITIAL  PARAMETERS  Airport  CORRECTED  NUMBER OF  NUMBER OF  Year P  a  DIVISIONS  X  2  DIVISIONS  X  2  A  1981  79.5  27.9  15  78.1  13  75.8  B  1978  94.7  39.3  21  94.2  20  92.6  1979  105.4  37.6  22  55.1  19  53.9  1980  110.3  42.7  21  82.4  20  82.0  1981  84.9  39.5  20  133.9  18  132.6  1982  99.8  30.5  20  73.1  16  55.4  1980  51.9  17.2  12  60.1  9  34.7  1981  49.0  16.0  10  94.7  8  52.8  1981  86.6  49.4  23  276.2  22  270.7  1982  85.0  46.6  24  199.0  21  194.1  C  G  74  APPENDIX B  TABLE BV  X CALCULATON FOR THE POISSON DISTRIBUTION BY AIRPORT 2  (AIRPORTS WITH MULTIPLE FLIGHTS)  INITIAL  Airport  Year  CORRECTED  PARAMETER  NUMBER OF  NUMBER OF  U  DIVISIONS  X  2  DIVISIONS  X  2  A  1981  79.5  15  58.5  15  58.5  B  1978  94.7  21  255.4  16  240.4  1979  105.4  22  122.6  17  120.3  1980  110.3  21  226.1  17  210.2  1981  84.9  20  535.7  16  528.5  1982  99.8  20  49.3  16  46.6  1980  51.9  12  78.2  11  78.2  1981  49.0  10  131.3  10  131.3  1981  86.6  23  3411.9  16  2228.7  1982  85.0  24  2161.3  16  1488.9  C  G  75  APPENDIX B  TABLE BVI  X CALCULATON FOR THE LOGNORMAL DISTRIBUTION BY AIRPORT 2  (AIRPORTS WITH MULTIPLE FLIGHTS)  PARAMETERS  Airport  Year  CORRECTED  INITIAL  NUMBER OF  NUMBER OF  LOG  LOG  DIVISIONS  X  2  DIVISIONS  X  2  A  1981  1.87  .15  15  31.2  14  28.5  B  1978  1.94  .20  21  1670.  19  71.5  1979  1.99  .17  22  62.1  20  59.1  1980  2.01  .18  21  58.0  20  52.7  1981  1.88  .23  20  109.4  19  109.4  1982  1.99  .14  20  43.2  16  28.2  1980  1.69  .15  12  9.4  10  9.2  1981  1.67  .14  10  9.6  9  9.3  1981  1.86  .28  23  103.1  22  99.0  1982  1.86  .27  24  91.0  23  75.9  C  G  APPENDIX C  ACTUAL DECILES BY FLIGHT EVENT  77 APPENDIX C TABLE CI ACTUAL DECILES BY FLIGHT EVENT  AIRPORT  FLIGHT  A  10th  20th  30th  40th  50th  60th  70th  Al A2  42 58  47 66  53 74  58 80  63 88  69 96  74 105  80 118  89 132  B  Bl B2 B3 B4 B5 B6 B7 B8 B9 BIO Bll B12 B13 B14 B15  59 76 86 76 67 38 46 52 49 56 69 76 75 26 70  67 88 99 83 74 44 54 62 59 68 81 87 94 32 77  75 95 106 89 81 49 61 71 66 74 92 94 103 36 84  80 101 115 96 86 56 67 77 75 84 102 103 109 41 93  84 109 123 105 92 63 77 89 86 93 115 114 120 44 100  88 118 128 113 98 70 87 103 98 101 127 124 131 48 111  97 126 136 123 106 77 101 111 110 111 138 136 147 55 122  113 141 149 131 114 90 115 128 124 127 150 152 164 74 135  141 157 168 141 129 119 143 151 146 144 163 169 188 106 151  C  CI C2 C3 C4  29 40 28 37  35 46 31 42  38 51 34 46  41 57 37 49  44 61 41 53  48 64 44 57  52 68 47 61  58 74 51 68  66 83 58 78  D  Dl D2  38 42  44 51  50 56  54 61  60 67  65 73  71 78  81 84  91 95  E  El E2 E3  69 73 51  77 85 61  87 97 67  92 105 74  98 115 81  106 124 89  115 134 94  122 146 105  136 163 122  F  Fl F2  72 78  85 89  93 97  100 102  108 109  116 116  121 125  131 136  144 154  G  Gl G2 G3 G4 G5 G6  22 56 95 22 45 79  28 65 106 27 61 99  31 72 119 33 68 111  34 76 129 37 74 121  37 81 140 41 80 130  40 86 151 45 75 141  46 91 166 50 93 156  54 99 178 57 100 165  61 109 198 65 110 190  H  HI H2 H3  54 57 48  65 67 59  73 75 64  80 81 68  86 86 73  93 93 79  100 100 84  108 107 91  116 115 102  80th  90th  78  APPENDIX C TABLE CII ACTUAL DECILES BY FLIGHT EVENT  PERCENTILES BY EVENT AIRPORT  YEAR  10th  20th  30th  40th  50th  60th  70th  80th  90th  A  1981  47  55  62  69  75  81  90  104  119  B  1978  47  60  70  79  87  98  115  132  155  1979  60 58  81  92 97  101  1980 1981  71 71  84  106  111 117  122 130  139 147  160 174  1982  36 67  46 74  56 81  70 88  82 95  93 103  106 113  121 126  139 141  1980 1981  32 30  37  41  60  51  55  66 60  74  40  50 47  54  36  45 43  70  D  1979 1980  38 42  44 51  50 56  54 61  60 67  65 73  71 78  81 84  91 95  E  1979 1980  69 73 51  77 85 61  87 97 67  92 105 74  98 115 81  106 124 89  115 134 94  122 146 105  136 163 122  72  85 89  93  100  108  116  121  131  144  97  102  109  116  125  136  154  39 42  53 55  67 66  79 77  90 90  105 104  128 122  162 156  C  1981 F  G  1981 1982  78  1981  31  1982  31  APPENDIX D  HISTOGRAMS  80 KEY  EXAMPLE FOR NORMAL AND POISSON  TO  HISTOGRAMS  OBSERVED- o : EXPECTED- • : VARIABLE (COLUMN NO.) 1 1501  U  C u cu  u  100  CJ  o  o  >1 o c  0)  3  <u  M  [=4 NUMBER OF ENPLANED + DEPLANED PASSENGERS  EXAMPLE FOR LOGNORMAL  NUMBER  OF  ENPLANED+DEPLANED  PASSENGERS  Expected  Frequency  Distribution  Observed  Frequency  Distribution  AIRPORT A, FLIGHT A l  (Normal missing)  POISSON  OBSERVED- o  EXPECTED-  s  • • VARIABLE  f COL!.  7 5  o o o o o o o « « e o » ® »  50  2 5  9 9 9 » 9 8 9• 90998999® ®09®»®9 0»8 00999S900G 9 I  I  50  !  I  100  as i  o o i?0  LOGNORMAL  EXPECTED: * OBSERVED: o 80  40  9 99 9 50  100  SO.) I  82 AIRPORT A, FLIGHT A2  OFSEEA'ED-  v TJ jr r<  0  \ZTAPLE ':C0L J':: • rO . }1 ;  75 |  o o ® o e * o ® ® e e C ® s ® ® s ® ® e s ®  50 I  1 1 1 1  25 |  0  1 1 1 1 1  ®  o  ®  0 0  ®  1  ®  ®  1  100  EXPECTED- ®  :  C  1 »1  150  VA RI ABIZ  O O o O ® o « O o e 0 0 o 0 o ® e » o »  ( c o i v ; : s so •) i  8 8 SO8 » O 8 8 8 S 8 8 o9 ss 8 o9 8c o 88 8 o 9o S 9 819®98 8S 81 8 80 9 8 99 O»Rs  1 1 1 1  5 |  1 1 1 1 1  o  0  50  •a  O O  ICO  O  o  1  P o : "0 •  !  OBSERVED: o  EXPECTED: 60  30  0  1 200  O  50 I  LOGNORMAL  ®  0  ® ®  1  75  0  ®  50  OBSERVED- o  2  9 0 9 o o 8 0 9 9 oo 0 »s8 8 o 9 8 o0 9 9 8 9oo0 oO s»9® Os » 1 1 ®  0  ®  « «  50  100  150  . ! 2  f0  83 AIRPORT B, FLIGHT B l  NORMAL  OBSERVE P- o  "-  r-ftpi.p Vf-  » :  ( c o i v r v ro.) i  u0 |  0 o o o 0 o o o o o c o o o » ® ® 0 e »  |  30  |  | |  j  | 20 | | | | | 10 | | | | 0 1 0  0ESERV3V-  ® ® ® ©  ® ® ® ®  ® ® ® ®  ®  o o e 0 ® ® o O O 0 ® ® ® e a o C ®  |  POISSON  « ® ® 8 8 8 9®9® 8 8®®8 ® o ® ® ® o  1  o  1  .1  EXPECTED  -  50  I  100  8  ® o 0 O O  ® ® 0 ® o O * ® ® 0 0  ]  |  s  0 ® s |®  150  |  200  ( COLU:'-' :;0 . )  VA HIABLE  1  250  1  40 I  | || || | || || ||  O O O O o o  3 0J .  20 ] |  10 I  g [  0  LOGNORMAL  EXPECTED: * 40  0 08 9 9 8 8 8 88 9 8 8809 9 9 8 0 9 * 99 | | 1 | 9 8 |9 |  o o o s o s  1  o o o ® ® ® O S ® O ® o o  S o o ® ® c O a ® o O O « ® o O © ® ® O S c O c C O S S O S ®  1  50  OBSERVED: o  O  S O  1 CO  50  O  O C S2 00  1  2 50  84 AIRPORT B, FLIGHT B2 NORMAL  e  EXPECTED-  OBSERVED- O  :  VARIABLE  (coivn  >Vf). ) 1  40 |  !  1  o  o  0  o e e  1  o ® e o e « o ® e ® o ® e ® o ® e e  30 |  0  1  1 1  20 |  1  0  1  0  ®  1 1 10 |  0  ® e ® « ®  e  e  9 ® ®  ®  ® e ®  e  e  0  i+O  1  1  lo  5 0  O O e 0  o c  o O o o * c 0 I 1* «  1  VAPTARLE  2 00  ' OOF,!!!' "0. )  1 1 1 1  O O o O o o o e o « 0  r  0  e s  s  c » o ® ® s ® e  1  8® 8 *  « 8 8 O * 8* 8 88 ® ® ® «8 8 ® 8 88 888 « 8 ® ® « 88 88 888 ® 888 ® 8 ® « 88 8 ®8 8 « 8« ® « ® ® « 8® 8 ® 8 ®8 8 8 * ® »® ® 81 1 1 ® 1 O O  ®  » »  e  0  O O c  e  e 0 e c o o  lo  1 CO  s  C O o c c  1 .=0  C C O C O  O  o e * o 1 2f0  LOGNORMAL  OBSERVED: o  to  o  9 ® e  *  o  ® S  *  ®® O  s  8  9  • ••• • 8 ® 9 ® ® 8 ® 0 ®  «  ®  «  «  ®  ®  «  *  * ® ® ® ® ® 8 ® ® 9 ® ® ® ® ® 0 0  50  1  0  i i i i  1 1 1 1  o  ft 8'1  o  1 0|  EXPECTED: *  0  |  i 30 I  0  e  0  o ® o o o e c o  1 0 1  !  2 o  e  0  OP-SERVED- o : F. XPF.CTETie  POISSON  e  8 8 8 * ® 8 8 8 ® RS 8 ® 88 8® 8 8 « 8 S1 8 8 1 1  «  o ®  !  1 1 1  8 8 ®® « ® 8  100  150  200  *  c  8 81  2 f0  85 AIRPORT B, FLIGHT B3  NORMAL  OBSEEVED-  FX?  o  ECTED-  9  VA  iii  ±0 I 1  3  1  o  j  30 | ! 20 I  |  9 9 9 8 9 89 9 9. O 9 O 9  j  | | 1C I [  | | o1  1  50  0  POISSON  1  to |  | |  8 9 99 9 9 9 9 9 9 9 » 8 9 9 99 9 »  100  8:  EXPECTED-  .OBSERVED- o  0 c O  9 9 9 98 9 88 O 8O O99 9 98 9 9* 9 9 |  O o o o * 0 S o 0 0 0 o  98 9 9 9 8 9 9 89 98 9 9 89  1  O » O O O O  150  O  9  O O1  oO o o  1  2 50  2 00  - r. . )  VA FT A ELI ( CO Lb  1  O O o o O o o O 9 O o 8 8 9 o 9 9 8 8 9 9 9 9 8 9 9 9 9 O 9999 O9 O 8 9 9 9 o 9s o O 9 9 9 o 8 9 O 98 8 8 o 8 8 a 9* 9 99 9 o O 9 * O 8 a 9 9 O 9 8 8 o »8 9 o 9 999 O 8 » O9 9 9 O * 9 8 o o o Oo 9s S O 9 O 9 9 o 0 9 o » 9* » 9 O88O 9 9 o o c o o 9 9 9^ o o  |  | 30 | | |  |  |  ® a  20 | | | | | 10 | | | |  c  c  |  0 1 0  O O o O a o o 0 s 0 o S O O o  •••.V ^0. ) 1  8 989 8  o o O o  1  (COLI  A BL;  1  1  50  1  1  100  I  I  1 so  !  !  "0  !  !  : 50  LOGNORMAL  EXPECTED: * OBSERVED: o  HO  20  0--  9 O 99 9 9 99  O O O O OO a s9 9 <> 9 O B9 9 O * 9 6 99 9 9 9 S 99 9 9 9 99 99 9 * O 9 9 99 9a 9 9 O 9 8 99 9 9 9 99 8 98 98 9 9 9 9 99 9 8 9 8 99 8 9 9 99 99 9 89 100  150  B« B 9s « 9  i  O 9O 9 9 8O 99 89 9 8 200  86 AIRPORT B, FLIGHT B4  NORMAL  ED- 9 : VA P.I?i£ A ( C01VK'<!  o  OBSERVED-  1  50 |  9 'S  o o ® ® o » ® o ® o o ® s 0 « » e o  1 1 1  9  1  2.5 | |  |  ®  1 ®e 1  0 1 50  POISSON  -  9 c O O  O O 9 9  9 Se 9 O O O »  &  9 e 9 9 9 9 0 9  0 e ® e 9 O0 °  1  1  1  9 9 9 9  1  «  150  100  o ®  1  2 00  _ .. ..  OBSERVED- o  E'/.PEClED- 9 : VARIABLE  :  ( COLVUS  50 |  o  1 1  o o 0 o o 9 ® 9  O ® 9 ® ®  O O 9 O ® 25 9 ® 9 1 9 ® ® O 9 8 9 ® O O 9 9 l» o 9 » 9 ® lo 0 9 9 ® o 1 o |9 0 1 ' 1 1 1 150 2 00 100 50 1  1 1  9 O O O  S CC O S O ®O C O  l» s s  -  9 O O O  O  •  LOGNORMAL  EXPECTED: * OBSERVED: o 50 o 0 9  25  *  *  9* 9*  O  9  9 0 0  O  9 9  »  9  9  9  9 99 9 ®  9 9  * 9 9  a  O  9 9  : : : :9 9  9 9 9 9 ®9 9 99 9 9 99 9 9 99 9  O 9 50  • :  9 9  i  :  100  :  O  9 9 8 9  O O  0 9: 99 99 9 99 9 9 99 9 9 9 9 150  1  87  AIRPORT B, FLIGHT B5  NORMAL  9  "'0-  | | | 30  | | | | | | | |  10 |  | | | |  01 0  1+0  O o o 0 0 o o o  1 50  o o  0 o o o o o o o 0 0 o o o  o  O OO  1  100  50  VARIABLE  OBSERVED- o  POISSON  2 0-0  { COlVy-S  h'O. )  8  EXPECTED-  30  20  10  EXPECTED:  i+0  9 8 O  9O 1 > 99 >O O ©9 50  LOGNORMAL  i  ®  0 o  1  )  0  s  20|  "'l>.  '. CCLW::  OO 99 89 8 8 9 8 9 88 9 9 9 9 8 8 O 8 8 O 88 8 9 8 8 8 8 O 9 9 9 8 8 O o 9 98 89 S9 9 OO OO 8 9 88 8 O O 8 ' 9 O8 89 9 O 9 8 9 8 9 8 « 8 9 99 8 1 9 99 99 1 | 9 9 9 | o o o o o  |  VA ?.IA  I  o o  I  ICO  1 50  OBSERVED: o  20 o  9 O9  2 0o  1  88 AIRPORT B, FLIGHT B6  NORMAL  3 a  0  G S (3 0 a 0 a 01 o o i  c a a  0 a £}  0 a SI a 0 i  a a a SI 8)  0 0  0 a  o o * o a u a  o a o o a a o O O 0 j  j  i  POISSON  VtD-  o  s  EX;-' „-„C" ' t i : —  a  ;  VAN I A  30 i  ! I  1 i 25 i i I  i i  " a 0  o a o a o a a o a a a a a a a a o a a a io  SI a c 0  a o  0 0 c 0  a 0  a  D q  0  0  0  &  0 o  a  o c o o a o o  lOo  G  a  ai s  a  a  89 AIRPORT B, FLIGHT B7  Jjl'lN  UfcSStKV  NORMAL  o aa aa a a a . 0a 3)a a 0 a a a a aa a a 8 a a a a a 8 0 D 0 o >a a a aa a a 0  0  u  3  0  0  0  6)  0  Q 0  0  0  a 0 0 n 0  0  j  POISSON OBSERVED-  o  • EXP  50 I i  o 0  i 25 i i i  o a a  o o a  i i  o  0 i  c» a a a  i  0  a  EI  j  a a  C) 0 0 c  WlftiiLh  a  a a  0  o 0  £10 0 0 £1 0 00 a o a a  0  0 0  3 a a  N O , ' / i.  a  a 0  a 0 c Q 0  G O 0  i  £) o o  a a  o o  o a o a i  i :o  33  iCOLUMN  G G  a  ;  a  o a  a o a a  ,. 0  a :  2 CO  LOGNORMAL  -  EXPECTED: * OBSERVED: o 50 O o o o * a a 9 9 9 9  o o 9 9 9 9  25  ffi  a  * a a a a  9 9 ® 9 9 9 9 9  * * * a 9 9 9 9  * a 9 a 9 9  * * * a  a a  O O  a 9 9 9 a  a a 9 9 9  9 a 9 a 9  a 9 9 9 9  9 9 9 9  9 9 9  O 9 9  9  9  9  9  9  9  9  <ft  wTOS *S 9 9 9 9 ® 9  9 9 9 9 *® 9 50  9 9 8 9 © 9  9 9 9 9 © 9  100  O O O a  o 9  i9  O O  * *  9  9  '>  9  9  150  90 AIRPORT B, FLIGHT B8  NORMAL OBSERVcD-  o •  -  EX PL  fc.L  V,-  ABLE  COL  0  Q 0  ;  i  0  0  a  0 0 3 a 0 a 0 a 0 a a 8 0 a 0 a a a a c a 0 a a a a D o 1  25 i i i  i i  0 i  5< )  0  -  a  Q 0 0 0 0 0  0 G G 0 0  0 0 G G 0  a a  a  a a a a c o o a G y ) a [i  1 o  1 15! )  IOC  oI a  a  >• ;!  200  ; 250  -•  POISSON  ObSfc.KVfc.JJ-  o  :  i i 1  E X P E CT E E  -  a  0 0 a 0 3 a 0 0 a a 6 SI a s o a a a G o a a a 0 a a a a a o 0  25 i  j  I ! i 01  o  t  !  e a  (COLUMN  NO.)  1  « i O  8  a a  0 0 0 a £) 0 G 0 a 0 G G a a 0 G G o a a o 0 0 0 o a a a a o o 1  11 i<3  50  0  v'AK I A B L E  1  © 8  150  C 230  200 a  LOGNORMAL  EXFECTED: * OBSERVED: o  50  o 0 0  99 9 9 9 25 9 9 9 9 9* 9 9 9 ** 9 9 9 9 8 9 99 9 9 9 9 9 9 8 9 9 9 9 9 99 9 9 9 9 9 99 99 9 9 399 9 9 9 9 99 50 O  * * *  * *  9 9 9 9 8 9 9 9 9 9  100  o  9 8 ® 88 9 9 9 9 99 9 99 98 9 9 o  *  9 9 9 9 9  O o  9 8 9 9 8  8 8 9 9 9 89 9 9 9 99 9 9 99 ® 0 O  O  *  1 50  200  91  AIRPORT B, FLIGHT B 9  NORMAL  POISSON OBSfc.KVb.D- o 40  i ii  0  i ii i !  ii  0  0  0  0  0  0  •  0  0  0  0  0 0  0 0  0 0 0  0 0  0 0  6)  1 1  i  i  1  0 i  l  0  1  150  50  50  EXPECTED: * to  0 0 a 0 a a aa a si a 0 0  u  0  1  3 »:J 0i 0  l  I 250  OBSERVED: o  0 o  0 o o o 9 9 9 9 e 9 9  e S 9  0  •  0  9  0  e> a  1  s  iO. )  •  10 1  * *  fiN f  (CC  s  1 1 1 1  20  V A RIA BLE  0  3 0 1  0  a  0 0 aa a 0a aa aa 0 a a e a 0 0 a a s a a 0 0 0 a a a 0 0 0S I a 0 a a 0 S I8 a aCI 0 0 a a 0 0 0 o . 0 0CIa o 0 0 0 SI o a aIa e >a o a S a 0 0 o 0 a CI •o aa 8 0 0 0 0 0 o a a a a S ) a 0 0 0 0 00 a a 6 a ) s 0 0 o 0 0 a a a S a I a c o a a aa a  1 1  20  -  £XF'bC~  9 9 9 9 9 9 9 9 9 9 a a 9 9  50  o a 9 9 a 9 a a a 9 a a a 9 a 9 9 9  * *  a a a 9 a a a 9 a a a 9 a 9 9 9  * *  a a a a a a 9 a a 9 9 a 9 9  * * *  9 a 9 a 9 9 9 a 9 a 9  a a a 9 a a 9 a 9 9 9 9  100  o o o 9 9 9 9 9 9 9 9 9 a  * 00  a a 9 a 9 a  a a 9 9 9 9  o 9 9 9 9 9  0  9 9 9 150  o o 8 9 9  o o 9 9 200  92 AIRPORT B, FLIGHT BIO  NORMAL OBSERVED-  l>.D- a  o  i 20 1 1  j VARIABLE  0 0 0 0 0 0 a 0 a a aa 0 8 a a a  . 1 i  1  101 i  aa a 8 )) a a8 8)! 8 ) 8 a a C ) 0 a 8) 8) a a 0 6) 0 8) 8) 81 a a a  0  1 1 1  a  a  a a  El  a  i  a  a  a  a aa a a  a  a  o a a S)  0 1 0  (COLUMN NO  a a  a  1  5< )  a  a a  a  0  0  a a  a a  a a  0 £) a a  0  o  a  i  IOC  a  • I 150  3 «| 3 200  POISSON  JBStRVEu- o  tXh'ECTtU-  30 I i I I I 20 I  VARIABLt  0 0 a • 0 a 0 a a 0 a a a  a a a a a a  a a a a a a  08 ))' 0 8 0 9!  10 i  a a  a a a a  a  (COLUMN  NO.)  i  a  0 a 0 a a 0 0 a 0 0 a  0 ei  a  0 0 0 8) 0 0 0 0 8) 00 •  a  o •  0 c 0 0  £•) a  a a 6! a a a a  a  a a a a i a  ICO  2 Co  ItO  LOGNORMAL  EXPECTED: * 30  OBSERVED: o  * * * 9 9 a 9 9 9 9  15  0  50  9 9 9 9 9 9 9 9 9 9 9 9 9  O 9 9 9 9 9 9 9 9 9 9 9 9 9 9  * 9 9 9 a 9 a a a a 9 9 a a  9 9 a a a a a a 9 9 9 9 9  O O 9 9 9 9 9 9 9 a 9 a 9  100  * * * * 9 a 9 a a  0 0 0 o 9 9 9 a 9 8 9  O 9 9 9 9 9 9  O 9 9 9 a 150  9 9 ®  O 9 a  * a 200  93  AIRPORT B, FLIGHT B l l  NORMAL OBSERVtD-  o  VARIABLE  :XPECTED-  a  UMN  0 aa 0 0 a sa a 0a 0 0a aa 0aa a 0 0 0aa a 0 a a 00 0aa a a aa a a a a a a aa ffl a a a a 0 0 0a a a «)a 0  pii'j . )  I.  El  C!  SI  0  0  SI  0  ci  0  0  SI  100  150  2'JO  1  POISSON OBSERVLD-  Q  :  E X P E C T ED-  :  0  ( C J L L MN NO . )  VARIABLE  1  50 i  0a a a a 8 0 a a a as «0 a a 0 0 08 a a a a Da « o a 0 4a ) e sa 0 0 0 aa aa a a a a 0 0 0a D 8a 8 «) aa sa a i i  1  SI  8  1 I  SI  £>  i ii i  25 1  I  0  0  0  0  0  0  50 i  00  0  «l  0 0  8  0 0 0  o  siI  i  1 150  1 10 0  no o  |  i "250  LOGNORMAL  EXPECTED: * 50  OBSERVED: o  o «  9 9  25  9 9 9 9 9 9 9  50  100  O 0 0 0 0 0 0 o  o o  150  9 9 9 9  o  9 9  9  9 9  9 9  9 9  9 9  9 9  * * *  * *  200  94 AIRPORT B, FLIGHT B12  NORMAL U d o b. P V b .U — G 1  a  EXPELOEI—  L-  VHR  OLI. 'PIN  NO. )  1  40 i 0 1 i  SO  a aa a 0 0 a a a 0 Q 0 a a a 03 0a a a a a aa a a aa aa a 0 a a 0 0 6 ) D0 8 0 aa a aa a a a a a a aa 0 0 0 a a aa aa D a a si a a aaa asia aa 0a 6) 0 a aa a si Co!  i 1 i 1  1 1  20  i ii i  o  0  8)  8!  0  0  0  8)  0  0  0  0  8)  0  0  0  •  0  8)  0  0  0  0  •  0 0 0 0 0  O  a a a  0  a  a a  3  a  -  D  8)  0  0  0  8)  G  •  0  D  0  0  G  j  i 1.00  a:  C)  D  i  15<  8)  i  2 0 0  f: D L L UN  VAKIA t L E  0  0  0  0  0  8)  •  0  8)  0  0  8)  0  0  81  0  0  6)  0  0  o 0  0  9  a  N O . .1  j.  8)  0  0  0  8!  0  0  0  8)  •  0  •  0  0  8)  0  0  G  0  0  G 0  G  0  0  0  a  0  0  a  10 i  i  i o 50  0 1 0  i  0  0  0  0  O  0  0  0  0 0  0 O  G G  0  S)  0  0  10  OBSERVED: O  0 0 0  o  9 9  9 * 9 * 9 9 9 9 9 9  9 9  9 9  o  20  9 9  0  0 0 a a a a a a a a a aa a a a a a a a aa e a a a a a aa 00 a 0 0 0 0 0 0a a a 0 0 a 0 D 0 a 0 a a a a a a a a a a a a a a a a a a a a a a a a a a a sia a a 0 0 a aa a  :  9  0  0  0  8)  1  G  0  8)  o  20 1  50  a  0  EXPECTEE  ii ii ii ii  0  0  0  i 1 1 1 30 i 1 i  * 9  0  0  o 1o 50  40 i  EXPECTED: * 40  0  8)  1 1 01 0  LOGNORMAL  0 o  0  1  'OBSERVED-  0  •  •  1 1 10 1  POISSON  0  9 9 9  9 9  9 9  9 9  r r 100  —  150  i  o o a si  a a. a o  si !i ; '  ;.:;'; 0  r  1  V Hn I ABL  AIRPORT B, FLIGHT B13 4 0 :  NORMAL  io  o o o a  ObStRVtD- o  POISSON  tXKfcCI ED-  a  L Jf-'IN NLi . )  VARI  1  50 i  1  \  •  0  •  0 0 0  401 i i  1 1  0 0 0 0 8 £1« 8 S ))0 0 8 0 S 0 0 0 0 0 0 8 0 0 D 00 0 S) 0 0 0 0 0 000 0 0 0 0 S !0 0 00 0 0 8 0 8 ) 0 0 0 0 0 G C i 3 0 c Q 0 0 • 3 O 0 0o 00o 90 t a  30 1  1  1 I 20 1 i  1  a a 0 «)a o a a  0 0 S) C 80 8 £)  10 1  c  it 0 a  "  •  l  0  5 0  a a a  a a a a a  a a a a a a  a  »  •  a a a  a  a a a a  0  a e> •  a a a  a a a  a  a  •  c  •  'o  a  o a i  ) 0  1 50  a  a 0 a o a o o o a o a a o i) >:> i  i  i  .'0  O  250  EXPECTED: * OBSERVED: o 50 LOGNORMAL  25  *  0 8 0- —  o 8 8 8 ------  9 9 9 9 9  * 9 9 9 9 9  * * * *  9 9 8 9 9 8  * * 9 9 9 9 9 9 9 9 9  O O O O O 9 9 9 9 9 9 9 » 9 9 9 9 LOO  * * 9 9 9 9 9 9 9 9 9  O O 9 9 9 9 9 9 9 9 9 9  0 9 9 9 9 9 9 9 8 9  •  9 9 9 9 9 9 9  8 8 9 9 9 9 8  150  49 «9 «9 i9 i9  O 9 9 9 8  O 9 8 8 9  0 9 9 9  O 0 O O 8 9  200  i9 «9  * * *  * 8  96 AIRPORT B, FLIGHT B14  NORMAL  OBSEKVEJJ-  ' P F *":TF Ei—  0  a  t V A R I A B L E CO' iiLUriN  NO. ) 1  100 !  /•-' !  1 1 1  0  1  0 0  t)  •  0 0  50 i 1 i i 1 25 1 1  a a a a a a  a 1 1 ' a 0 1 0 1 .  0 0 0 a  0 0 a  a  a a a  a a  a a  i  0  ;  0  0 sii a a (9 a a a a a a a a s 0 a s) 0 a a o 1  J  50  .  0  OBSERVED—  POISSON  0 0 0 0 o  a a a  a a  a 0  •  a  i  o o  a  a a  a a a  o o • a a o o ! 1 o a! a a 100  t X h ' E i . : 1'fc.D- a  :  0 a  i SO V A R I A B L E (OC i L O i l N  a a ] 200 MO . ) ;,.  100 I  J  0 '0  75 1 1  0  1  i i 50 i  0 •  1  i 1 1 25 1 1 1 ; 0 1  0 0 0  a  0 a a a i  0 0 0 c a a  0 o c: o « a a a a s a a o a  a  a a o  a a o a 0 6)  a a a  a  a o  a a  o o o o  0  LOGNORMAL EXPECTED: * 80  10  OBSERVED: o  f  bo-  a a a a a a 0 !  a a  o a o a a o  o o a ! 10 0  o o o a a a ai a a a 15 0  si a ; 200  97  AIRPORT B, FLIGHT B15  NORMAL  EX F E C 7 E D -  a  o  40 I  1 ! :  a  0 0 a a a  i  i I 20 i  1 i i i  a a a 0  io i i i I I  8  8  0  a 0  o 0  o 0  0 I 0  1 50  o  :  a a » a  a a a a a a a  a a a a a a a  1  E X P E CT E D -  1 1 1 30 1 1  0 0 0  l 1 1  0 0 0  20 i I 1  a a o . a a  i 1 10 i i  a  a a  a  S)  o a si  o a  s a a a e> a  a  a a 0  a a a a a  a 0 0 0 0  8 8 8  6)  0 0  •  0  8 8  0 0 0 0 0 0  0 0 0 0 0 0  0 0 0  a a 8  3 8  0 0 0  a a a  a a a  0 0 0  0 0 0  0 0 0  a  a a a a a a a  a a a  0  o  i L or  0  0 8  a « 8  i  a s 3  •• VA R I A B L E  •  0 0 0 0  0 0 a a a a a a a a  a a  a  8  0  a a 8  0 0 0  a  e a a a a a  0 0 0  a a a a 0  0 a 0 0  0 0  0  0 0  0 0 0  3 3 a  3 o  0  0 0 0  0 0 0  0 0 0  8 3 8  0 0 0  0 a 3 a  a  0  0  0  8  0  a a  0 0 0  0 0  0 0  a  o  o  0  100  a 0 1  0 0 0  a a 0  a 3 a  0 0 0 a 8 a  £> 0  0  8 | a 3 200  NO•)  i.  0 0  0  a  0 D 8 a  l O JU. MN  a a 8  a  0  1 15C  a  0 0 0 0  1  a 0 a a a  a a a  a e a a a « « a  40 1 j  1 i  o  0  30 i i  OBSERVED-  AC-  0 0 8 S) 0 0 00 0 0 0 8 S) 0  1  POISSON  i" 1  UBSEK'v'fc-iJ — G  a a  o o  C) a a  a 3  3  3  a  a  a o  S)  c  a  0 I a  20o  i  i 250  AIRPORT C, FLIGHT CI -  ODSEKvEDNORMAL  E  a  ; VARIABLfc.  (COLUi'W N O .  o 0  i  0  75 1 l  0 0 0  1 1  a a a  50 1 1 1 1  a a  a a  1  0  a  v i 1 1 i 1  0  c  0  00 0  a  1  a  0 1 0  0  a  a a a  D a  a a  a  a a a  a CI  a  a a a  0  0  a  C)  a a  0  a a  a  0  0  0  a  a a a a  1  0'  a  0  CI  a  •  8  0  0  a  0  0  0  a  a  I  1  0  i  a 1 a 100  5C  OBSERVED-  S EXPE CTEE —  a  :  | 150  < C 0 L 0I'l N N 0 .;  VARIA BL E  100 i  J i 1  0  o  751 1 1  D 0  '-'5  0  1  i 1 1 i  1  00  0 8  a  0 0  0 0  a a a a a a  a a a a  a a  1 1  0  o a  0  50 i 1 i  0  a  o a  0  1  LOGNORMAL  -  iooi i  POISSON  "EE  -  a a a a  0  0  a  a  0  a  0  1  a a a  a 8)  a  a a  a a a a  a a a a i 50  EXPECTED: * 100  0  a a  0  a  0  0  a  0  0  0  0  0  0  o  a a o |0  0  1  j  1 CO  i 150  OBSERVED: o ®  9« a a  a a a a  o o  a a  a a  50 *  9 9  0  9 a  a a a a  99999 9 9 9 ® 9 9 9 9 9 a  a  50  a  a  a  o  100  i.  99 AIRPORT C, FLIGHT C2  O B S E R V E D -  a  ;  £>  E X P E C "  NORMAL  ;  VAHIABLE  f CCL'JF'iN  i'4 0  , }  i  J 50 1 I i i 1 25 i 1 J i i 0 1 0  OBSERVED-  o  0 0  a 8  e 0  :  0  0 a 8 8 8 a a  a SI 0 c 0 0 0 0 0  8) El S) SI SI t) £1 0 SI 0 3 S) 0 8 6) 0 0 0 SI a 0 3  1 50  1  j 3  8 6)  100  EXPECTED-  1 1 5 0  (COLUMN  VARIABLE  POISSON  NO.>  75 i  0 0 o  50 i  CI 0 0 8 SI 8 8 8) 8 8 SI 8 3 8) 8 8 8 8) 8 3 8 61 SI I i0 0 8 8 3  8  0  I  0  3  3  3 3 0 0 3 O 0 SI 8 SI | 0 0 0  LOGNORMAL  150  100  50  EXPECTED: * OBSERVEDt 0 Q 60  O O O * O  * * * . * ® ®  0 © ® ®  ®®® O  30  e 9 9 9 9 *  9  ® ® ® e ® ® ® ® ® ®  ® $ ® ® ® ® ® ® ® ®  50  ® ® ® ® ® ® ® ® ® ®  0 ® ® ® ® ® ® © ® ®  *  ® ® ® ®  ® 9 ®  * ®  100  9  ®  i  100 AIRPORT C, FLIGHT. C3  OBSERVED-  o  EX PEC  1  c. Li-"a  2  iOOl 1  | I I  1  0 a a a  a  a a  a a a  a  a a a  0 0  a a a  a  a a  a a  I  50 i  a  0 CI  a 0  0  6)  a a  I  0  a  25 i  a  a  ei  0  a a a a  a a a o  a a a a  0  8 a 0  i  i 20  0 1  -  o  EX  0  a  70 1  :  ( C OLUi'lN  V A K I A B L E  a a  0 i  0  a  !  i I  OO  a a a SI a  i  0 a CI  a 0 a a a a a  a a a  a a a a a a a  1  20  a a a a a a a  6; a a  75  s  * 9  8 20  a a  a  9  9  9  9  9  a  a a  9  9  9  9  i  a  0  a a o  c  ;  SO  0  9  9  a  9  9  9  9  a  9  9  9  0 0 a  •;o  *  LOGNORMAL  a a  o  JO  0 —  NO . )  0  a a a a a a a  8 8 8  i  0  0 a a a a a  0  1  i  SO  0 0 0 0  1  0 0  3  i  •  1  a a a a  1 4 ;i  0  1 i i i 50 1  0 Q 0  •  PECT E D -  i 00 i 1  £5 i  i.  a  i  O B S E R V E D -  ( C j L i. J n i'-i NO „ /  I r- i B L E  VMP  40  O 9  9 9  a  a  9 9  9 9  60  9  9  80  ;  i .-. CO  101 AIRPORT C, FLIGHT C4  OBSERVED-  NORMAL  i  1 no  0  EL i  E X P  I j 75 i  0  0  a  a  a  i  a a a a a a a  i  5) 8 ©  a a  s 0  a a a a a  0 i 20  OBSERVED-  0  o. G 0  a a a  Q  0  8 a a a  o  3 1  EXPECl ED-  0  0  0 0  0  0  a  0  I '  0 a  8  ! z'O  VARIABL  :  a  0  0 1 iO  3  a a a  a 0  0  a  a  i .40  MO. )  c;  a a  a  (C 3LUM*  a a a  a a  a a  o  1 1  1 1  a a a  Q 0  i 50 1  A B L E  es  i  i 25 i 1  Li- a  0  1 i  POISSON  L  :  i  0 8  ;  100  ( C O L U M N NO , )  i  1 1 20  1  i oo i  1 1  0  i  1 75 1 i I 1  50 1 I I 8 25 1 I 1 l .  1  o 1 2 0  8 8 a 3 0  0 8 a 8 8 8 a  a 8  -  •  G  0 0 0 0 0 0  0 0 o  3 a a a a a SI a SI  e 8 8  a  a  a G 3  0 a 8 8 8 "  8  a  a a a  a a a SI  o 0 D G  8 SI  i 6 0  i  8 a a a 0  !  a a a 0  a 0  3 3  0  0  a  D  c  0  i  l  30  1  j0  4 0  OBSERVED: o  • EXPECTED:* 100  a a a a a  a a a a a a a a a a a a a a  a a a a  a a a a  LOGNORMAL  50  a a 0  40  0  a a a a a a a a a a a a a  a a a a a a a a  3  a 9 a a  9 a a  60  * a a 9 a a 80  a 9 a a  o  a a  a 100  :2 0  102 AIRPORT D, FLIGHT D l  NORMAL - K V E D -  C) 8 8 8  I  0 SI 0 0  a  SI 0 0 0  8 8 8  8 a 8  0 0 0  a a a 0 0  a 8  a  8  8  0  0  0  •  0  e  8 8  a  a  3 8  a  0  0  8  0 0  8 8  0 8  a a  0 0  0 0  a 0  I  a  I  EXPE  OESERVED-  s s  a 8  I  cT E E -  SI  I  8  :  VAK i A ELir.  0 0 0 c 0  a  C C O U J h -i N O . )  751 CI £1  i 1 1 1 50 1 i i 1 '|  25 1 1 1  a  P o  0 1 0  1  0  0 8  o a  0  8  8  8  8  3  SI  a  a  0 S3  0 SI a 8 SI SI SI  0 0 0 0 0  0 a a a a a  8 a a a a a  a a 8 8 a a i 50  •  0  a 8 8 3 8 3 8  a o  j  si si a o i  1 i >o  EXPECTED: * OBSERVED: o 80  i 15 0  i.  103 AIRPORT D, FLIGHT D 2  OBSERVED-  :  0  t ' X P E C r t LI-  a  V Af I A B L E  NORMAL -  (COLUMN NO.  0 0  a  a 0  a a a  0 0 0  a a a a a  0 a  a  0  a  0  a a  0 0  a a  0 0  3  a a a a a  a 0 a 0 a 0  a a a  0 D 0  a D 0  0 a  a a  a a  0 0  a a  0 0  D 0  a a  a a  a  0 0  a a a  0 a  I  50  POISSON  OBSERVED-  0  ;  EXFE  751 1 "l 1 i  TEE  -  a  0 0  0  0 a  a a  a  a a a a a a a a a  a a  a a a  25 i 1 1 1 i  a a a a a  a a a a a  VARIABLE  ( C O L UflN  a 0  a a  a a a a  1  0 C) 0 0 a a a a a a a a a a a  !  0 o 0 •0 0 0 0 0  EXPECTED: * 80  a 3  a 0 0 0' 0  a 0 0 0 0  a 0 0  a a 0 i  i 1  0  i 5 0  '0  OBSERVED: o  O  9  o  a  a a e a a a a e a  o o o o o o  a  * a a a a a a a a a  a a  a a  a a  a  a  a  a  a  * * * * a a  40  o  :  150  0  50 1 1 1 1 1  0 i 0  LOGNORMAL  100  50  a a a a a a  9  0 a a  a a a  100  NO . )  i  104 AIRPORT E, FLIGHT E l  NORMAL OBSERVED-  -  o  i ABLE  9  < COLUMN  NO.) i  751  |  1  s  50 1 | 1 I  a  j  a a  a  | I I  a a  D  0  a a a ai a a a  a  a a a a  a  a  a a  si o o oo aa o o 1 i a a 150  a1 a  1  200  .i 250  -  • -'  -  8 83 0 0  »  1 8 100  I  50  0 8 8 98 8 98 8 8 8 88 8 88 88  aa  a  25 i |  01  0 0 039 09 9 0 9 9 39 38 9 9 9 3 0 0 1 8  POISSON  OBSERVED-  :  o  EXPECTED  -  3:  VARIABLE  (COLUMN  NO.) 1  75 l  j  a  I •  0 000 0 a 8 0 9 8 9 0 8 8 8 88 3 88 8 89 33 8 38 8 8 9 8 0 8 3a 8 8 8 a 0 • 8 . a a a 8 8 8 89 8 a 3 0  50 i 1 I •  «  |  a 8  |  25 1 i I  8  e  8  a  a a a  8  e a a a  |  1  a  0 01  a  o |  a  a  a  a  a a 8] 8)  0  i  1  o c 150 i  100  50  o  8) 200 i  ;  i  - -0  LOGNORMAL  EXPECTED: 60  * OBSERVED:0 O O o  O O  9  0  9  0  9  9  9  0  9  9  9  9  O  9  9  9  9  9  0  9  9  9  9  9  9  9  9  9  9  O O  *  9  9  9  9  9  9  *  9  9  9  9  9  9  *  9  9  9  9  9  8  9  9  9  9  9  9  9  *  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  8  9  8  8  9  *  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  8  9  9  9  9  i  9  8  9  8  «9 9  9  »  30  *  o  ®  9  9  50  9  9  9  * * *  9  8  9  100  9  9  *  150  *  O 9  8  9  200  105 AIRPORT E, FLIGHT E2  NORMAL OBS'tRv'tD-  0  EXPEC1 ED-  a  .  50 1 i  a  G  a  9 a  G 0  8 a  a o  a  a a o a D a  0 0 0 0 0  a a 6) 8  0 o o o o  9 a a a a  1 25 1  •  i 1 1 1 0 1 0  POISSON  0  a 0  a  0  o  e 6) 8 tl 0 0 0  8 8  1  a e  1  50  a s 8 a  o 0  1  8  0 a 8 0 50  0  50  «a  0 a a  •  a  0  0  a  a a a a a  0 0 o 0 G  a a a a a  1O0  100  a a a  a a a a a  a a  a a a a  a a a  £)  a 0  a a a a a  0 0 0 0 0  0 0 a  £1 8 0 i a  i  15< i  VARIABLE  50 i  0 8 a  a  I  i 00  EXPEOTEB-  OBSERVEU-  a  i.  a  a  1  i  C O L I ii-if •1 NO . )  V A H1 A E L L  a  200  (COLUMN  NO.)  |  ! 2 5O  i  a a a 8  a 0 0 a 0 a "0  a a a  0  a a  L50  200  150  250  200  106 AIRPORT E, FLIGHT E3  NORMAL OBSERVtDhXPECTLB-  i  a  0  50 t i  0  0  3  0  8 8  8 8 8 8  e  8  8 8  i 1 i -'5 i  8  8 8!  0  8  8  8  8  ! 1 1 i  8 8 8 8 , e 3 0 8  8 3  8) 8 8) 3 6) 8  3 8 9  8  8)  8  0  8  8  0  9 8  0  0  9  0  0  3  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  )  100  POISSON  OBSERVED-  o  <PECTED-  150  >I A B L E  3  (COLUMN N O . :  75  0  Q 0  8  9 8! 8 8) 8  8 9 8 9  0  • O 0 0  a 0  8 8 8  9 3 8 8 8  a a a8 8  8 8) 8 8) 8) 8 8) 8 8  3  9 3  9 0  3 9  0 0  0  0  0  8 8  0  0  0  0  0  0  0  0  0  0  0  0  100  a o. o a 0  0  8 10  200  8 0  0  I •  l5o  107 AIRPORT F, FLIGHT F l  NORMAL  OBSERVED-  o  :  E X P E c T ED-  :  V ARIABLE  a a  a a  ( C O L JMN  MO . )  i.  0  50 1 1 i .  a  a  a a a  a "a a a  a 'a a a  a "a ~ a a  a a a a  a a a a  a a a a  a a a a  a a a a  :  i 100  a  i  _ . . .. . _  a  25 1 1 i i  0 0 0  1  a  0 1  •  a  S) a a a a a 0 o I i  50  a  a »  0  a a a a  1  a 0 0 0 o a a |  •  a i  i 50  a  aia a  I  1  200  250  POISSON  OBSERVED-  o  EXPEC""ED-  VARI ABLE  a  50 1  a  a a a  a a a a  0 a a a a  o o o •  a a a a  a a a a  a a a a  1  •  1  I I -'5 i  1 i i 1 0 1 0  a o a a a a o I  LOGNORMAL  EXPECTED: * 60  OBSERVED: o  50  a a a  1  i  1 -0  ( C O L U M I vi NO . )  0 0 a a a a  a a a  0 a a  a  a a a a  a a a a  a a a a  a o a o o a o o o a  1  C)  1  i 15  0  a  1 o" a 1 a 2 Co  a  |  1  2'r  0  108.  AIRPORT F, FLIGHT F 2  NORMAL  OBSERVED -  o  ;  EXPECTED-  |  e  • V A R I A B L E ( C C LUNN  0 8 8 £•) 08880 8  1 1  98880 0 8888009  25 1 1 i  888B8 000S 80888800008 890888 8 00000  i f  93000088900000080 0 | ! 8 0 889 8 888 0 1880| 0  OBSERVED-  1  0 • 00 0 08  50 1 I 1  POISSON  NO. )  100  o  200  EXPECTED-  i  300  VARIABLE  < COLUMN  a 000 0 0 8 0 8 8 088808 8980 08 9899009 88 8880008 0088 8 800008 809888000008 88008989OD000088  8  I  8  I  ICO  I  18888 8 880)  200  0  SCO  NO.)  i  109 AIRPORT G, FLIGHT G l  NORMAL OBSERVED-  o  150 i  I  0 0  100  0 0 S 0  POISSON  8  8  0  8  8> 8  0  8  8) 8 8 8 • 8 8 8) 0 8 8 u i 0 0  0 0 0 0  0 0 0 0  OBSERVED-  o  :  8) 0 0 ) 8|8 i  EXF'ECTED-  oo  'VARIABL  150  (COLUMN  1501 i I I 1 i  0 0  i  0  1 1 1 i 1 j  0 8 0 8 8 8 8 8 8 8 I 8 8 8 1 8) 8 8 8 0 i o 0  LOGNORMAL  EXPECTED: * 150  9 0 0 0 0 0 0  8 O 0 0 0  I  OBSERVED: o  0 8|8 100  150  NO,)  1  110  AIRPORT G, FLIGHT G2  S  NORMAL OBSEKVhLl-  EXPEC TEO-  0  75 1 1  0  0 a  0 a  a 0  a a a a a a a a si a si a  3 a a a a s  0 0  si a a a  a a  0 D  o 0  0 0 • 0  si a  a  0  0  0  0  0  0  a  1 1 0  a 0  0 a  1  0  OBSERVED—  0  :  a  a 0  oo I  si a 1 o aIa  a  a  150  VARIABLE  si  j  200  (COLUMN  NO.) 1  0  a 0  ~'5 1  LOGNORMAL  NO.) 1  3 0 0  1  i  o 0 0  I  o  a  i  E X h ' t C l"ED-  50 i 1 1 1  0 i  si a  a 0 0 0 0 0  a  5 J  751 i 1 I I  1 1 I i  (COLUMN  0  25 i 1 1  POISSON  VARIABLE  0  50 i i 1 1 I  0 i  a  a  a •  s a  a a 0 o  0 0 0 0 i 50  0 a o a a a a a si a si a a a si a  a si a a I  0 0 0 0 a a s a  a a a a  3  a s> a  •  a  a a a a  o 0 0 0  a 0 0 0  a a 3 3  CI  i 100  a si D  0 i  a 3 3 3 0 0 I0 150  S!  SI  SI  I 2O  0  111  AIRPORT G, FLIGHT G3  OBSERVbiJ-  o  j  t X P E C 1 DE  X AbLE  ( C JL  MO, )  1  40 i  NORMAL  j  L)  1  30 1  0 0  1 1 1 20 1  0 0 0 a  1 1  o  1 10 1 ! 1 1  1 0 1 50  OBSERVtD-  o  a  a a  a a  a a  0  0  a  a a a  a  0 0  a 0 0 0  a 0  •  0  a a  a  a a 0  a a  a a  0 0 0 D  0  0  0  a a  0 0  0 0  0 0  b 0  a  C)  a a  a a  0  0  0  0  a  a a  •  0  0 o  0 o  a a a a a a 1  a  a a  a  a  a  a  a  a  a  a  a  0  0  a 0 a e o a  a a a  a a a  a a a  a a a  a a a  0 0  0  0 0  0 0  0 0  0 0  0 0  0 0  o a  i  0  :  a  a  a  a  1 100  a  1  E X P E C " 'EE  •  i 15C  -  a  0 0  a  a a  a a a  a a  o  0  a a  a a  a a  0 a  a a  a a  0  a a  a a  1 500  VA R I A B L f  0 a  a• a 1  i  250  o : D L L MN N O . )  401  POISSON  J i 30 i 1 1  20 1 1 1 I 1 10! 1 1 1  a a  0 ! 50  EXPECTED: * to  0  a  o a a a a  0  a  a  0 0 0  1  LOGNORMAL  a  a a i  a a  a a  a  0 0 0 0 0 a a a a a a a  0 a a a a a a a a a  a  8)  a a 1  100  a a  a a a a a a a a a a a a a a 1  OBSERVED: o  a a  a  0 a a 0 0 a D 0 a 0 0 0 0 D 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 0 0 0  a a a 0 0 0 0 0 0 0  a a a a a a a 8)  0  0  0  0  a  •  0 0  •  0 0  0 G  c  0 0  1 15 0  G  0 a a 0 a a  a 0 D  a  0 0  a  a  G  a  0  0  a a a 81 a  0  a a  a a a  0 0  a  0 0  0  C)  !  I jO  j 250  1  112 AIRPORT G, FLIGHT G4  -  O B S E R V E !  NORMAL  75  i  0  ;  c X P E C  3  TtE  :  C O L U M N  V A R I A B L E  NO,)  i  N O . )  1  3 a a 8a 8 a 3 a 8 0330 0 a 3 a 8a3 0 0 aaa03 88a 0a a8 aa 9a 80 00 0 aa3300a a 0a a8 88 a8 30 00 0a a80 3 /  D  50 1  2 5 !  ij 1 f  POISSON OBSERVED  1  1  1  5  -  •  1.00 1  ; EXPECTED  -  3  ;  V A R I A B L E  ( COLUMN  .0 0 08 088a a 8 a 1 0 0 a 8 8 a8 3 a8 8 8 a ij 3 a a 8a83a 0a a8a8808 0a a a 8 0 a 18 a 3 a a 3 0 a 3i a 3 3 0 0 03a 0  75 I  0  1 1  !  50 1 I  1  a  a a  -;CT 1 1  !  0 i 0  LOGNORMAL  D  1  50  •1  100  EXPECTED: * OBSERVED:O 80 * a o * a o * a o * a a a a a a a a a a a a a a a a a a a a HO a a a a a a a a a a a a * a a a a a a a a a a a a a a a a a a a a a 50  O O o  0 a a a a a a a a a a  o a a a a a a  a a a a  a a  *  a a  113  AIRPORT G, FLIGHT G5  OBSERVED- o -EXPECTED- 0 : VARIABLE (COLUMN NO.) 1 :  NORMAL  75|  50|  o e e  0 0 0 0  » e « e 25|  0 a 0 e e 0 o 9 O 9 0 9 0 0 0 9 0 0 0 0 0 9 0 0 0 0 9 0 0 0 0 0 0 O 1 I I I O 9|9  0|* 0  50  100  150  200  OBSERVED- O : EXPECTED- 0 : VARIABLE (.COLUMN NO.) 1  POISSON  751 o o o  50|  O 0 9 O 0 0 O 9 9 9 0  25|  O 9 O  a o I 10 o  0 9 0 50  EXPECTED: * OBSERVED:o 50  o  9  o o  <9  9  0 o  * *  i9 i»  9  9  9  9  B  0  0  *  0  t  *  »  9  9  t t  * *  »  9  9  9  9  9  9  9  9  9  9  '  9  9  9  9  9  t  0  O O  *  9  30  O O  I o o| 9 0 9 0| • 15 200  O O O  o  O  0 o o o  o  9  0  9  O  9  0  O O 9  9  9  9  9  9  9  9  9  9  9  9  *  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  9  0  100  * *  * 9  9 9  150  9  9  9  9  9  114 AIRPORT G, FLIGHT G6  NORMAL  O B S t K V h D - -• o  :  hXi'-'hCTLD-  a  : • V A R I Al- L E  (C O L U M N  NO, )  1  NO ., )  1  4 0 i 1  ii 0 00 u a e o o a ei a o o ; o 8) a a o a a aaao oa o 8)8)8)0 083 aaao ooa a a a ei o o o s aaaaoooaa oaaaaaoooaa o o oaaaao o o aas o oa oaaaaoo oaaa o oa o aaaao ooa3aa aaoaaaaoooaaoat) ©808888)000380880 88808aaaoooea0888 0 aaaasaoaaasioooaaoaaasia  1  30  i i 1 1  i  20  i f i 1  I  10  i  1  i i  1  oo  0 1 0  O B S E R V E D -  POISSON  I  I  100  o  :  i  •  E x P E u  1E D - a  :  i  |  200  300  VAKI Ab'Lh  < COLUMN  401  oaaa 8888 o 8aa o 8o oaaaoao aaao oaa aaao oea aaao o oa aaaaoooea 888 8 00080 o aaaao ooao o 088 a S 8) 000003 0 0088888) 000808 0 ooaaaaao ooa oaa o a a a a S) si o o o a o o a o o a a a a a a o o o a o o o si o oaaaaaaao ooao oaaaoa o aaaaaaaao o oao oaaaa o 883 i i i |  30 1  i 1  20  i i i  |  i  1 1  i 10 1 1 1  I i 0 i  ICQ  \  2 CO  0  LOGNORMAL  .EXPECTED:* to  OBSERVED: o  O  O  9 9  0 o o 9 9 9 9  9 9 9 9 9  9 9 9 100  * * * * * 9 9 9 9 9 9  * * * * 9 9  9 9 9 9 9 9 9 9  9 9  * * 9 9  0  O  9  0  9  9  0  9  9  0  *  9  0  0  0  9  9  0  0  0  0  9 9 9 9 9 9 9 a 9 9  9 9 9 9 9 9 9 0 9 9  9 9 9 9 9 9 9 9 9 0 9  9 9 9  9 0 0  9 9 0  9 9 9 150  O  o o 9 9  O O  o  9  9  9 9 9 9 9 9 9 9 9 9  9 9 0 9 9  9 0  9 9 9  O O O O  9 9 9 9 9 9 9  »  9  O  9 9 9 9 9 9 9 9  O O O  * * 9 9 9 9  200  o 9 9 0 9 9  O  9 9 9 9  * 0 0 0 9  9 9  * * * 9  115 AIRPORT H, FLIGHT HI  o  OBSERVEDNORMAL  :  t X h ' h C TEL"  -  a  (C 0 L UM N N0 . 1  V AR I ABLE  75 i 1 i  a  1  a  50 l  0  1  1 i  1 25 1 1 1 1 i  a a  3 o  01 0  o  OBSERVED-  POISSON  a a a a a a  :  0  a a a  a 1a  a a a  » a a a a  a a a a  a  751 1 •  a a  a a  a aa a a a  a  a  a a  a  i  oIa  a  a  a  150  :  VARIABLE  a a a a e a a a  a a a a a a a a  j  200  (COLUMN  NO.)  1  0  1  .  •  a a a a a  1 1OC.  50  -  0 0 0 0 0 0 0 0 a 0 a 0 s  a a a a  1  E X P E C ""EE  a  a a a a a a  1 1 501 1  0  0 0 a  a  0 a  I 1 i  a a a  251 i 1  a  1  a  1  0 1 0  o  a  a  a  a a a a <i 8) a a 8) a e 8 > a  a a a a a a a a  8) 8) a  a  1 - 50  a  I  0  a  i 100  0  a a a a a a  8) 81  0 0 0 i  a o o  a  a a a o 1 o o  a  a  150  I  200  LOGNORMAL EXPECTED: * OBSERVED: o 60 *  * *  * * a a  a a a  a a a  O a a a a  9  9  9  a e a  O o O o O a a  9  9  9  9  9  9  9  9  9  a a a a a  9  9  a  9  9  9  9  9  a  a a a  9  9  9  9  9  9  9  a  9  9  9  9  *  *  »  0  o a a a a  a a a a a a a a  a a a a a a a a  a  a  a  a  *  30  a  • a a  50  a  O a a a a 9  100  O O O O a a a a  9  a  a a  a 9  *  *  a  a  ©  ®  ®  150  ©  ©  ®  116 AIRPORT H, FLIGHT H2  -  NORMAL  O B S E R V E D - (J  ;  a  t: X r' b. L I E  VAR I A B L E  (C OLUilN  NO. ) 1  75 i  | 50 1  a a a  1 1 1  1 25 1  a  i  a  1 1 1  a a  0 !  a  • 0  0  a a  a 0  0 0 0 0 •  8  0 0 0 ®0 a a" a 0 a a a 0 a a a 0  a a a  a a a a  0  a a a a  a a a a  1  a a a  i  50  a a  a  o  a  o  a  a  c  a  a  o  a  a  o  i  i OC  a  a  a  ]  !  15C  200  POISSON OBSERVED-  o  E XFEC TED-  a  VARIABLE  XUMN  NO'. ) 1  751  j  0 0 0 0 0 a a  50 1 i s i 1  25 1 i  1  0  1  01  i  a 0  a o o  0  LOGNORMAL 60  a  a  a a a a  a a a a  a a a  a a a  a a a  a a a  a a a  a a a a  a a a a  0  1 -  a  i  a  s  o o  a a  a a a a  o o o o  0  a o  a  o a a 0 0 0 a a i 10 0 It 0  i  | 20Q  OBSERVED: o  * * * * 30  C! 8 a a a  ]  So  *  0 0  9 9  9 9 9 9  9 9 9 9  9 9 9 9  * * *  0 9  9 9  0 9 9  0  0  » 0 9 9  0 0 0 0  0 9 9  9 9 9  9 9  9 9 9  9  0 9  0 O  0 O  0 9 9 9 0 9 0 9 9 9 0 9  0 O O a 9 9 9 9 9 9 0 9  9 0  a 0 9  9 o  ^ 50  100  150  9  9  117 AIRPORT H, FLIGHT H3  OBSEKVED-  0  ;  E X F _U- •E J —  8  ifilABLL-  ( C O L U M N NI- ! . )  i  NORMAL o  i i  0 SI 0  i i 50 1  Si S)  ]  i  1 1 251  a  0 0 0  i i 1  a  i  01 0  POISSON  OBSERVED-  •  o  :  / _i 1 1'  .  i 50  8 a  SI 8 a SI 81 9 SI 8 S) 8  8) 9 SI 9 SI a 8) 8 81 a i  EXPECTED  -  9  8 0 a 0 8 0 8 0 8 0 8 0 8 D  8 8 0 0 SI 0 0 8 SI 0 i a 1  1 00  a  j  150  VARIABLE  ( C O L U M N NO - )  0  I  i  1 50 i 1 i  i i  25 I 1 1  i  LOGNORMAL  o  8 9 0  8 0 0 0 0 0 0 0  SI 3  f  9  0 ! 0  o.  0 0 0 0 0 0 0 0 9 0 SI a a . S) 9 a 8 81 a a a si a 8 8 9 8) a 8 0 8 6) a 9 8 0 t SI 8) a 9 8 0 6 8) a 8 8 0 9 SI 8 8 1  1  8 0 0 8 o 9 0 8 0 0 0 0 0 0 10o  50  8 a 8 0 8) a Q 9 0 !  i  15Q  EXPECTED: * OBSERVED: o 80 0  O 9 9  9  * *  9  9  9  9  *  e  9  *  O O O O  9  8  9  9  9  9  9  9  9  9  9  * * *  O  9  9  9  9  9  9  9  9  9  8  9  9  9  8  9  9  9  9  9  9  9  9  9  9  9  9  9  9  8  s  9  9  9  9  9  9  9  9  O  9  9  9  9  9  9  9  9  9  8  *  9  9  9  9  9  9  9  9  8  9  8  40  o  O  9  50  100  1  AIRPORT A, 1981  OBSERVED- o : EXPECTED- e : VARIABLE (.COLUMN NO.) 1 NORMAL  150|  O O O  100  o e o 0 o 0 « e  •«  50  9 0 0 0 0 0 0 0 O 0 0 0  0 0 oo 0 0 0 0  I 50  POISSON  I  100  I® 0 I 150  200  OBSERVED- O : EXPECTED- 0 : VARIABLE (COLUMN NO. ) 1 150|  100  50  0 0 0 0 »  9  0 0 0 0 0  0 O 0 0 9 O O O O O  50  LOGNORMAL  EXPECTED: * OBSERVED: o 150  0 0 O O O O  I 100  0  o o 0 O o o o  O 0 0 0  |o o 150  200  AIRPORT B,  1978  0  : EXPECTED-a : iv/l/ET^BI/T (COLUMN NO.) 1  OBSERVED100 1  1 7  o oo oa ao a o aoa o o ®aoo a o9 aaoa a o oa a a o a a a oaaaaoa oa®aao o a oa oo a oo a ooa o oa a o o a ooo  0 00  5|  | ]  e  j j  50|  | | | |  25 | | j |9  e  0 |  0 0  o  0 1  8 1 8 8 18  8  50  0 0 000 0 000 00 1  100  a  o o oao o ao oa ao o a aa 1  150  10 200  1  1  1  250  OBSERVED-O : EXPECTED-a : VARIABLE (COLUMN NO.) 1 100| |  a a a a oa a ooe a a oa oa a a oa o a a oa o a a o oe o o a a a oa a oa a a o o aa o o a a a o o aa o o a a a o o aa o o p a o a a a oooooa o a a a ooo oa oaaa o ooa oa a a a oooooa oa a a a oo ooa ooooa  j j  | 751 |  |  I  | 50| | |  I I  25|  1  I  j  | 0 |e 0  «  LOGNORMAL  1  0 0 0 0 00 0 000 00000 1  50  1  o  o  100  1  a o a o o a ao a a o o a a ao 1  15o  9O a|a 2C0  1  |  1  250  EXPECTED: * OBSERVED: o 100  * *  50  9  *: O O : O  ; : : : ': : :  a a a s 99 99 9 9 93 99 9 99 39 99 9 a a3 9 3 9 50  a 8 a 9 9 8 9 3 9 9 9 9 9 9 9 99 8  9 8 9 8 9 3 8 9 3 8 9 9 9 9 9 99 9  100  *O O *9B O8OO 9 99 98 8 0O O 8 9 89 99 9 9 O « 9 3 3 9 9 O 9 9 8 8 ' 9 8 3 9 8 9 8 9 8 99 9 93 99 9 9 8 98 9 *9 o  o o  * *  S  150  200  120 AIRPORT B, 1979  OBSERVED- o :EXPECTED- « : VARIABLE (.COLUMN NO.) 1 1001  NORMAL  oo oe«® 0999  75|  o  99900  0®99®009 09999009 09999009  501  999990099 999990090 99999OO0O 999999000090  j 25| |  I o| 0  c3 9 9 9 9 9 9 0 0 0 0 9 0 <B 9 9 9 9 9 9 0 0 0 0 9 9 9 <B 9 9 9 9 9 9 0 O O 0 9 9 0 O  ocx 100  200  300  OBSERVED-o : EXPECTED- 9 : VARIABLE (COLUMN NO.) 1 100 i  999 00099  00900009 09900009  50| 9990000099 0099900000900 0 9 9 9 9 0 0 0 0 0 9 0 9 *w 0 9 9 9 9 9 0 0 0 0 0 9 0 9 8 >90  0 1 99| 0  |  |  200  100  30  0  .  O LG N O R M A L  EXPECTED: * OBSERVED: o 100  ** 9 99 *9  9 9 9 9 9 9 O  O  B 9  O O lr  50  O  o  O O  o 0  * 100  200  121 AIRPORT B, 1980  1 OBSERVED-o : EXPECTED-0 : VARIABLE (COLUMN NO.) 75| |  NORMAL  o o o o  |  j 50| | | | j 25|  | j | |  01 0  o o o 0 o 0  o 9 • o0  0 0 0 O 0 0 O 0 9 0 O 0 0 o O 0 9 0 O 0  eo 9 ee e 0 o a e e e 0 o o O O 9 9 0 o o 8 0  0  1  1  1  50  O  0  9 0 O 0 0 O 0 0 O 0 O 0  0  o o o 0 o 0  0  O 0 0 O O O 0 O O 0  o  O 0 O O O O 0 o o O 9 0 O O O O O 0 0 O O O 9 o 0 O O O O 0 0 0 0 O 0 1 1 1 1 1 0 1  100  150  1  250  200  1 OBSERVED-o ; EXPECTED-0 : VARIABLE {COLUMN NO.) IS]  o  1 1  0 0 0  1 o o o o o  50|  1 1  1 1  25|  1 1 1 1  01 0  LOGNORMAL  EXPECTED:  80  *  OBSERVED:  O  O  0 0 0  0 9 0 0 0 0 0 0 O 9 O 0 e 0 O 0 o o o  0 0 O 0 O O 0 O O 0 O O 0  O O 0 O O 0  0 0  0 0 0 O O 0 0 0 0 0 0 | | 0  50  o o o o o  O 0 O 0 O 0 O 0 O 9 1  100  o o o o o o o  © o O 0 o O 9 0 o o oo o o O 0 « ) O o o o o « ) 0 0 o o o « > O o 0 o o « 1 1 1 150  O 0 0 O 0 0 0 0 O 1 9  200  0  e  |  250  122 AIRPORT B, 1981  OBSERVED-o : EXPECTED-9 : VARIABLE (COLUMN NO.) X ISO] NORMAL  |  O  o  100 I  1 1 j. 1  o  0 o  50 |  | j j j  o  9  9 9  9  o  9  O 9  O  9  0  9 O  O 9  O  O  9  9  9 O  O 9  O  O  9  9  O 9  O  O  9  9  9  9  O  O  9  9  9  9  0  0  9  9  9  9  9  0  0 9  0  0  9  9  9  9  9  9  0  9 9  9 O  9  9  9 9  9  9  9  9 9  9  O  9  9 9  9 O  1  0  OBSERVED-o  :  9  0  9  ol  POISSON  ®  0  o o o o  1  1  1  50  O  1  100  9  9  1  O | 9  150  9|9  |  1  250  200  EXPECTED- 9 : VARIABLE (COLUMN NO.) 1  ISO] 9  o  100 I 1 1 1 1  50|  o o o  |  j j  150  9  9  9 O  9  9  9 O  9  9  9  O O  0  9  9  O  O  9 O  O O  o  O  O  O  O  9 O  O O  O  O  O  9  9 © O  O O  O  O  O  9  O  o O O o o o o  O  O  O  9  9  0  0  0  9  9  9  0  0  0  0  0  9  9  9  9  9  0 O  9  9 O  9  9  9  9 © 9 9  01  9  |  EXPECTED: * OBSERVED: o  9  9  0  O  LOGNORMAL  9  9  o o o o o  j  0  9  1  50  O  1  9  |  100  O  |  O  |  150  0  0 9  9  9|9  200  |  1  250  AIRPORT B,  123  1982  -  ......  OBSERVED-0 : EXPECTED- 9 100  I I I I I  o o o o o  1 I I I I 1  9  9 9 0  9 9 9 0 9 9 9 9 9 0 9 9 9 O O « 9 0 9 O 0 9 0 9 o o 0 9 9 0 1  50  0BSERVED-o : EXPECTED100!  |  I 1 j 1  O O 9 9 9 9 0 0 9 9  50|  25|  I 1 1 I  01 0  9 O 9 0 9 o 9 o 9 9 o 9 9 9 o 9 0 9 0 9 0 0 0 o O 0 0 0 o O o 0 9 o O O 0 9 o O. O 9 9 o O O 9 9 o O O 9 9 o O O 9 9 0 O O 9 9 o o O 9 1  100  0  0 O O 9 O 9 o 0 0 0 0 0 0 1  0  | 9 9|0  150  0  |  200  1  250  : VARIABLE (COLUMN NO.) 1  o  j j j 75|  1 1 1 I  0  9 0 0 0 0 9 © 0 9 e 0  O O 0  50|  01 0  VARIABLE {COLUMN NO.) 1  o o o e 0 9 9 9 o 9 9 9 0 9 9 e 9  75|  1 1 25 I 1 1 1 1  :  9 O 9 O 9 O 9 9 O 9 |  8  O o o o o O 0 9 o O 0 O o 0 O 0 0 O 0 0 o 0 O 0 9 0 O 0 9 0 O 9 9 O 0 0 0 0 O 0 0 9 O o 0 0 O o 0 9 O o 0 0 O o 0 9 o o 9 9 0 o 9 9 0 0 9 o o 0 |  '100  50  0 9 o  0 0  o o o o o o  0 0 1  0 0 9 9 0 9 0 0 0 0  9 0 O 9  O O O O  O O 0 O 0 9 O 9 O 9 9 | | O OI> 9  15°  200  •  |  1  250  LOGNORMAL  EXPECTED: * OBSERVED: o 100  O O  l O  i  I::: I  9 9 8 9  50  * 9 9 8 3 8  r  '. o  9  9  9 9 9 50  9 9 9 9 9 9  8 8 9 8  99 89 85 89  0 8 9 9 9 8  !, 6:9 S9 ?9 S9 59  9 9 8 8  9  9 9 9 3 9  *  O  9 9 9 9  *  0  8 8 8  8 8 9  O 0 O  9 9 9 9 9  9 9 3 9 3 9  9 8 9 9 9 8  9 8 9 9 9 9  9  "" """loo  O  8 3 9 9 3  O  9 9 9 9  '""150"""  o  9 8 9  8 9  9  9  9 200  8  124 AIRPORT C, 1980  •-  -  --  OBSERVED-o : EXPECTED- e : VARIABLE (COLUMN NO.) 1 ISO] | j  0 O  j 100 |  9 9  O 0  1 1 1 1  50 1 | | j j  o| 0  9 9 9 9  s  9 9 9 O 9 9 09 9  9  0  O  1  OBSERVED-o  POISSON  9 9 9 9 9  9 9  9 9  O O 0 0 0 0 O O 0 O  9 9 9 9 9 9 9 O 9 O 9 0 9 9 O 9  1  1  50  9 .  |9 9 9  |  100  150  EXPECTED- 9 : VARIABLE (COLUMN NO.) 1  ISO I | j  |  100 I  1 1  J  o  O O O OO  0  9 9 O o 9 9 9 a 9 9 9  50 |  | | j  | ol 0  9 o 9 9 9 9 o 9 9 9 9 o 9 9 9 o 1 1  50  9 9 9 -  O 9 O O 9 O O O 9 9 •|0 O 1  |  9-  100  150  LOGNORMAL  EXPECTED: * OBSERVED: o 150  9 9 50  9 9 100  *  9  9  AIRPORT C, 1981  125 OBSERVED-o : EXPECTED-® : VARIABLE (COLUMN NO.) 1 200| I I  NORMAL  O 0 o  1  9  150| | | | | . 100 I  9 9 o 9 o 9 9 9 9 9 9 9 9 9  1  | | j 50|  01  0  POISSON  9  O O O O  o  1  9  |  O O O O O O O O O O O O O O  9 9 9 9 9 O 9 9  I I  I  9  o  9 9 9 9 9 9 9 9  9 9  O O O O 9 O 9 OO OO 0 OO 9 O  1  1  50  |  «|9  100  |  150  OBSERVED-o : EXPECTED-9 : VARIABLE (COLUMN NO.) 1 2001 | j | | 1501 |  o o o o  0 o O 0  j  o o o o 9 9 o 9 9 9 9 9 9 9 9 9 9 O 9 9 9 O 9 9 9 9 O O 9 9 9 O O 9 9 9O 9 O 9 9 9 O 9 O 9 9 9 O 9 O 9 9 9 O  | | 100  I 1 1 1  501 | | | | 0 1o 0  I  9 9 9 9 9 O 9  O O 9 O O O 1  1  50  9 9 |o  100  |  |  150  EXPECTED: * OBSERVED: LOGNORMAL  200 o  * 9  9 9  0  100  9 9  9 9  « 9  » 9 9 9  50  O  9  «  100  126 AIRPORT G, 1981  OBSERVED- o :EXPECTED- ® : VARIABLE (COLUMN 110.) 1 150 | 1 1 100 i 1 j  o o o o oo  oo ®A®®  |® 0090®®®00®®  50|® 0®ec>®eeoo®®e | v www>®e®oooo®® .  BulUnA/WV^/VB  I®oe®®o®®eooooooo®®o  | ®0®®«0®®»0000000®Se8000  0 |o 0  POISSON  |  1 100  1  |»«® I | 200 300  OBSERVED- o : EXPECTED- e : VARIABLE (.COLUMN NO.) l' 150|  9  ]  | j 100| 1  j  o O o  «ee 9®®9 ®®®®®  o  eoo®9®  oo ®oo®«®  1 ooooooooo®® so | oooooooooae 1 ooeoooooooo® 1 00*000000000® j 009900000000099000 1 o®®®ooooooooo®®90ooooo | | as®®®» | 0 |«»e I 0 100 200  LOGNORMAL  EXPECTED: * L50  OBSERVED: o  | 300  AIRPORT G, 1982 OBSERVED-  o  100 I  1 1  : EXPECTED-  a  VARIAB :,E  :  (COLUMN  HO.)  1  o  0 oo  I  75|  0999  00099099 009990099 0009990009 oo®«e®oooo® 1® 0 0 9 9 9 9 0 0 0 0 9  50 |® o ® ® a « ® o o o o ® ®  25  1* o e e e e a o o o o e ® |8 ©®&©®&ooooo®© 1® 8 9 9 9 9 9 0 0 0 0 0 9 9 |s« 8 9 9 9 9 9 9 0 0 0 0 0 0 0 9 0 |9«6 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 |9Ca a a a a a a o o o o o o o o e jec 3®®®®a®oooooooo®®  o  |oc 3 ® a e « a a o o o o o o o o a e o ® a o o 1  0 1 0  POISSON  1  1  100  |  OBSERVED-o : EXPECTED- 9 150|  9®9|  200  :  1  300  VARIABLE (COLUMN NO.) 1  9 999 aaa®a  o ®aa®a O 009999  100 I | |  | j 50|  009000999 009000009  00090000009 00090000009  | 009900000009 | ooaaooooooooooo | 00999000000009000 0 j oeaaeooooooooaeaooooo  0|a 9  0  LOGNORMAL  EXPECTED: * OBSERVED: o 150  |  |  100  |  8998999|  200  J  300  

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