CONCEPTS, COMPONENTS & CONFIGURATIONS computer modeling, EMS system; EMS syste.m, computer modeling
Computer Modeling of Emergency Medical System Performance Emergency medical services (EMS) system managers face difficult problems when determining the need for system expansion and unit deployment. Information relevant to the decision is often limited and frequently not in a usable format. This lack of usable information often results in decisions that create less-than-optimal EMS systems. A constant search for greater efficiency prompted the development of a computer simulation model to analyze the current EMS system operated by the Tucson Fire Department and to provide statistical information on the effects of potential vehicle base locations on system performance. The simulation model generates data that reflect a variety of parameters necessary in base location analysis. Included in the performance statistics for each unit and ,for the entire system are indicators of unit use rates, m i n i m u m and maxim u m response times, and proportion of calls reached within the critical response time of eight minutes or less. The model has been carefully validated and used in unit redeployment and unit activation in Tucson, Arizona. [Valenzuela TD, Goldberg J, Keeley KT, Criss EA: Computer modeling of emergency medical system performance. Ann Emerg Med August 1990; 19: 898- 901.]
Terence D Valenzuela, MD* Jeffery Goldberg, PhDt Kevin T Keeley¢ Elizabeth A Criss, RN* Tucson, Arizona
INTRODUCTION
Address for reprints: Terence D Valenzuela, MD, Section of Emergency Medicine, Arizona Health Sciences Center, 1501 N Campbell Avenue, Tucson, Arizona 85724.
Two of the most difficult problems in the management of an emergency medical services (EMS) system are knowing when an additional emergency unit is required and knowing where a new unit should be located. Efficient use of EMS resources depends on the answers to these questions. Many factors are relevant to these questions, such as the number of emergency incidents, the size of the service area, the response times considered acceptable by the community, and the time required to service each call. The addition of a new EMS unit, or change in location of an existing unit, has a "domino" effect. System modifications result in changes in the response time profile of all other units within the system, in the EMS system as a whole, and in particular geographic areas of the city. The challenge to an EMS planner is to make changes that will result in a medically acceptable, yet uniform, level of service throughout the response area at the lowest possible cost. We describe a cooperative effort between the University of Arizona Colleges of Medicine and Engineering and the Tucson Fire Department that resulted in the development of a computerized model of the city's EMS system. Recent historical data from the city's EMS experience were used as the basis for the development of various model components. Ease of operation and accuracy of prediction make the computer model a valuable method for evaluating and planning for the needs of a municipal EMS system.
From the Section of Emergency Medicine, Arizona Health Sciences Center,* and Department of Systems and Industrial Engineering,t University of Arizona; and Tucson Fire Department,¢ Tucson, Arizona. Received for publication May 8, 1989. Revision received October 9, 1989. Accepted for publication February 1, 1990. Presented at the Society for Academic Emergency Medicine Annual Meeting in San Diego, May 1989.
HISTORICAL PERSPECTIVE Initially, EMS systems were designed to provide definitive care to victims of cardiac arrest.~, 2 During the past two decades, this sphere of responsibility has expanded to include a multitude of other prehospital emergencies.3, 4 In addition, many fee-for-service and public providers are facing tightening budget limitations in conjunction with the increasing demand for service. In light of the need for fiscal accountability and maintaining quality patient care, EMS managers are looking for additional
19:8 August 1990
Annals of Emergency Medicine
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COMPUTER MODELING Valenzuela et al
m e t h o d s of s y s t e m evaluation. Past w o r k in the area of EMS unit location has focused two approaches: q u e u e i n g m e t h o d s and set covering m e t h o d s . T w o e x a m p l e s of t h e queueing approach to system evaluation models include Larson's Hypercube model 5 and Jarvis' spatially distributed queueing model, A-Hypercube. 6 The Hypercube m o d e l uses a p r o b l e m - s o l v i n g t h e o r y t h a t assumes the present distribution of the system to be i n d e p e n d e n t of the history of the system. This type of ass u m p t i o n in the H y p e r c u b e m o d e l l i m i t s the validity of the results. The m o d e l also assumes that service t i m e for the u n i t s is exponentially distributed and is not a function of the call l o c a t i o n or the a m b u l a n c e that services t h a t call. T h i s m o d e l can require c o n s i d e r a b l e c o m p u t e r t i m e due to the n u m e r o u s c o m p u t a t i o n s required in the p r o b l e m solving. A-Hypercube solves the p r o b l e m of excessive c o m p u t a t i o n ; however, it requires that service t i m e be identically distributed over the entire area. N e i t h e r m o d e l c o n s i d e r s t h e dyn a m i c a n d c h a n g i n g n a t u r e of an EMS system. S e v e r a l set c o v e r i n g a p p r o a c h e s have been reported in the literature, including the optimization models d i s c u s s e d b y T o r e g a s et al z a n d D a s k i n / These m e t h o d s a t t e m p t to locate the o p t i m u m set of base locations to cover the m a x i m u m n u m b e r of c a l l s . A s s u m p t i o n s of v e h i c l e availability and equal vehicle use can c o m p r o m i s e the v a l i d i t y of the results. M a n y a u t h o r s have used s i m u l a tion to evaluate EMS unit locations. T h e m o s t significant set of m o d e l s was generated by the Rand Corporat i o n in t h e m i d - 1 9 7 0 s . 9 , Io T h e s e studies i n c l u d e d a d e t a i l e d s i m u l a tion m o d e l and an associated set of travel t i m e models. The models have been v a l i d a t e d in a wide v a r i e t y of urban areas; the m a i n d r a w b a c k is that t h e y require a large a m o u n t of d a t a and can be v e r y e x p e n s i v e to run. C i t i e s u s i n g t h e s e s i m u l a t i o n m o d e l s have d o c u m e n t e d costs bet w e e n $5,000 and $15,000.1~ T h e l a c k of a d e q u a t e a n a l y t i c a l models and practically sized simulation m o d e l s was the basis for the dev e l o p m e n t of our s i m u l a t i o n model. We developed a simpler m o d e l w i t h o u t p u t that reflects the d y n a m i c nature of t h e s y s t e m . V a l i d a t i o n tests 92/899
d e m o n s t r a t e d t h a t even though our m o d e l contains less detail than other simulation models, we still accurately e m u l a t e actual s y s t e m behavior and performance. MODEL DEVELOPMENT AND VALIDATION
Tucson Fire D e p a r t m e n t personnel p r o v i d e both a d v a n c e d life s u p p o r t (ALS) a n d b a s i c life s u p p o r t (BLS) care to a m e t r o p o l i t a n area of approxi m a t e l y 145 square miles with a popu l a t i o n base of 365,000. The simulator p r o g r a m was d e v e l o p e d on the operation of seven full-time ALS rescue vehicles. The fire d e p a r t m e n t responds to more than 19,000 requests for assistance per year through an enhanced 911 system. The c o m p u t e r program for the simu l a t i o n m o d e l was w r i t t e n in the PASCAL p r o g r a m m i n g l a n g u a g e and was i m p l e m e n t e d on a VAX 11/780 (Digital Equipment Corporation, Maynard, Massachusetts) m a i n f r a m e computer. Each run of the model requires a p p r o x i m a t e l y 15 seconds of computer-processing time. Each simulation e x p e r i m e n t requires 100 runs. W i t h an e x p e r i m e n t of this size, the p e r c e n t a g e of calls r e a c h e d w i t h i n the c r i t i c a l r e s p o n s e t i m e of e i g h t m i n u t e s or less (chosen for its relat i o n s h i p to successful t r e a t m e n t of v e n t r i c u l a r f i b r i l l a t i o n 1) can be predicted to _+ 1.5% w i t h a 90% confb dence level for e a c h zone. A c o m plete experiment requires approxi m a t e l y 25 m i n u t e s of c o m p u t e r time, but this may represent two hours of actual time. The difference is due to the c o m p u t e r time-sharing r e q u i r e m e n t s w i t h i n the u n i v e r s i t y and d e p e n d s on the c o m p u t e r load while the program is running. The s i m u l a t i o n model and its components were based on historical data o b t a i n e d from the Tucson Fire Dep a r t m e n t dispatch and incident data bases. I n i t i a l l y , d a t a f r o m t h e first half of 1986 were used. A description of the i n c i d e n t data base s y s t e m operated by the fire d e p a r t m e n t is published elsewhere; lz the data set inc l u d e d i n c i d e n t date, t i m e of dispatch, t i m e of arrival on-scene, t i m e of return to service, and incident address and responding unit identification for 10,650 calls. Each i n c i d e n t address was assigned to a geographi c a l l y c o r r e s p o n d i n g zone for analysis. O u r zones are one-half squarem i l e sectors of the city that directly Annals of Emergency Medicine
correspond to those used by city traffic planners to develop and evaluate travel time and road n e t w o r k models. T h e modeling process consisted of two m a j o r steps: travel t i m e m o d e l d e v e l o p m e n t and s i m u l a t i o n m o d e l d e v e l o p m e n t and validation. A high degree of reliability in the prediction of t r a v e l t i m e is a p r e r e q u i s i t e to s i m u l a t o r use. W i t h o u t this level of a c c u r a c y , s i m u l a t o r o u t p u t w i l l be v i e w e d skeptically. Use of o u t p u t by EMS p l a n n e r s is c o n t i n g e n t on validation of the s i m u l a t o r model. The travel t i m e m o d e l uses a comb i n a t i o n of general traffic m o v e m e n t data and actual emergency unit travel times. The general traffic data consist m a i n l y of the road network. Roads in the c i t y were categorized into four types: freeway (limited access), m a j o r r o a d s (five to s e v e n lanes), nonmajor roads (three or four lanes), and local roads. D e l i n e a t i o n of these road types was a m e a n s of compensating for the variation in vehicle speed found within the city. The next step involved separating each v e h i c l e trip into d i s t a n c e s traveled on each road type. Finally, the distances were correlated with actual travel times, and speed coefficients per m i l e of each road type were developed. T h e r e s u l t was a series of equat i o n s t h a t was u s e d to p r e d i c t expected travel t i m e based on the n u m ber and type of roads traveled on any p a r t i c u l a r trip. T r a v e l t i m e p r c d i c tion error was evaluated by comparing a c t u a l t r a v e l t i m e s w i t h t h o s e predicted by the equation using linear regression analysis. T h e s i m u l a t i o n m o d e l was developed in various levels of complexity. The base model, described here, uses a general p u r p o s e q u e u e i n g s i m u l a tion format. The input data for this level consist of a serics of r a n d o m l y selected, h i s t o r i c a l l y a c c u r a t e emergency calls. For each call, the simulator selects the nearest available vehicle as indicated by the program parameters, generates travel times according to the travel t i m e model, and places the vehicle in service. T h e result is a set of performance statistics for each vehicle, each zone, and the entire system. A n example of the statistics available from each exp e r i m e n t is given (Figure}. These stat i s t i c s i n c l u d e v e h i c l e use (proportion of t i m e a u n i t can expect to be in service}, m e a n and m a x i m u m re19:8 August 1990
Individual Units
TABLE. Performance statistics for individual zones - batch results of I00 simulations (results sorted in several formats)
Zone Number Sorted by Performance Within Critical Response Time
EMS unit 1 at zone 23 Number of responses, 1,866 Maximum response time, 37.47 + 1.82 minutes Mean response time, 4.90 + 0.01 minutes Proportion of responses under 8 minutes, 0.91 Number of false alarms, 322 Use rate, 0.17
Calls Reached Within Critical Response Time (%)
23
0.970 + 0.006
131
0.967 + 0.008
51
0.965 + 0.004
49
0.962 ± 0.003
57
0.960 ± 0.010
29
0.960 -+ 0.004
133
0.960 ± 0.003
Systemwide System size, 7 EMS units Mean total number of responses, 9,296 Mean overall response time, 5.22 - 0.002 minutes Mean overall proportion of responses under 8 minutes, 0.90 Mean overall use rate, 0.14
Sorted by Demand for Service (Descending Order) 1
0.953 ± 0.002
66
0.907 ± 0.004
91
0.947 ± 0.003
27
0.942 ± 0.003
117
0.928 ± 0.004
75
0.941 ~: 0.003
115
0.938 ± 0.003
spouse t i m e s (travel t i m e required to reach a call), and percentage of calls reached w i t h i n the specified critical response t i m e limit. In addition to vehicle performance statistics, the s i m u l a t o r o u t p u t also generates p e r f o r m a n c e data on each geographic zone w i t h i n the system. This type of analysis allows for isolation of p a r t i c u l a r zones w i t h i n the s y s t e m t h a t are n o t being serviced w i t h i n the critical response time. At the c o m p l e t i o n of each e x p e r i m e n t a l set, t h e s i m u l a t o r produces a zone listing, sorted into several formats, t h a t i n c l u d e s the p e r c e n t a g e of the calls r e a c h e d w i t h i n the critical response t i m e for that zone {Table). Phase 2 in the d e v e l o p m e n t of the s i m u l a t o r was the m o d e l v a l i d a t i o n process. T h e initial step was to determ i n e if all r e l e v a n t o p e r a t i o n a l det a i l s n e c e s s a r y to e n s u r e a c c u r a t e p r e d i c t i o n s w e r e c o n t a i n e d in t h e s i m u l a t i o n m o d e l . To a c c o m p l i s h this, we c o m p a r e d m o d e l - g e n e r a t e d p e r f o r m a n c e s t a t i s t i c s of h i s t o r i c a l calls w i t h those m e a s u r e d in the actual EMS system. T h e use of historical calls as the basis for v a l i d a t i o n e n s u r e d t h e a c c u r a c y of t h e t r a v e l
19:8 August1990
t i m e data. These validation tests demonstrated model-generated travel t i m e s to be w i t h i n 2% of the actual s y s t e m travel times. Careful adjustments during a s i x - m o n t h period were required to reach this level of accuracy. To verify the accuracy of the travel t i m e model, 1987 data were entered into the computer, and the response time predictions remained within the 2% error rate.
COST COMPARISON W i t h m o r e t h a n 90% of BLS and ALS care being handled by the Tucson Fire D e p a r t m e n t , it is i m p o r t a n t to m a i n t a i n a high level of service. In previous years, as the city expanded and it became necessary to reh)cate or activate an engine, ladder, or param e d i c c o m p a n y to m e e t the d e m a n d for service, m a n y p e r s o n n e l h o u r s were c o m m i t t e d to data e x t r a c t i o n . U n t i l t h e i m p l e m e n t a t i o n of t h i s c o m p u t e r s i m u l a t i o n model, the data n e e d e d for u n i t l o c a t i o n a n a l y s i s werc c o m p i l e d from field records and i n f o r m a t i o n available in the i n c i d e n t and dispatch data base, frequently involving hand computations. This
Annals of Emergency Medicine
FIGURE. Statistical output from computer simulation: Batch results of 100 simulations. task often required from two to two and one-half weeks for c o m p l e t i o n at a cost of $1,250 to $5,000 depending on the detail needed for the justification and provided only a limited view of the i m p a c t on the entire syst e m of a u n i t - d e p l o y m e n t pattern. U s e of t h e s i m u l a t o r m o d e l has greatly reduced the p e r s o n n e l costs a s s o c i a t e d w i t h EMS planning. T h e initial setup costs for the c o m p u t e r simulation model were approxim a t e l y $3,000; however, these were o n e - t i m e o n l y costs. A c o m p r e h e n sive analysis, i n c l u d i n g d e l i n e a t i o n of the vehicle base location, requires only 30 m i n u t e s of c o m p u t e r t i m e and a p p r o x i m a t e l y one to two hours of p e r s o n n e l t i m e ; t h i s r e p r e s e n t s a b o u t $100 in a c t u a l costs to complete the analysis.
SU
MAWl
A c o m p u t e r m o d e l of the EM8 syst e m in Tucson, Arizona, has been de.veloped and i m p l e m e n t e d effectively. The model predicts the effects on response times in the system, postulating a w i d e v a r i e t y of h y p o t h e t i c a l c h a n g e s i n t h e e l e m e n t s of t h e s y s t e m (eg, alternative emergency vehicle base locations). The weaknesses of p r e v i o u s m e t h o d s for EMS vehicles are avoided, including the cost of
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COMPUTER MODELING Valenzuela et al
s y s t e m o p e r a t i o n . T h e u s e of a c t u a l E M S d a t a f r o m c a l l r e c o r d s as t h e b a s i s for a t r a v e l t i m e e q u a t i o n a n d for t h e g e n e r a t i o n of e m e r g e n c y call sets used to evaluate the response p e r f o r m a n c e of h y p o t h e t i c a l a l t e r n a tives results in very accurate predictions. In Tucson, the computer simulation model has resulted in a red e p l o y m e n t p l a n for fire d e p a r t m e n t paramedic units. System analysis demonstrated on the zone level that s p e c i f i c a r e a s of t h e c i t y w e r e b e i n g reached within the critical response t i m e of e i g h t m i n u t e s or f e w e r less t h a n 8 0 % of t h e t i m e . U s i n g t h e abili t y of t h e m o d e l to e v a l u a t e p o t e n t i a l vehicle locations, a new configurat i o n w a s e s t a b l i s h e d to p r o v i d e m o r e u n i f o r m c o v e r a g e t o all areas of t h e city. In November 1988, t h e c i t y a d o p t e d t h e u n i t r e l o c a t i o n p l a n . Performance statistics from the first
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q u a r t e r of 1989 d e m o n s t r a t e d t h a t the unit redeployment had improved u n i t a n d c i t y w i d e p e r f o r m a n c e . Predictions generated from the computer output were realized.
REFERENCES I. Cobb LA, Alvarez H, Copass MK: A rapid response system for oubof-bospital cardiac emergencies. Med Clin North Am 1976;60:283-291. 2. Eisenberg M, Bergner L, Hallstrom A: Paramedic programs and out-of-hospital cardiac arrest: II. Impact on community mortality. Am J Public Health 1979;69:39-42. 3. Jacobs LM, Sinclair A, Beiser A, et al: Prehos pital advanced life support: Benefits in trauma. J '&auma 1984;24:8-13. 4. Cwinn AA, Pons PT, Moore EE, et ah Prehospital advanced life support for critical blunt trauma victims. Ann Ernerg Med 1987;16: 399-403. 5. Larson R: A hypercube queueing model for facility location and redistricting in urban emergency services. / Comput Operat Res 1974;1: 67-95.
Annals of Emergency Medicine
6. Jarvis J. Optimization in Stochastic Systems With Distinguishable Servers. Cambridge, Massachusetts, MIT Operations Research Center, June 1975. 7. Toregas C, Swain R, ReVelle C, et al: The location of emergency service facilities. Operat Res 1971;19:1363-1373. 8. Daskin M: A maximal expected covering location model: Formulation, properties, and heuristic solution. Transport Sci 1983;17:48-69. 9. Hausner J: Determining the Tr~veI Charac teristics of Emergency Service vehicles. New York, The New York City Rand Institute, April 1975. 10. Carter G, Chaiken J, Ignall E: Simulation Model of Fire Dep~rtment Opercztions. New York, The New York City Rand Institute, De cember 1974. tl. Walker WE, Chaiken JM, Ignall EJ (eds): Fire Department Deployment Analysis: A Public Policy A n a l y s i s Case Study. New York, Elsevier North Holland, 1979, p 399-400. 12. Valenzuela TD, Keeley KT, Criss EA, et ah Implementation of a comp~:~terizedmanagement information system in an urban fire depart~ ment. Ann Ernerg Med 1989;18:573-578.
19:8 August 1990
Computer Modeling of Emergency Medical System Performance Emergency medical services (EMS) system managers face difficult problems when determining the need for system expansion and unit deployment. Information relevant to the decision is often limited and frequently not in a usable format. This lack of usable information often results in decisions that create less-than-optimal EMS systems. A constant search for greater efficiency prompted the development of a computer simulation model to analyze the current EMS system operated by the Tucson Fire Department and to provide statistical information on the effects of potential vehicle base locations on system performance. The simulation model generates data that reflect a variety of parameters necessary in base location analysis. Included in the performance statistics for each unit and ,for the entire system are indicators of unit use rates, m i n i m u m and maxim u m response times, and proportion of calls reached within the critical response time of eight minutes or less. The model has been carefully validated and used in unit redeployment and unit activation in Tucson, Arizona. [Valenzuela TD, Goldberg J, Keeley KT, Criss EA: Computer modeling of emergency medical system performance. Ann Emerg Med August 1990; 19: 898- 901.]
Terence D Valenzuela, MD* Jeffery Goldberg, PhDt Kevin T Keeley¢ Elizabeth A Criss, RN* Tucson, Arizona
INTRODUCTION
Address for reprints: Terence D Valenzuela, MD, Section of Emergency Medicine, Arizona Health Sciences Center, 1501 N Campbell Avenue, Tucson, Arizona 85724.
Two of the most difficult problems in the management of an emergency medical services (EMS) system are knowing when an additional emergency unit is required and knowing where a new unit should be located. Efficient use of EMS resources depends on the answers to these questions. Many factors are relevant to these questions, such as the number of emergency incidents, the size of the service area, the response times considered acceptable by the community, and the time required to service each call. The addition of a new EMS unit, or change in location of an existing unit, has a "domino" effect. System modifications result in changes in the response time profile of all other units within the system, in the EMS system as a whole, and in particular geographic areas of the city. The challenge to an EMS planner is to make changes that will result in a medically acceptable, yet uniform, level of service throughout the response area at the lowest possible cost. We describe a cooperative effort between the University of Arizona Colleges of Medicine and Engineering and the Tucson Fire Department that resulted in the development of a computerized model of the city's EMS system. Recent historical data from the city's EMS experience were used as the basis for the development of various model components. Ease of operation and accuracy of prediction make the computer model a valuable method for evaluating and planning for the needs of a municipal EMS system.
From the Section of Emergency Medicine, Arizona Health Sciences Center,* and Department of Systems and Industrial Engineering,t University of Arizona; and Tucson Fire Department,¢ Tucson, Arizona. Received for publication May 8, 1989. Revision received October 9, 1989. Accepted for publication February 1, 1990. Presented at the Society for Academic Emergency Medicine Annual Meeting in San Diego, May 1989.
HISTORICAL PERSPECTIVE Initially, EMS systems were designed to provide definitive care to victims of cardiac arrest.~, 2 During the past two decades, this sphere of responsibility has expanded to include a multitude of other prehospital emergencies.3, 4 In addition, many fee-for-service and public providers are facing tightening budget limitations in conjunction with the increasing demand for service. In light of the need for fiscal accountability and maintaining quality patient care, EMS managers are looking for additional
19:8 August 1990
Annals of Emergency Medicine
898/91
COMPUTER MODELING Valenzuela et al
m e t h o d s of s y s t e m evaluation. Past w o r k in the area of EMS unit location has focused two approaches: q u e u e i n g m e t h o d s and set covering m e t h o d s . T w o e x a m p l e s of t h e queueing approach to system evaluation models include Larson's Hypercube model 5 and Jarvis' spatially distributed queueing model, A-Hypercube. 6 The Hypercube m o d e l uses a p r o b l e m - s o l v i n g t h e o r y t h a t assumes the present distribution of the system to be i n d e p e n d e n t of the history of the system. This type of ass u m p t i o n in the H y p e r c u b e m o d e l l i m i t s the validity of the results. The m o d e l also assumes that service t i m e for the u n i t s is exponentially distributed and is not a function of the call l o c a t i o n or the a m b u l a n c e that services t h a t call. T h i s m o d e l can require c o n s i d e r a b l e c o m p u t e r t i m e due to the n u m e r o u s c o m p u t a t i o n s required in the p r o b l e m solving. A-Hypercube solves the p r o b l e m of excessive c o m p u t a t i o n ; however, it requires that service t i m e be identically distributed over the entire area. N e i t h e r m o d e l c o n s i d e r s t h e dyn a m i c a n d c h a n g i n g n a t u r e of an EMS system. S e v e r a l set c o v e r i n g a p p r o a c h e s have been reported in the literature, including the optimization models d i s c u s s e d b y T o r e g a s et al z a n d D a s k i n / These m e t h o d s a t t e m p t to locate the o p t i m u m set of base locations to cover the m a x i m u m n u m b e r of c a l l s . A s s u m p t i o n s of v e h i c l e availability and equal vehicle use can c o m p r o m i s e the v a l i d i t y of the results. M a n y a u t h o r s have used s i m u l a tion to evaluate EMS unit locations. T h e m o s t significant set of m o d e l s was generated by the Rand Corporat i o n in t h e m i d - 1 9 7 0 s . 9 , Io T h e s e studies i n c l u d e d a d e t a i l e d s i m u l a tion m o d e l and an associated set of travel t i m e models. The models have been v a l i d a t e d in a wide v a r i e t y of urban areas; the m a i n d r a w b a c k is that t h e y require a large a m o u n t of d a t a and can be v e r y e x p e n s i v e to run. C i t i e s u s i n g t h e s e s i m u l a t i o n m o d e l s have d o c u m e n t e d costs bet w e e n $5,000 and $15,000.1~ T h e l a c k of a d e q u a t e a n a l y t i c a l models and practically sized simulation m o d e l s was the basis for the dev e l o p m e n t of our s i m u l a t i o n model. We developed a simpler m o d e l w i t h o u t p u t that reflects the d y n a m i c nature of t h e s y s t e m . V a l i d a t i o n tests 92/899
d e m o n s t r a t e d t h a t even though our m o d e l contains less detail than other simulation models, we still accurately e m u l a t e actual s y s t e m behavior and performance. MODEL DEVELOPMENT AND VALIDATION
Tucson Fire D e p a r t m e n t personnel p r o v i d e both a d v a n c e d life s u p p o r t (ALS) a n d b a s i c life s u p p o r t (BLS) care to a m e t r o p o l i t a n area of approxi m a t e l y 145 square miles with a popu l a t i o n base of 365,000. The simulator p r o g r a m was d e v e l o p e d on the operation of seven full-time ALS rescue vehicles. The fire d e p a r t m e n t responds to more than 19,000 requests for assistance per year through an enhanced 911 system. The c o m p u t e r program for the simu l a t i o n m o d e l was w r i t t e n in the PASCAL p r o g r a m m i n g l a n g u a g e and was i m p l e m e n t e d on a VAX 11/780 (Digital Equipment Corporation, Maynard, Massachusetts) m a i n f r a m e computer. Each run of the model requires a p p r o x i m a t e l y 15 seconds of computer-processing time. Each simulation e x p e r i m e n t requires 100 runs. W i t h an e x p e r i m e n t of this size, the p e r c e n t a g e of calls r e a c h e d w i t h i n the c r i t i c a l r e s p o n s e t i m e of e i g h t m i n u t e s or less (chosen for its relat i o n s h i p to successful t r e a t m e n t of v e n t r i c u l a r f i b r i l l a t i o n 1) can be predicted to _+ 1.5% w i t h a 90% confb dence level for e a c h zone. A c o m plete experiment requires approxi m a t e l y 25 m i n u t e s of c o m p u t e r time, but this may represent two hours of actual time. The difference is due to the c o m p u t e r time-sharing r e q u i r e m e n t s w i t h i n the u n i v e r s i t y and d e p e n d s on the c o m p u t e r load while the program is running. The s i m u l a t i o n model and its components were based on historical data o b t a i n e d from the Tucson Fire Dep a r t m e n t dispatch and incident data bases. I n i t i a l l y , d a t a f r o m t h e first half of 1986 were used. A description of the i n c i d e n t data base s y s t e m operated by the fire d e p a r t m e n t is published elsewhere; lz the data set inc l u d e d i n c i d e n t date, t i m e of dispatch, t i m e of arrival on-scene, t i m e of return to service, and incident address and responding unit identification for 10,650 calls. Each i n c i d e n t address was assigned to a geographi c a l l y c o r r e s p o n d i n g zone for analysis. O u r zones are one-half squarem i l e sectors of the city that directly Annals of Emergency Medicine
correspond to those used by city traffic planners to develop and evaluate travel time and road n e t w o r k models. T h e modeling process consisted of two m a j o r steps: travel t i m e m o d e l d e v e l o p m e n t and s i m u l a t i o n m o d e l d e v e l o p m e n t and validation. A high degree of reliability in the prediction of t r a v e l t i m e is a p r e r e q u i s i t e to s i m u l a t o r use. W i t h o u t this level of a c c u r a c y , s i m u l a t o r o u t p u t w i l l be v i e w e d skeptically. Use of o u t p u t by EMS p l a n n e r s is c o n t i n g e n t on validation of the s i m u l a t o r model. The travel t i m e m o d e l uses a comb i n a t i o n of general traffic m o v e m e n t data and actual emergency unit travel times. The general traffic data consist m a i n l y of the road network. Roads in the c i t y were categorized into four types: freeway (limited access), m a j o r r o a d s (five to s e v e n lanes), nonmajor roads (three or four lanes), and local roads. D e l i n e a t i o n of these road types was a m e a n s of compensating for the variation in vehicle speed found within the city. The next step involved separating each v e h i c l e trip into d i s t a n c e s traveled on each road type. Finally, the distances were correlated with actual travel times, and speed coefficients per m i l e of each road type were developed. T h e r e s u l t was a series of equat i o n s t h a t was u s e d to p r e d i c t expected travel t i m e based on the n u m ber and type of roads traveled on any p a r t i c u l a r trip. T r a v e l t i m e p r c d i c tion error was evaluated by comparing a c t u a l t r a v e l t i m e s w i t h t h o s e predicted by the equation using linear regression analysis. T h e s i m u l a t i o n m o d e l was developed in various levels of complexity. The base model, described here, uses a general p u r p o s e q u e u e i n g s i m u l a tion format. The input data for this level consist of a serics of r a n d o m l y selected, h i s t o r i c a l l y a c c u r a t e emergency calls. For each call, the simulator selects the nearest available vehicle as indicated by the program parameters, generates travel times according to the travel t i m e model, and places the vehicle in service. T h e result is a set of performance statistics for each vehicle, each zone, and the entire system. A n example of the statistics available from each exp e r i m e n t is given (Figure}. These stat i s t i c s i n c l u d e v e h i c l e use (proportion of t i m e a u n i t can expect to be in service}, m e a n and m a x i m u m re19:8 August 1990
Individual Units
TABLE. Performance statistics for individual zones - batch results of I00 simulations (results sorted in several formats)
Zone Number Sorted by Performance Within Critical Response Time
EMS unit 1 at zone 23 Number of responses, 1,866 Maximum response time, 37.47 + 1.82 minutes Mean response time, 4.90 + 0.01 minutes Proportion of responses under 8 minutes, 0.91 Number of false alarms, 322 Use rate, 0.17
Calls Reached Within Critical Response Time (%)
23
0.970 + 0.006
131
0.967 + 0.008
51
0.965 + 0.004
49
0.962 ± 0.003
57
0.960 ± 0.010
29
0.960 -+ 0.004
133
0.960 ± 0.003
Systemwide System size, 7 EMS units Mean total number of responses, 9,296 Mean overall response time, 5.22 - 0.002 minutes Mean overall proportion of responses under 8 minutes, 0.90 Mean overall use rate, 0.14
Sorted by Demand for Service (Descending Order) 1
0.953 ± 0.002
66
0.907 ± 0.004
91
0.947 ± 0.003
27
0.942 ± 0.003
117
0.928 ± 0.004
75
0.941 ~: 0.003
115
0.938 ± 0.003
spouse t i m e s (travel t i m e required to reach a call), and percentage of calls reached w i t h i n the specified critical response t i m e limit. In addition to vehicle performance statistics, the s i m u l a t o r o u t p u t also generates p e r f o r m a n c e data on each geographic zone w i t h i n the system. This type of analysis allows for isolation of p a r t i c u l a r zones w i t h i n the s y s t e m t h a t are n o t being serviced w i t h i n the critical response time. At the c o m p l e t i o n of each e x p e r i m e n t a l set, t h e s i m u l a t o r produces a zone listing, sorted into several formats, t h a t i n c l u d e s the p e r c e n t a g e of the calls r e a c h e d w i t h i n the critical response t i m e for that zone {Table). Phase 2 in the d e v e l o p m e n t of the s i m u l a t o r was the m o d e l v a l i d a t i o n process. T h e initial step was to determ i n e if all r e l e v a n t o p e r a t i o n a l det a i l s n e c e s s a r y to e n s u r e a c c u r a t e p r e d i c t i o n s w e r e c o n t a i n e d in t h e s i m u l a t i o n m o d e l . To a c c o m p l i s h this, we c o m p a r e d m o d e l - g e n e r a t e d p e r f o r m a n c e s t a t i s t i c s of h i s t o r i c a l calls w i t h those m e a s u r e d in the actual EMS system. T h e use of historical calls as the basis for v a l i d a t i o n e n s u r e d t h e a c c u r a c y of t h e t r a v e l
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t i m e data. These validation tests demonstrated model-generated travel t i m e s to be w i t h i n 2% of the actual s y s t e m travel times. Careful adjustments during a s i x - m o n t h period were required to reach this level of accuracy. To verify the accuracy of the travel t i m e model, 1987 data were entered into the computer, and the response time predictions remained within the 2% error rate.
COST COMPARISON W i t h m o r e t h a n 90% of BLS and ALS care being handled by the Tucson Fire D e p a r t m e n t , it is i m p o r t a n t to m a i n t a i n a high level of service. In previous years, as the city expanded and it became necessary to reh)cate or activate an engine, ladder, or param e d i c c o m p a n y to m e e t the d e m a n d for service, m a n y p e r s o n n e l h o u r s were c o m m i t t e d to data e x t r a c t i o n . U n t i l t h e i m p l e m e n t a t i o n of t h i s c o m p u t e r s i m u l a t i o n model, the data n e e d e d for u n i t l o c a t i o n a n a l y s i s werc c o m p i l e d from field records and i n f o r m a t i o n available in the i n c i d e n t and dispatch data base, frequently involving hand computations. This
Annals of Emergency Medicine
FIGURE. Statistical output from computer simulation: Batch results of 100 simulations. task often required from two to two and one-half weeks for c o m p l e t i o n at a cost of $1,250 to $5,000 depending on the detail needed for the justification and provided only a limited view of the i m p a c t on the entire syst e m of a u n i t - d e p l o y m e n t pattern. U s e of t h e s i m u l a t o r m o d e l has greatly reduced the p e r s o n n e l costs a s s o c i a t e d w i t h EMS planning. T h e initial setup costs for the c o m p u t e r simulation model were approxim a t e l y $3,000; however, these were o n e - t i m e o n l y costs. A c o m p r e h e n sive analysis, i n c l u d i n g d e l i n e a t i o n of the vehicle base location, requires only 30 m i n u t e s of c o m p u t e r t i m e and a p p r o x i m a t e l y one to two hours of p e r s o n n e l t i m e ; t h i s r e p r e s e n t s a b o u t $100 in a c t u a l costs to complete the analysis.
SU
MAWl
A c o m p u t e r m o d e l of the EM8 syst e m in Tucson, Arizona, has been de.veloped and i m p l e m e n t e d effectively. The model predicts the effects on response times in the system, postulating a w i d e v a r i e t y of h y p o t h e t i c a l c h a n g e s i n t h e e l e m e n t s of t h e s y s t e m (eg, alternative emergency vehicle base locations). The weaknesses of p r e v i o u s m e t h o d s for EMS vehicles are avoided, including the cost of
900/93
COMPUTER MODELING Valenzuela et al
s y s t e m o p e r a t i o n . T h e u s e of a c t u a l E M S d a t a f r o m c a l l r e c o r d s as t h e b a s i s for a t r a v e l t i m e e q u a t i o n a n d for t h e g e n e r a t i o n of e m e r g e n c y call sets used to evaluate the response p e r f o r m a n c e of h y p o t h e t i c a l a l t e r n a tives results in very accurate predictions. In Tucson, the computer simulation model has resulted in a red e p l o y m e n t p l a n for fire d e p a r t m e n t paramedic units. System analysis demonstrated on the zone level that s p e c i f i c a r e a s of t h e c i t y w e r e b e i n g reached within the critical response t i m e of e i g h t m i n u t e s or f e w e r less t h a n 8 0 % of t h e t i m e . U s i n g t h e abili t y of t h e m o d e l to e v a l u a t e p o t e n t i a l vehicle locations, a new configurat i o n w a s e s t a b l i s h e d to p r o v i d e m o r e u n i f o r m c o v e r a g e t o all areas of t h e city. In November 1988, t h e c i t y a d o p t e d t h e u n i t r e l o c a t i o n p l a n . Performance statistics from the first
94/901
q u a r t e r of 1989 d e m o n s t r a t e d t h a t the unit redeployment had improved u n i t a n d c i t y w i d e p e r f o r m a n c e . Predictions generated from the computer output were realized.
REFERENCES I. Cobb LA, Alvarez H, Copass MK: A rapid response system for oubof-bospital cardiac emergencies. Med Clin North Am 1976;60:283-291. 2. Eisenberg M, Bergner L, Hallstrom A: Paramedic programs and out-of-hospital cardiac arrest: II. Impact on community mortality. Am J Public Health 1979;69:39-42. 3. Jacobs LM, Sinclair A, Beiser A, et al: Prehos pital advanced life support: Benefits in trauma. J '&auma 1984;24:8-13. 4. Cwinn AA, Pons PT, Moore EE, et ah Prehospital advanced life support for critical blunt trauma victims. Ann Ernerg Med 1987;16: 399-403. 5. Larson R: A hypercube queueing model for facility location and redistricting in urban emergency services. / Comput Operat Res 1974;1: 67-95.
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6. Jarvis J. Optimization in Stochastic Systems With Distinguishable Servers. Cambridge, Massachusetts, MIT Operations Research Center, June 1975. 7. Toregas C, Swain R, ReVelle C, et al: The location of emergency service facilities. Operat Res 1971;19:1363-1373. 8. Daskin M: A maximal expected covering location model: Formulation, properties, and heuristic solution. Transport Sci 1983;17:48-69. 9. Hausner J: Determining the Tr~veI Charac teristics of Emergency Service vehicles. New York, The New York City Rand Institute, April 1975. 10. Carter G, Chaiken J, Ignall E: Simulation Model of Fire Dep~rtment Opercztions. New York, The New York City Rand Institute, De cember 1974. tl. Walker WE, Chaiken JM, Ignall EJ (eds): Fire Department Deployment Analysis: A Public Policy A n a l y s i s Case Study. New York, Elsevier North Holland, 1979, p 399-400. 12. Valenzuela TD, Keeley KT, Criss EA, et ah Implementation of a comp~:~terizedmanagement information system in an urban fire depart~ ment. Ann Ernerg Med 1989;18:573-578.
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