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COMPUTER SIMULATION SYSTEMS Saunders, Makens & Leblanc

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Input process. suhs of system alterations. Previous health care simulation models have been limited by their simplicity or by their requirement for expensive, sophisticated mainframe computers 13,14 Our purpose was to show that a very sophisticated simulation model can be run for a complex ED, even using inexpensive c o m p u t e r hardware and software. Our simulation methodology may be used in any ED, although the results, as in all simulation studies, are unique to the particular situation studied. We developed a detailed computer simulation model of ED operations using simulation software. The model tracks individual staff m e m b e r s and patients, includes multiple levels of preemptive patient priority and all c o m m o n laboratory and consultant procedures, and allows patient service processes to proceed simultaneously, sequentially, or repetitively. We, then, systematically varied s e l e c t e d ED r e s o u r c e s to demonstrate the simulated effect on output data, such as patient waiting times and rates of resource utilization. The simulation model can be run with an animation software package, in which a computer monitor shows simulated patients, staff members, and s p e c i m e n s m o v i n g a m o n g rooms, laboratories, and the work station. The use of animation is a helpful tool for demonstrating the validity of any simulation, although it is clearly not a substitute for a sound experimental design. METHODS The dynamics of the ED care process were modeled by means of a flow diagram depicting patient movement among stations or events. Both ambulatory and ambulance patients arrive and are evaluated by a triage nurse and assigned to a triage acuity level decreasing in seriousness from 1 to 4, registered, and transported to a treatment room when one becomes available (Figure 1). They undergo a physician evaluation, after which a combination of tests, procedures, or c o n s u l t a t i o n s m a y occur. In this model, each patient is assigned an individual nurse and physician who do not change throughout the care pro38/135

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cess. This feature is an advance over previous simulation models~3, ~4 and more closely reflects the real-life process. Then, the patient moves among the substations of each test, procedure, or c o n s u l t a t i o n (Figure 2). Each process is broken down into its c o m p o n e n t parts. For example, a blood test is composed of waiting for specimen collection, specimen collection, specimen transport to laboratory, specimen analysis, communicaAnnals of Emergency Medicine

t tion of results, waiting for the physician to become available to review the results, and physician review of results. Simulated patients may also loop back to reenter a flow branch should the results of a test require it. T h e y m a y m o v e along several pathways simultaneously, as occurs, for example, when blood and urine specimens are obtained concurrently. Although the analysis of each requires a different process with different service times, the specimen anal18:2 February 1989

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yses m a y o c c u r s i m u l t a n e o u s l y , though the results of each may become available independently and produce a different outcome. Eventually the patient is either admitted, held for observation, or discharged (Figure 3). A discrete-event computer simulation model was developed, written in the SIMAN language, ~S in which patients, personnel, or resources change at discrete points in time. SIMAN is a high-level s i m u l a t i o n language widely used by industrial engineers that simplifies the task of developing s i m u l a t i o n models. Versions are available for both microframe and mainframe computers. At each substation in the ED care process, an action occurs that results in a variable waiting period before a patient may progress. The duration of each wait is determined by a ran18:2 February 1989

domly distributed time for process completion (or constant time variable for simple tasks, such as specimen collection or medication administration); a time interval dependent on availability of a resource that may be in use elsewhere and must first be m a d e a v a i l a b l e (eg, p h y s i c i a n s , nurses, e x a m i n a t i o n rooms); the n u m b e r of patients already in the same queue; and the p r e e m p t i v e priority (triage acuity level of 1 to 4) of each patient in the queue. The r a n d o m l y d i s t r i b u t e d time variables used at various points in the system were based on either exponential, normal, uniform, Weibull, or empirical probability distributions, depending on the nature of the process and previous experience with time-study data from a similar emergency service. 1 The u n i f o r m and nonuniform random variate generaAnnals of Emergency Medicine

tors used in the SIMAN language have been statistically validated. Input data probability distributions were based on actual historical data from ED log sheets, which included patient arrival times, triage acuity category assignments, tests and procedures performed, and diagnoses. Output data included patient waiting times and queue lengths at key stations or groups of stations, utilization rates for various personnel and resources, and patient t h r o u g h p u t times. To determine the effects of representative system manipulations, several s y s t e m parameters, i n c l u d i n g the n u m b e r of nurses, physicians, t r e a t m e n t rooms, and laboratory specimen analysis times, were varied systematically. Only one factor at a time was varied in the simulation; hence, the experimental design was a one-way analysis of variance. The resultant output data were determined as a function of the values of each system parameter. In the control case, in which there were 15 beds and three nurses and two physicians on duty, the median laboratory turnaround time was 60 minutes (uniformly distributed between 40 and 80 minutes). Patient arrival rates, methods of arrival, and acuity profiles were modeled after actual historical data and were not changed between the control and the experimental cases. Model validation was done at three 136/39

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FIGURE 4. Patient throughput time versus patient triage acuity level. [For the graphs shown in Figures 4 through 16, the difference between two points is statistically significant if the notches do not overlap. The width of the notches on each box plot corresponds to 95% confidence interval around the median. See reference 18 for an explanation of box plots.] FIGURE 5. Waiting t i m e until patient sees physician versus patient triage acuity level. FIGURE 6. Patient throughput time versus the number of nurses on duty.

levels. First, the simulation output (eg, time in system, number in various queues) was compared with data gathered during a previous M T M study. 1 D i s c r e p a n c i e s were noted that n e c e s s i t a t e d changes in the model and input data distributions. The next level involved a comparison of the simulation model with t h o s e in p r e v i o u s s i m u l a t i o n studies 13,14 of a similar nature. The most important level of validation i n v o l v e d an a n a l y s i s of the procedures, pathways, and logic used in the model by experienced emergency physicians and nurses for reasonableness and realism. RESULTS

In the control case and in each experimental case in which a resource parameter was changed, 50 simulations were run, and the output data 40/137

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for each case were combined. Identical i n p u t data d i s t r i b u t i o n s w i t h identical random number streams for the patient creation process were used. For each output data set, the median and its 95% confidence interval, 25th percentile, and 75th percentile were calculated and displayed graphically with the data range. Each simulation was run for a period of eight simulated hours. During each simulation, an average of 40 patients were simulated (an average of four a m b u l a t o r y patients and one a m b u l a n c e p a t i e n t arrived during each hour). A typical ED never really reaches "steady state," because average arrival rates vary by time of day. Nevertheless, waiting times for patients arriving during the first four hours were ignored so that more realistic numbers of patients were at various stages in the system before observations were recorded; this was based on the replication-deletion approach of Kelton and Law. 16 The patient's severity of illness as indicated by the triage acuity level was examined for its effect on the total time spent by a patient in the system, or throughput time (Figure 4). As expected, progressively more serious illnesses (lower triage acuity level) resulted in longer throughput times. A statistical analysis showed that the decrease in patient throughput time was statistically significant when the patient acuity level decreased from 1 to 2. This is the result of a greater n u m b e r of tests, procedures, and consultations for the more seriously ill patients. A patient's waiting time to see a physiAnnals of Emergency Medicine

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cian was also directly related to the severity of illness (Figure 5}, with virtually no time required for category 1 (critical) patients and more than 30 minutes for category 4 patients. As the number of nurses increased, the p a t i e n t t h r o u g h p u t t i m e decreased to a certain point and then no further decrease was seen (Figure 6). This represents a point where a nurse surplus occurs and the number of nurses is no longer a rate-limiting factor. This is further evidenced by a rapid decline in nurse utilization rate time as the n u m b e r of nurses increases (Figure 7). Similarly, as the number of physicians increased, the patient throughput time decreased with a plateau effect at more than three physicians (Figure 8). This same leveling-off rel a t i o n s h i p is s h o w n b e t w e e n the number of physicians available and the patient's waiting time before seeing a physician (Figure 9). Again, a relative surplus of physicians is responsible because physician utilization rates showed the same rapid decline as the n u m b e r of physicians increased (Figure 10). Increasing the number of examination beds, however, had no effect on patient throughput times (Figure 11). This is because an adequate supply of beds already existed, so additional beds would not be used (Figure 12). As the number of beds is increased to 25, the number used changes very little, and the utilization rate declines rapidly (Figure 13). The bed queue was initially small, and further additions of beds quickly eliminated it (Figure 14}. 18:2 February 1989

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The blood test t u r n a r o u n d time was found to have a direct effect on patient throughput times (Figure 15) and on the size of the patient queue waiting to have a laboratory test (Figure 16). The increase in the queue size does n o t o c c u r i m m e d i a t e l y , however. This implies that the blood test time, until it is more than 60 minutes, is a relatively insignificant factor in influencing the size of this queue, which is contributed to by all patients waiting for any laboratory test. The type of animation that can be used for this ED simulation is shown (Figure 17). Patients and their colorcoded charts are displayed to represent triage acuity. In this animated simulation, patients enter the waiting room, move to the triage nurse, enter the bed queue, and finally move to a room. Physicians, nurses, 18:2 February 1989

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patients, and patients' specimens can be shown moving to and from rooms, laboratories, and the work station. Thus, the a n i m a t i o n allows visual display of where excessive queues will build up. DISCUSSION As hospitals increasingly examine methods of cost containment, tools from i n d u s t r y m a y be adapted to evaluate s y s t e m efficiency in the health care setting and to suggest improvements. In a busy ED, efficiency of service may be indirectly related to quality of care, with the possibility that prolonged waiting times will cause ill patients to deteriorate and that excess personnel utilization rates will be associated with errors in care. From the patient's perspective, an efficient ED service implies rapid access to care and is related to perAnnals of Emergency Medicine

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FIGURE 7. N u r s e utilization versus the n u m b e r of nurses on duty. FIGURE 8. Patient throughput t i m e versus the n u m b e r of physicians on duty. FIGURE 9. Waiting t i m e before patient sees physician versus the n u m ber of physicians on duty. FIGURE 10. P h y s i c i a n u t i l i z a t i o n versus the n u m b e r of physicians on duty. FIGURE 11. Patient throughput t i m e versus the n u m b e r of ED t r e a t m e n t beds. FIGURE 12. ED t r e a t m e n t beds used versus the n u m b e r of ED t r e a t m e n t beds. ceived better service and greater sat138/41