We discuss a simulation and analysis software tool 'BartSim' that has been developed by .... Figure 1: The ambulance dispatch and service delivery process. 3.
Development of a Simulation and Data Visualisation tool to assist in Strategic Operations Management in Emergency Services
Shane G. Henderson
Andrew J. Mason
Industrial and Operations Engineering
Department of Engineering Science
University of Michigan
University of Auckland
1205 Beal Avenue
Private Bag 92019
Ann Arbor, MI 48109-2117, USA
Auckland, NEW ZEALAND
ABSTRACT The problem of determining where ambulances should be stationed, and at what times they should operate, has received a great deal of attention in the literature. This is a difficult strategic problem whose solution requires careful balancing of political, economic and medical objectives. Quantitative decision processes are becoming increasingly important in providing public accountability for the resourcing decisions that have to be made. We discuss a simulation and analysis software tool ‘BartSim’ that has been developed by the authors as a strategic decision support tool for use within the St John Ambulance Service (Auckland Region) in New Zealand (St Johns). The novel features incorporated within this study include •
the use of a detailed time-varying travel model for modelling travel times in the simulation,
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methods for reducing the computational overhead associated with computing timedependent shortest paths in the travel model, and
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the development of a geographical information sub-system (GIS) within BartSim that provides spatial data visualisation of both historical data and the results of what-if simulations.
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Our experience with St Johns, and discussions with emergency operators in Australia and Europe, suggest that emergency services do not have good tools to support their operations management at the strategic level of resourcing decisions. Our experience has shown that a customised system such as BartSim can successfully combine GIS and simulation approaches to provide a quantitative decision support tool highly valued by management.
1. INTRODUCTION The St John Ambulance Service (Auckland Region), henceforth referred to as St Johns, contracts to Crown Health Enterprises to supply emergency medical transport. The contracts stipulate that St Johns supplies a minimum level of service as specified by certain performance targets. These targets relate to response time, which is defined as the time interval between receiving a call, to the time that an ambulance first arrives at the scene. The performance targets are broken down by the location of the call (whether the call is in metropolitan Auckland, or in a rural area) and the priority of the call. St Johns classifies its emergency calls (as opposed to patient transfers etc.) into two levels. Priority one calls are those for which an ambulance should respond at all possible speed, including the use of lights and sirens. Priority two calls are calls for which an ambulance may respond at standard traffic speeds. The performance targets that St Johns faces are as follows.
Priority 1 Metropolitan
Rural
Priority 2
80% in 10 mins, 80% in 30 95% in 20 mins
mins
80% in 16 mins,
no target
95% in 30 mins Table 1: Contractual Service Targets
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It is interesting to note that no guidance is given in the contract as to how these figures need to be interpreted. Interpreting the targets as applying, for example, to the entire Auckland area over the entire year will lead to far lower resource requirements than assuming, for example, that the targets must be met in each suburb during each hour of each day. One of the goals of this project has been to develop tools to assist management to explore performance under a range of possible interpretations of the contract. St Johns uses a computer-aided dispatch (CAD) system that logs, in a database, information on every call that is received. The database then enables St Johns to prepare monthly reports that describe how well they meet their performance targets. Recent reports indicate that St Johns is finding it more and more difficult to meet its service targets. It is believed that this is primarily due to increasing congestion on Auckland roads. Clearly, there is a need for a planning tool that can assist St Johns in determining how to allocate their ambulances and staff to the various stations around Auckland. The emergency service location problem has been extensively studied, and the literature on this subject is vast. An excellent entry point to the literature is Swersey (1994). Further references may be found within this paper, but only those that are directly relevant to our work are included. We first approached the St. Johns problem through a queueing analysis. We used the M / G / ∞ model, originally considered for emergency service application in Bell and
Allen (1969), together with some small extensions. The queueing analysis suggested that more ambulances were needed in some areas, but the assumptions underlying the model were such that we were not confident in advocating wholesale adoption of the results. A more accurate model was warranted, and so we turned to simulation. Our use of discrete-event simulation in emergency service planning is certainly not new. For example, Swoveland et al. (1973) used simulation to fit the parameters of a metamodel, which was then optimized using a branch and bound algorithm. What is new is our detailed modeling of travel times, and the visual analysis techniques we developed to analyze both historical and simulated data.
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It is important to accurately capture travel times within models for emergency service planning. For example, Carson and Batta (1990) describe how the 30% savings predicted by their model turned into a 6% savings in actual tests, primarily due to the model not effectively capturing a certain travel time/distance relationship. BartSim uses a comprehensive travel time model adapted from that used by the Auckland Regional Council for planning purposes. The model captures time-dependent effects, such as morning and evening rush periods, that have a dramatic effect on travel times. The simulation requires travel time information for determining which ambulance should be dispatched to a call, determining how long it will take an ambulance to reach the hospital, and so forth. These travel times may be computed via shortest path calculations on a network where the travel times are time-dependent. Rather than compute these shortest paths during the simulation, which would slow the simulation down tremendously, we instead precompute all shortest paths in the network. It would require an exorbitant amount of computer storage to determine all shortest paths in the network for trips starting at all times, so we employ heuristic methods to limit the computation required. Even with these heuristics, the computation required is still formidable, and so we employ the concept of a decision node to reduce the required computation dramatically. The decision node concept could be applied in other contexts to reduce the computational effort required in large shortest-path problems. The second major contribution of this paper is the introduction of visual analysis techniques for understanding both historical and ‘what-if’ simulated data. To our surprise, none of the ambulance service providers that we have talked with have used such tools in the past, and all have been tremendously excited by their potential. The enthusiastic response of emergency service managers we have spoken to suggests that our project will be of interest to many emergency service organisations. This paper is organized as follows. In Section 2 we discuss the process that is followed when St Johns receives an emergency call, and the queueing model is discussed in Section 3. Section 4 provides an overview of the simulation model underlying BartSim. Section 5 discusses the travel model and the heuristics we use to reduce computational
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overhead. In Section 6 we introduce BartSim itself, and explain some of its analysis capabilities. Some conclusions are offered in Section 7. For further details on BartSim, please visit the BartSim web site BartSim (1999).
2. THE DISPATCH PROCESS Figure 1 shows the process that occurs when a call arrives at St Johns. Staff in the control room identify the closest available ambulance (i.e., an ambulance either idle at its base station or returning from a previous job) and dispatch this vehicle to the scene. After initial treatment at the scene, the ambulance typically transports the patient to a hospital, performs a ‘handover’ to hospital staff, and then returns to its base station. Where transport is not required, the ambulance returns directly to its base. In either case, the vehicle is considered available to receive calls as soon as it begins returning to base. Figure 1 shows the two times of most interest in a call response. T8 is the contractual response time discussed earlier, while T8+T9 is the service time for a call. These times were used in the formulation of a queuing model approximation of the process.
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Ambulance waiting at station A: New call arrives Call being dispatched(T1) B: Call allocated to closest free ambulance Ambulance preparing to depart (T2)
T8
C: Ambulance departs for incident scene Ambulance travelling to scene (T3) D: Ambulance arrives at scene Treating patient at scene (T4) E: Ambulance departs for hospital Travelling to hospital (T5) F: Ambulance arrives at hospital
T9
Patient admission at hospital (T6) G: Ambulance departs for station Ambulance returning to station (T7) H: Ambulance dispatched to new call I: Ambulance arrives back at station Ambulance waiting at station
Figure 1: The ambulance dispatch and service delivery process
3. THE QUEUEING MODEL The queueing model presented in this section was an attempt to obtain a first approximation to the required number of ambulances at each of the 16 ambulance bases currently operated by St Johns. Consider one of the 16 ambulance bases operated by St Johns in the Auckland region. We will assume that the ambulance base serves calls within the local area, and does not send ambulances to help relieve demand in adjacent areas. We can then study the base in isolation, effectively ignoring the interactions that result from ambulances being sent to other areas. We will discuss how reasonable this "locality assumption" is later in this section.
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We further assume that when no ambulance is available at the base when a call arrives, an ambulance from some other location handles the call. This is, in fact, what happens in reality. We consider periods such as morning rush, evening rush, and weekend nights (for example) separately, because the call arrival rates and service times can vary considerably. The service time variation is primarily due to time-dependent travel times caused by traffic. With the above assumptions in place, it is possible to model the number of active calls (the number of calls to which an ambulance has been assigned) using an M/G/∞ queueing model. This model has been previously studied in conjunction with emergency service provisioning (Bell and Allen 1969, Fitzsimmons 1973). The M/G/∞ model assumes a Poisson call arrival process, i.i.d. service times and an infinite number of servers. The infinite number of servers results from our assumption that calls that cannot be handled from the local base are handled by ambulances stationed elsewhere. The arrival rate λ is easily calculated from the data available to us as the ratio of the number of calls that arrive to the total observation time. Calculating a mean service time
µ-1 is more problematical, due to the fact that ambulances may answer calls from locations other than the base if, for example, they are returning to base after completing another callout. We took a call service time to be the time interval T8+T9 from when an ambulance was dispatched, to the time the ambulance became free. An ambulance becomes free either by completing treatment of the patient at the scene with no patient transport, or by completing transport of the patient to a health facility. Note that the service time does not include a time component allowing the ambulance to return to base. We were then in a position to compute the steady-state probability pn that n ambulances (both based at the station, or based elsewhere) are busy via e−ρ ρ n pn = , n!
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where ρ=λ/µ (see, for example, Wolff 1989, p. 79). The number of ambulances required at the station is then computed as follows. Suppose we are considering the requirement that 80% of priority one calls are reached within 10 minutes. We first calculate the proportion, r say, of calls that are more than 10T1-T2 minutes travel time away from the station. (We assumed some typical values for T1 and T2.) Assuming that an ambulance responds from the ambulance base (a strong assumption), it follows that there is no way to reach these calls within the 10 minute timeframe. Now, let us assume that the only way to answer a call that is within the 10 minute radius on time is if an ambulance is available when the call comes in. If there are N ambulances stationed at the base, then the probability qN say that an ambulance cannot immediately respond to the call is qN = pN + pN+1 + ... = 1 -
∑p
k 95% target time
Figure 2: Response Time Performance in the Auckland Region One can use this tool to advantage in tailoring the allocation of ambulances to stations. In particular, during periods of low call demand, a few stations cover the entire Auckland region. We can identify the “reach” of these stations by producing plots like that of Figure 3. In this plot, we computed the travel time from a single station to all calls. By colouring the call locations as above, we obtain a vivid picture of the area that can be covered by positioning an ambulance at a given station. Since travel time varies dramatically with the time of day, we can obtain a clearer picture of the station's reach at a given time by filtering the calls, so that we only display those arriving during a subset of the week. Figure 3 contains only those metropolitan Priority 1 calls received in the late morning/early afternoon on weekdays. By repeating such plots for several stations, we can identify a suitable subset of stations that may be used to cover Auckland during various times.
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Key: Response time T8... ≤ 80% target time ≤ 95% target time > 95% target time
Figure 3: Plot of the "reach" of Pitt St Station during the late morning/early afternoon period on weekdays As mentioned above, we can filter the calls so that one can "zoom in" on a particular time, or a particular area of Auckland, or both. The performance measures for the time and area of interest are then calculated, allowing one to identify response time performance for centrally located calls, for example. A sample screenshot of such an analysis is given in Figure 4. The small window in the upper screen area contains detailed information on contractual target performance for a case where ambulance allocation is too light, so that the targets are not met.
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Figure 4: Filter applied to results to identify performance in the city centre. The plots described above are very useful, providing an excellent overview of performance. In addition, plots such as those in Figure 4 allow one to provide precise numerical information on performance in a localised region. It is also desirable to be able to summarise on-time performance (relative to the contractual targets) over the entire Auckland region at once and Figure 5 is an example of such a plot. In this plot, the Auckland region has been broken down into rectangular regions. Within each region, we compute the percentage of Priority 1 calls reached within the required time limit (10 minutes for urban calls, 16 minutes for rural calls). To allow one to focus on regions containing significant numbers of calls, regions containing a small number of calls are suppressed in the output. Furthermore, the size of the rectangles reflects the number of calls received within the region. We can also substitute other performance measures, such as the number of calls received, or the percentage of Priority 2 calls reached within the required time limit, in place of the performance measure given here.
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Figure 5: Plot of the number of calls and average service quality for grid areas in Auckland. Figure 5 is perhaps the most useful of all the plots described thus far in terms of determining required ambulance allocations. We vary the ambulance allocations between bases, run the simulation, and then observe the performance in terms of these plots. Using these plots we can locate areas with poor overall on-time performance and large numbers of calls, to identify good candidates for extra ambulance resources. Furthermore, by filtering the calls by time and producing the same plots, we can identify times when extra ambulances are most likely to make a large impact. These plots revealed something unexpected when applied to historical data for the St Johns organisation. There was a small suburban area (not shown) in which a disproportionate (relative to neighbouring areas) number of calls were appearing. Upon investigation it was discovered that there are several accident and emergency clinics in this area, and such clinics generate many calls for St Johns. The St Johns organisation 18
was apparently unaware of this situation, and is considering our recommendation that they ensure an ambulance be relocated close to this vicinity. BartSim can also produce simple histograms of various characteristics of calls, such as response time, time spent by an ambulance at the scene, etc. In particular, Figure 6 presents a histogram of the time from when a call is received until when an ambulance is dispatched for a set of simulated metropolitan Priority 1 calls. The histogram shows very clearly that for many of the calls, a large amount of time is spent before an ambulance is dispatched to a call. Time spent within the dispatch process reduces the amount of time that an ambulance has to reach the scene of a callout (within contractual performance targets). A plot similar to this for the historical data recorded by St. Johns was one of our most important findings for the organisation. Small decreases in these dispatch times can have (as simulations quantified) a large impact on contractual performance, so that it is worth devoting considerable effort to determining ways in which the dispatch time can be reduced.
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Figure 6: Distribution of the interval (in minutes) between a call being received and an ambulance responding that it is en route. (Distribution is illustrative only.)
BartSim also produces statistics on ambulance utilisation. These statistics may be imported into a spreadsheet (we use Microsoft Excel), and analysed from there. An example of the type of graphs that can be produced is given in Figure 7. This graph depicts the underlying demand near one of the stations operated by St Johns. Each row of bars reflects the performance that can be expected over the week when a given number of ambulances are stationed at the base. In particular, each individual bar reflects, for a given number of ambulances and time of the week, the percentage of time that no ambulance is available to respond to incoming calls. This information is extremely useful for getting a first approximation to the number of ambulances required at each individual base at different times of the week. Of course, one would cover some proportion of these calls from other stations, but the plot gives an impression of the underlying demand.
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1 Amb
Ambulance Requirements at one Station
2 Amb 3 Amb
Percent of time no ambulance available to respond to incoming calls
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Thu0600
Wed1200
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Wed0000
Wed0600
Tue1200
Tue1800
Tue0000
Tue0600
Mon1200
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0
Figure 7: Ambulance utilisation/requirements at one station.
7. CONCLUSIONS BartSim was recently used to evaluate several decisions considered by St Johns, including the use of a dedicated non-emergency patient transfer service, the possible introduction of a new dispatching method, and changes to where and when ambulances would be allocated. The results of that study have been used to shape policy at St Johns, and we continue to work with them on these and other issues, including rostering requirements for their staff. This experience has convinced us that simulation is a powerful tool in emergency service planning that is currently underutilized. Good simulation visualisation tools have proven invaluable as a communication tool for describing our work to management and staff in St Johns. The spatial data visualisation capabilities have provided management with a significantly improved understanding of their current performance and, in conjunction with the simulation model, allowed results from what-if analyses to be readily communicated and understood. It is important in simulation models to accurately capture travel time information. We have developed heuristics that allow both accurate modeling of travel times, and rapid
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simulation run times. In addition, we introduced the notion of a decision node, which dramatically decreases the time required to compute shortest paths in the networks used in this work. This concept may be of interest in other applications where shortest paths must be calculated in large networks. The combined simulation and data visualization tools introduced here have been of tremendous help to St Johns, and several other ambulance companies have expressed interest in using the system within their organisation. To the best of our knowledge, such data visualization tools have never been used in the ambulance industry before. In our experience, their use with simulation leads to more informed decision making, and better utilization of resources.
ACKNOWLEDGMENTS The authors would like to thank the management and ambulance officers at St Johns for their support of this project. Tony Francis’s technical assistance has been most useful, while the contributions of Shaun Camp, Marion Etches, Pauline Mellor and Scott Osmond have all proven invaluable. We are also very grateful to Russell Jones, Don Houghton, Anatole Sergejew, and the rest of the ART team at the ARC for making their transport model available to us. We wish to acknowledge the outstanding contribution of Jenny Smith in her work on the queueing model discussed in this paper. Finally, we are most grateful to to Michael Clist for programming assistance in the early stages of BartSim’s development. This work was partially supported by New Zealand Public Good Science Fund grant UOA803.
REFERENCES ART 1994. Auckland Transport Models Project: Technical Working Paper 1 ‘Network Development And Inventory,’ Environment Division, Auckland Regional Council, Auckland New Zealand, October 1994 BartSim (1999). http://www.esc.auckland.ac.nz/stjohn/
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Bell, C. E., D. Allen. 1969. Optimal planning of an emergency ambulance service. Journal of Socio-Economic Planning Science 3, 95 - 101. Bratley, P., B. L. Fox, L. E. Schrage. 1987. A Guide to Simulation. Springer, New York. Carson, Y. M., and R. Batta. 1990. Locating an ambulance on the Amherst Campus of the State University of New York at Buffalo. Interfaces 20, 43-49. Fitzsimmons, J.A. 1973. A methodology for emergency ambulance deployment. Management Science 19, 627 - 636. Papadimitriou, C. H., and K. Steiglitz. 1982. Combinatorial Optimization: Algorithms and Complexity. Prentice Hall, Englewood Cliffs New Jersey. Pritsker, A. A. B. 1998. Life & death decisions. ORMS Today, August 1998. Swersey, A. J. 1994. The deployment of police, fire, and emergency medical units. In Pollock, S. M., M. H. Rothkopf, A. Barnett, eds., Operations Research and the Public Sector. North Holland, Amsterdam. Swoveland, C., D. Uyeno, I. Vertinsky, R. Vickson. 1973. Ambulance location: a probabilistic enumeration approach. Management Science 20, 686-698. Wolff, R. W. 1989. Stochastic Modeling and the Theory of Queues. Prentice Hall, Englewood Cliffs, New Jersey.
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