Analysis of ambulance decentralization in an urban emergency medical service using the hypercube queueing model
Introduction
One of the major concerns of Emergency Medical Services (EMS) is to rapidly provide first care medical assistance to the victims. The time elapsed between an emergency call and its assistance, called response time, is one of the main factors that influence system performance. In urban areas, this time lapse depends on different aspects of calls and the EMS system such as: type and location of the request, number and location of ambulances, system congestion, local traffic conditions, weekday and time, etc. The United States EMS Act sets some standards: 95% of the emergency requests should be served within 10 min in urban areas and within 30 min in rural areas [1]. Similar regulations are found in other parts of the world; for example, in London and Montreal, the regulation states that 95% of the requests should be served within 14 and 10 min, and 50% and 70% of the requests should be served within 8 and 7 min, respectively [2], [3]. In Brazil, however, there is no specific regulation that specifies limitations for response times in EMSs.
When designing or modifying the configuration of EMSs, managers should balance the benefits of improving user service at the expense of increasing the investment in the system. This trade-off is typical in services as well as manufacturing systems (e.g., Bitran and Morabito [4]). Several studies are found in the literature proposing approaches to rationalize the usage of available resources and improve user service. Nevertheless, a number of them do not directly consider the probabilistic nature of user arrival and service processes and the fact that ambulances are not always available for servicing a call. Examples of probabilistic approaches for ambulance deployment appear in Brandeau and Larson [5], Eaton et al. [6], Goldberg et al. [7] and Fujiwara [8]. Surveys reviewing the most important studies in the last decades are found, for instance, in Kolesar and Swersey [9], Louveaux [10], Swersey [11] and Brotcorne et al. [12]. It should be noted that an accurate model for EMSs can be quite complex since elements of uncertainty appear in time, location and amount of required services (e.g., demands are temporally and spatially distributed) and there are particular dispatching policies.
The hypercube queueing model developed by Larson [13] and extended by other authors [11] is an effective descriptive model for planning server-to-customer systems. Given a system configuration, it is able to evaluate a variety of performance measures relevant for decision-making. It is not an optimization model in the sense that it determines an optimal configuration for the system, but it can provide a reasonably complete evaluation for each suggested configuration. It can also be combined in optimization approaches to deal with probabilistic location problems. For instance, Batta et al. [14] suggested its use in an iterative procedure as an alternative to relax the assumption of independence among the servers in the maximum expected covering location problem, MEXCLP (Daskin [15]). Chiyoshi et al. [16] analyzed non-homogeneous servers and compared MEXCLP and the adjusted maximum expected covering location problem, AMEXCLP [14]. Saydam and Aytug [17] developed a genetic algorithm that combines MEXCLP with a hypercube approximation algorithm developed by Jarvis [18] in order to solve MEXCLP with increased accuracy. Gendreau et al. [19], [2] used tabu search in similar contexts. Galvão et al. [3] applied simulated annealing in the solution of MEXCLP and the maximum availability location problem, MALP [20].
In the last decades, different examples of application of the hypercube model in urban service systems have been reported; for instance, the social service visit program [21], the ambulance location in Boston [5] and Greenville [22] and the police patrolling in New Haven [23] and Orlando [24]. In Brazil, some examples are the assistance of power interruptions, location and planning of fire rescue vehicles and the imbalance of workload among the ambulances on a highway [25]. Other references related to applications and extensions of the hypercube model can be found in Halpern [26], Jarvis [27] and Swersey [7].
The present paper studies the hypercube model application to the urban EMS of Campinas (SAMU-192), a city of almost one million people located in the state of Sao Paulo. In its original configuration, the system had all ambulances centralized at a single base adjacent to a general hospital downtown. This study analyzes the effects of decentralizing ambulances and adding new ambulances to the system, comparing the results to the ones of the original situation. It is shown how much mean response times, fractions of calls served by backups and other performance measures of the system are improved, as a larger number of ambulances are decentralized, while the ambulance workloads remain approximately constant. However, total decentralization as suggested by the system operators of SAMU-192 may not produce satisfactory results.
This case study paper is organized as follows: in Section 2 system SAMU-192 is briefly described, in Section 3 the application of the hypercube model is discussed, in Section 4 the results obtained with the model for different scenarios are analyzed and compared to the original system configuration. Finally, in Section 5 concluding remarks and perspectives for future research are presented.
Section snippets
SAMU-192
The World Health Organization has defined provision of basic life support to all risk situations involving people and goods as a main objective of an EMS. In Brazil, since the beginning of the nineties, efforts have been made in order to impel the organization of urban EMSs. Most Brazilian systems are public services and some of them are similar to the French model SAMU (Service d’Aide Médicale Urgente), operating for more than 20 years. SAMU's serve a city or a region containing several cities
Hypercube model
The hypercube model considers geographical and temporal complexities of the region and is based on spatial queueing theory and Markovian analysis approximations. Basically, the idea is to expand the state space description of a simple multi-server queueing system in order to represent each server individually and incorporate more complex dispatching policies. Once the model is calibrated, a number of performance measures of interest to how the system is managed can be estimated, either
Evaluation of alternative scenarios
As mentioned above, one of the major concerns in EMSs is to reduce the response time, which is composed of the setup time, the travel time and the waiting time (eventually spent in the queue). The waiting time is a function of the mean travel time to a queued call and the probabilities of satured states . In SAMU-192, the setup time is very short (around 1 min) and such probabilities are relatively low (order of in the original configuration), so that the mean response
Concluding remarks
This paper studied the application of the hypercube queueing model to the urban EMS of Campinas (SAMU-192) in Brazil. In its original configuration, SAMU-192 had all ambulances centralized in its central base. The hypercube model was successfully applied to analyze ambulance deployment, in particular, the effects of decentralizing ambulances and increasing their number. The results showed that the simple relocation of one single ambulance decreases system travel times (as one would expect). As
Acknowledgements
The authors thank SAMU-192 of Campinas for providing the data, especially Dr. Arine Campos O. Assis (former system coordinator and presently a consultant of the Brazilian Ministry of Health) for her support and incentive, and the two anonymous referees for their useful comments and suggestions. This research was partially sponsored by CNPq (Grant 800773/91-8).
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