Emergency service systems: The use of the hypercube queueing model in the solution of probabilistic location problems

Abstract

Probabilistic location problems are surveyed from the perspective of their use in the design of emergency service systems, with special emphasis on emergency medical systems. Pioneering probabilistic models were defined in the 1980s, as a natural extension of deterministic covering models (first generation models) and backup models (second generation). These probabilistic models, however, adopted simplifying assumptions that in many cases do not correspond to real‐world situations, where servers usually cooperate and have specific individual workloads. Thus the idea of embedding the hypercube queueing model into these formulations is to make them more adherent to the real world. The hypercube model and its extensions are initially presented in some detail, which is followed by a brief review of exact and approximate methods for its solution. Probabilistic models for the design of emergency service systems are then reviewed. The pioneering models of Daskin and ReVelle and Hogan are extended by embedding the hypercube model into them. Solution methods for these models are surveyed next, with comments on specialized models for the design of emergency medical systems for urban areas and highways.

Análise da configuração de SAMU utilizando múltiplas alternativas de localização de ambulâncias

“…Eles também precisam definir e analisar medidas de desempenho de maneira a serem capazes de avaliar adequadamente a configuração do sistema. Isso pode ser realizado com o auxílio de modelos analíticos de teoria de filas e modelos experimentais de simulação, com usuários e servidores do sistema espacialmente distribuídos na região de interesse e servidores considerados como distinguíveis ou indistinguíveis, dependendo da natureza do serviço em consideração (SWERSEY, 1994;MORABITO, 2008).…”

“…O modelo hipercubo, proposto originalmente por Larson (1974) e estendido por vários autores (GALVÃO; MORABITO, 2008) é um modelo descritivo baseado na teoria de filas espacialmente distribuídas, utilizado para analisar e planejar SAEs. O modelo considera os servidores do sistema individualmente e disciplinas de prioridade no despacho destes servidores, se houverem servidores disponíveis para despacho imediato, e fila com disciplina de atendimento FCFS (First Come First Served), no caso de todos os servidores estarem ocupados.…”

An ILP and simulation model to optimize search and rescue helicopter operations

“…Despite not being an optimization model, it gives an acceptable structure of facilities. Studies of Takeda et al (2007), Galvão and Morabito (2008), Iannoni et al (2009) andToro-Diaz et al (2013) are appropriate applications of hypercube model to find out more.…”

Hypercube Queuing Models in Emergency Service Systems: A State-of-the-Art Review

“…In a system with immobile servers, servers are usually considered indistinguishable from each other (e.g., seats of an airplane or beds of a hospital). In these cases, it does not matter exactly which server is busy, and only the number of busy servers is important [1]. On the other hand, mobile servers can be modeled as servers more precisely distinguishable from each other.…”

“…Given these conditions and, in general, the uncertainty in these problems, decision-making becomes more complex for managers. The design of ESSs requires strategic and tactical decisions [1]. The strategic decisions determine the number and location of servers.…”