A tutorial on hypercube queueing models and some practical applications in Emergency Service Systems

Abstract

ABSTRACT. This paper presents some extensions and applications of hypercube queueing models to describe server-to-customer type Emergency Service Systems. The classical hypercube is a well-known spatially distributed queueing model effective in analyzing these systems, based on Markovian analysis approximations. Experience has shown that each real life Emergency Service System may have its own unique characteristics so that each system may require a particular hypercube queueing model incorporating those characteristics. Some of these distinctive characteristics are considered in the extensions presented in this tutorial such as dispatch policy based on random selection of the server to take an incoming call; partial cooperation among servers whereby depending on where the call is coming from, some servers cannot take the call; servers with additional workload coming from walk-in nonemergency customers such as in customer-to-server systems; existence of calls requiring the dispatch of more than one server; existence of more than one type of servers in the system, for instance paramedical and medical units in emergency medical systems. In this study, we present a set of these models based on the smallest non-trivial service systems. For each model, the construction of the system of equations for equilibrium hypercube state probabilities and the evaluation of particular operational characteristics are described.

Aplicação do modelo hipercubo com prioridade na fila com mais de um servidor preferencial sem considerar a hipótese de backup parcial: estudo de caso em um SAMU

“…By the end of the solutions, a mean value is calculated to find the final probabilities for each state. On a different way, according to Chiyoshi et al (2011), is to solve a single model where the transition rates are shared among idle servers. For example, on a transition between {000} to {001}, where all servers on the same location and there is no difference of their dispatch preference, the transition rate is equal to 1/3 of the total arrival rate.…”

Recommendations for dispatching emergency vehicles under multitiered response via simulation

“…Their study is different from the previous studies since multiple servers can be assigned to each station. Chiyoshi et al () provided a survey of the hypercube model applied to EMS systems.…”

Modelo de apoio à decisão para um problema de posicionamento de bases, alocação e realocação de ambulâncias em centros urbanos: estudo de caso no município de São Paulo

“…Uma referência que cobre em detalhes o Modelo Hipercubo, bem como extensões e desdobramentos possíveis é encontrada em Chiyoshi et al (2011). Os autores, por meio de modelos reduzidos (tradução livre de Toy Models), apresentam formas de modelagem de diversas situações práticas encontradas nos sistemas de emergência.…”