Approximating the Equilibrium Behavior of Multi-Server Loss Systems

Abstract

A procedure is given for approximating the equilibrium behavior of multi-server loss systems having distinguishable servers and multiple customer types under light to moderate traffic intensity. Calls are assumed to arrive according to independent Poisson processes for each customer type. General service time distributions which may depend on both server and customer type are allowed. For N servers, the approximation routine consists of a simple iterative procedure in N nonlinear equations. Computational experience with respect to the convergence properties of the iteration and the accuracy of the approximation is given.multi-server queues, Erlang loss system, urban service systems

Optimal ambulance location with random delays and travel times

“…The main descriptive model that is relevant for our purposes is the hypercube model developed by Larson (1974) and subsequent approximate versions of that model (Larson, 1975 andJarvis, 1985). This model allows busy fractions to vary between ambulances and can accommodate ambulances responding to calls outside their assigned districts.…”

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

“…He also estimated server workload more accurately than Larson [14]. Furthermore, he could show that although the shape of service time distribution was not completely ineffective on the results of the HQM, its influence was very small [15].…”

“…Jarvis [15] extended the approximation procedure in [14] and presented an algorithm for loss systems (zero-line capacity). In his procedure, service time distribution is depended on the type of server and customer.…”

Modelo hipercubo integrado a um algoritmo genético para análise de sistemas médicos emergenciais em rodovias

“…O uso de métodos aproximados do modelo hipercubo (não baseados em sistemas com 2 N equações lineares; ver Larson, 1975;Jarvis, 1985) na abordagem AG/hipercubo pode ser uma alternativa para reduzir os tempos computacionais. Porém o modelo teria menor acuracidade em estimar as medidas de desempenho do sistema.…”

“…Por exemplo, Larson (1975), Jarvis (1985), Halpern (1977), Chelst e Barlach (1981), Burwell et al (1993) e Swersey (1994) estenderam o modelo original de forma a eliminar algumas hipóte-ses limitantes ou melhorar a eficiência computacional do modelo. Outros estudos têm sido dedicados a combinar o modelo hipercubo com métodos de otimização.…”