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Bayesian control of the number of servers in a GI/M/c queuing system

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  • Ausín Olivera, María Concepción
  • Lillo Rodríguez, Rosa Elvira
  • Wiper, Michael Peter

Abstract

In this paper we consider the problem of designing a GI/M/c queueing system. Given arrival and service data, our objective is to choose the optimal number of servers so as to minimize an expected cost function which depends on quantities, such as the number of customers in the queue. A semiparametric approach based on Erlang mixture distributions is used to model the general interarrival time distribution. Given the sample data, Bayesian Markov chain Monte Carlo methods are used to estimate the system parameters and the predictive distributions of the usual performance measures. We can then use these estimates to minimize the steady-state expected total cost rate as a function of the control parameter c. We provide a numerical example based on real data obtained from a bank in Madrid.

Suggested Citation

  • Ausín Olivera, María Concepción & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter, 2004. "Bayesian control of the number of servers in a GI/M/c queuing system," DES - Working Papers. Statistics and Econometrics. WS ws046917, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws046917
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    Cited by:

    1. Ramírez Cobo, Josefa & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter & Wilson, Simon P., 2008. "Inference for double Pareto lognormal queues with applications," DES - Working Papers. Statistics and Econometrics. WS ws080402, Universidad Carlos III de Madrid. Departamento de Estadística.

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