Bayesian control of the number of servers in a GI/M/c queueing system
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Bayesian control of the number of servers in a GI/M/c queueing systemDate
2007Citation
Journal of Statistical Planning and Inference, 2007, 137, p. 3043 – 3057
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.
Keywords
Birth–death MCMC
Multiple service channels
Optimal control
Multiple service channels
Optimal control
Editor version
ISSN
0378-3758