On the number of customers served in the M/G/1 retrial queue: first moments and maximum entropy approach

  • Authors:
  • M. J. Lopez-Herrero

  • Affiliations:
  • Escuela Universitaria de Estadistica, Universidad Complutense de Madrid, 28040 Madrid, Spain

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2002

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Abstract

In this paper we present general results on the number of customers, I, served during the busy period in an M/G/1 retrial system. Its analysis in terms of Laplace transforms has been previously discussed in the literature. However, this solution presents important limitations in practice; in particular, the moments of I cannot be obtained by direct differentiation. We propose a direct method of computation for the second moment of I and also for the probability of k, k ≤ 4, customers being served in a busy period. Then, the maximum entropy principle approach is used to estimate the true distribution of I according to the available information.