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Analysis of GIX/M(n)//N systems with stochastic customer acceptance policy

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Abstract

We investigate GIX/M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities. These results are then used to derive the continuous-time long-run distribution of the number of customers in the system. Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors of the computed performance measures.

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Authors and Affiliations

  1. Department of Mathematics and CEMAT, University of Trás-os-Montes e Alto Douro, Vila Real, Portugal

    Fátima Ferreira

  2. Department of Mathematics and CEMAT, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal

    António Pacheco

Authors
  1. Fátima Ferreira
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  2. António Pacheco
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Correspondence to António Pacheco.

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Ferreira, F., Pacheco, A. Analysis of GIX/M(n)//N systems with stochastic customer acceptance policy. Queueing Syst 58, 29–55 (2008). https://doi.org/10.1007/s11134-007-9057-2

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  • DOI: https://doi.org/10.1007/s11134-007-9057-2

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