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Analysis of a Priority Queue with Phase-Type Service and Failures

Alexander Dudin & Sergey Dudin

International Journal of Stochastic Analysis2016https://doi.org/10.1155/2016/9152701article
ABDC B
Weight
0.52

Abstract

We consider a single server queue with two types of customers. We propose a discipline of flexible priority in access that combines the features of randomization and the threshold type control. We introduce a new class of distributions, phase-type with failures (PHF) distribution, that generalizes the well-known phase-type (PH) distribution to the case when failures can occur during service of a customer. The arrival flow is described by the marked Markovian arrival process. The service time distribution is of PHF type with the parameters depending on the type of a customer. Customers of both types can be impatient. Behavior of the system is described by the multidimensional Markov chain. Problem of existence and computation of the stationary distribution of this Markov chain is discussed in brief as well as the problem of computation of the key performance measures of the system. Numerical examples are presented that give some insight into behavior of the system performance measures under different values of the parameters defining the strategy of customers access to service.

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https://doi.org/https://doi.org/10.1155/2016/9152701

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@article{alexander2016,
  title        = {{Analysis of a Priority Queue with Phase-Type Service and Failures}},
  author       = {Alexander Dudin & Sergey Dudin},
  journal      = {International Journal of Stochastic Analysis},
  year         = {2016},
  doi          = {https://doi.org/https://doi.org/10.1155/2016/9152701},
}

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Evidence weight

0.52

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.45 × 0.4 = 0.18
M · momentum0.80 × 0.15 = 0.12
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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