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

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  • Alexander Dudin
  • Sergei Dudin

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 ( ) distribution, that generalizes the well-known phase-type ( ) 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 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.

Suggested Citation

  • Alexander Dudin & Sergei Dudin, 2016. "Analysis of a Priority Queue with Phase-Type Service and Failures," International Journal of Stochastic Analysis, Hindawi, vol. 2016, pages 1-11, July.
    • Handle: RePEc:hin:jnijsa:9152701
    DOI: 10.1155/2016/9152701
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    Cited by:

    1. Sally McClean, 2021. "Using Markov Models to Characterize and Predict Process Target Compliance," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    2. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    3. Sergei Dudin & Olga Dudina & Konstantin Samouylov & Alexander Dudin, 2020. "Improvement of the Fairness of Non-Preemptive Priorities in the Transmission of Heterogeneous Traffic," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    4. A. N. Dudin & S. A. Dudin & O. S. Dudina, 2023. "Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    5. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities," Mathematics, MDPI, vol. 9(11), pages 1-17, May.

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