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The Mt/M/1 queueing system with impatient customers and multiple vacation

Author

Listed:
  • Ali Yousefi

    (Allameh Tabataba’i University)

  • Reza Pourtaheri

    (Allameh Tabataba’i University)

Abstract

This paper presents a queueing system that considers impatient customers and multiple vacation periods. This study uses the Mt/M/1 model and assumes that customers’ impatience is related to the server’s vacation. The system being analyzed exhibits exponential service times and arrival processes that follow a periodic (sinusoidal) Poisson distribution. The system under consideration has exponential service times and periodic (sinusoidal) Poisson arrival processes. We studied a novel analysis of an Mt/M/1 model including simultaneous vacations and impatient customers alongside the relative amplitude changes. The time-dependent probability generating functions and their associated steady-state solutions have been derived explicitly. The pointwise stationary approximation is utilized to calculate long-term average effectiveness sizes performance metrics. We focus on five performance measures: the expected number of customers waiting in the queue during vacation, the expected customer waiting time in the queue during vacation, the probability of the server being busy, the probability of the server being on vacation and the probability of customers’ impatience. Finally, we perform a sensitivity analysis using simulations to evaluate the parameters.

Suggested Citation

  • Ali Yousefi & Reza Pourtaheri, 2024. "The Mt/M/1 queueing system with impatient customers and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 2002-2022, December.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:4:d:10.1007_s12597-024-00768-y
    DOI: 10.1007/s12597-024-00768-y
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    References listed on IDEAS

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