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Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

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  • Cosmika Goswami
  • N. Selvaraju

Abstract

We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.

Suggested Citation

  • Cosmika Goswami & N. Selvaraju, 2016. "Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations," Advances in Operations Research, Hindawi, vol. 2016, pages 1-17, March.
    • Handle: RePEc:hin:jnlaor:4024950
    DOI: 10.1155/2016/4024950
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    Cited by:

    1. Laurentiu Rece & Sorin Vlase & Daniel Ciuiu & Giorgian Neculoiu & Stefan Mocanu & Arina Modrea, 2022. "Queueing Theory-Based Mathematical Models Applied to Enterprise Organization and Industrial Production Optimization," Mathematics, MDPI, vol. 10(14), pages 1-32, July.
    2. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).

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