Zahia Ezzourgui ; Hafida Saggou ; Megdouda Ourbih-Tari ; El Bay Bourennane - The Markovian Bernoulli queues with operational server vacation, Bernoulli's weak and strong disasters, and linear impatient customers

cm:10404 - Communications in Mathematics, December 14, 2022, Volume 31 (2023), Issue 1 - https://doi.org/10.46298/cm.10404
The Markovian Bernoulli queues with operational server vacation, Bernoulli's weak and strong disasters, and linear impatient customers

Authors: Zahia Ezzourgui ; Hafida Saggou ; Megdouda Ourbih-Tari ; El Bay Bourennane

    This paper studies the stationary analysis of a Markovian queuing system with Bernoulli feedback, interruption vacation, linear impatient customers, strong and weak disaster with the server's repair during the server's operational vacation period. Each customer has its own impatience time and abandons the system as soon as that time ends. When the queue is not empty, the server's operational vacation can be interrupted if the service is completed and the server starts a busy period with a probability q or continues the operational vacation with a probability q. A strong disaster forces simultaneously all present customers (waiting and served) to abandon the system permanently with a probability p but a weak disaster is that all customers decide to be patient by staying in the system, and wait during the repair time with a probability p, where arrival of a new customer can occur. As soon as the repair process of the server is completed, the server remains providing service in the operational vacation period. We analyze this proposed model and derive the probabilities generating functions of the number of customers present in the system together with explicit expressions of some performance measures such as the mean and the variance of the number of customers in the different states, together with the mean sojourn time. Finally, numerical results are presented to show the influence of the system parameters on some studied performance measures.


    Volume: Volume 31 (2023), Issue 1
    Published on: December 14, 2022
    Accepted on: December 2, 2022
    Submitted on: November 30, 2022
    Keywords: MSC 2020: 68M20,05D40,05A15 single server,working vacation,strong and weak disaster,server's repair,linear impatient customer,interruption vacation,[MATH]Mathematics [math]

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