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Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience

Bouchentouf Amina Angelika, Guendouzi Abdelhak, Houalef Meriem, Majid Shakir

Operations Research and Decisions

2022

Vol. 32, No. 2

16--33

In this paper, we analyze an M/M/1 queueing system under both single and multiple working vacation policies, multiphase random environment, waiting server, balking and reneging. When the system is in operative phase j = 1, 2, . . . , K, customers are served one by one. Whenever the system becomes empty, the server waits a random amount of time before taking a vacation, causing the system to move to working vacation phase 0 at which new arrivals are served at a lower rate. Using the probability generating function method, we obtain the distribution for the steady-state probabilities of the system. Then, we derive important performance measures of the queueing system. Finally, some numerical examples are illustrated to show the impact of system parameters on performance measures of the queueing system.

Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy

Bouchentouf Amina Angelika, Yahiaoui Lahcene, Kadi Mokhtar, Majid Shakir

Operations Research and Decisions

2020

Vol. 30, No. 4

5--28

This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using the probability generating function (PGF) technique, we obtain the steady-state solution of the system. Besides, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using a quadratic fit search method (QFSM). Finally, numerical examples are provided to visualise the analytical results.