Title: A queueing system with heterogeneous arrivals, two kinds of vacations and impatient customers

Authors: R.S. Yohapriyadharsini; V. Suvitha; Rakesh Kumar

Addresses: Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Ramapuram Campus, Chennai – 600089, Tamil Nadu, India ' Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur – 603203, Tamil Nadu, India ' Department of Mathematics, Statistics and Actuarial Science, Namibia University of Science and Technology, 13 Jackson Kaujeua Street, Windhoek, Private Bag 13388, Windhoek, Namibia

Abstract: We consider an M/ M/1 queueing system with two kinds of vacations and impatient customers. The server begins the 1st kind of vacation each time the system becomes empty after serving all the customers. If the system is empty, when returning from this vacation it takes the 2nd kind of vacation. When the server comes back from either 1st kind or 2nd kind of vacation, if there is at least one customer in the system, the server immediately starts the service. If the server is busy or on 1st kind of vacation when a customer arrives at the system, it activates an impatience timer. If the customer's service has not been finished before the customer's timer perishes, the customer leaves the system and never returns. The balance equations of the model are all derived using a state-transition diagram. Probability generating functions (PGFs) technique has been used to derive the steady-state probabilities. Various measures of performance are presented and numerical illustrations are also provided.

Keywords: busy state; vacations; steady state; performance measures.

DOI: 10.1504/IJMOR.2025.145607

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.2, pp.152 - 166

Received: 05 Jul 2023
Accepted: 25 Jul 2023
Published online: 09 Apr 2025 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article