Title: Transient solution of an M/M/∞ queue with system's additional tasks and impatient customers

Authors: R. Sudhesh; A. Azhagappan

Addresses: Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, Tamilnadu – 620 024, India ' Department of Mathematics, St. Anne's College of Engineering and Technology, Anna University, Panruti, Cuddalore District, Tamilnadu – 607 110, India

Abstract: This paper studies the impatient behaviour in an infinite server queue with additional tasks assigned to the system. Whenever the system becomes empty, the system as a whole is assigned a secondary task of duration U whose distribution is exponential. Any arrival during the period U becomes impatient due to the unavailability of service facility. Each individual waiting customer activates an independent impatience timer of duration T which is exponentially distributed. When the system comes back after the completion of U, before T expires, the waiting customers are simultaneously taken for service and they leave the system after the completion of service. If T expires before the completion of task U, the customers abandon the system and never to return. The transient system size probabilities of this model are derived explicitly for both single and multiple task cases. The time-dependent mean and variance of system size are also derived. Further, numerical simulations are also presented to analyse the effect of system indices.

Keywords: infinite server queue; single and multiple tasks; impatient customers; transient probabilities.

DOI: 10.1504/IJMOR.2020.104680

International Journal of Mathematics in Operational Research, 2020 Vol.16 No.1, pp.82 - 97

Received: 15 Jun 2018
Accepted: 29 Sep 2018

Published online: 28 Jan 2020 *

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