Title: A transient M^[X]/M^{(k, K)}/1 queue with reneging and setup time for service

Authors: Aliakbar Montazer Haghighi; Dimitar P. Mishev

Addresses: Department of Mathematics, Prairie View A&M University, P.O. Box 519 – MS2225, Prairie View, Texas 77446 0519, USA ' Department of Mathematics, Prairie View A&M University, P.O. Box 519 – MS2225, Prairie View, Texas 77446 0519, USA

Abstract: In this paper, we analyse a transient queuing model, in which tasks arrival in bulks of varying sizes with compound Poisson process. There is a single server serving batches of tasks with limited sizes with a minimum and a maximum, according with exponential distribution, with setup times for service with also exponential distribution, and impatient tasks that may renege while the server is busy with also exponential distribution. The transient probability generating function for the number in the system, special cases to verify it and some performance measures have been found.

Keywords: transient queue; Markov process; Poisson; reneging; exponential service; setup time; probability generating function; moments.

DOI: 10.1504/IJMOR.2025.147025

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.2, pp.164 - 181

Received: 16 Aug 2023
Accepted: 18 Aug 2023
Published online: 10 Jul 2025 *

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