Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods
Probability
2026-04-28 v1
Abstract
This paper considers the mean waiting times in discrete-time preemptive-resume and nonpreemptive priority single-server queues fed by K independent batch Markovian arrival streams with geometrically distributed idle periods. While being active, the k-th (k = 1, 2, ..., K) arrival stream feeds at least one customer to the queue, where the number of arriving customers depends on the state of the underlying Markov chain. Service times of class customers are independent and identically distributed according to a general distribution. For these queues, we derive explicit formulae for the mean waiting times of customers in each class.
Keywords
Cite
@article{arxiv.2604.23572,
title = {Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods},
author = {Tetsuya Takine},
journal= {arXiv preprint arXiv:2604.23572},
year = {2026}
}