Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods

Tetsuya Takine

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arXiv · 2604.23572

Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods

Tetsuya Takine

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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 $k$ 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.

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Tetsuya Takine. 2026-04-26. Mean Waiting Times in Discrete-Time Priority Queues with Geometrically Distributed Idle Periods. https://arxiv.org/abs/2604.23572

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