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

TL;DR

This paper derives explicit formulas for mean waiting times in discrete-time priority queues with multiple arrival streams, accounting for geometrically distributed idle periods and Markovian arrivals.

Contribution

It provides new explicit formulas for mean waiting times in complex priority queue models with Markovian arrivals and geometric idle periods.

Findings

Explicit formulas for mean waiting times are derived.

Results apply to both preemptive-resume and nonpreemptive queues.

The model accounts for multiple Markovian arrival streams with geometrically distributed idle periods.

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.