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

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.