Generalization and classification of two-queue JSQ–SLQ systems with zero and non-zero switch-over times

This paper considers a family of two-queue single-server queueing systems with the Join-the-Shortest-Queue (JSQ) routing discipline and the Serve-the-Longest-Queue (SLQ) service discipline. The main focus is on the classification of such models depending on whether server switch-over times are taken into account and on the priority rule used to choose the queue to be served. Models with zero and non-zero switch-over times are considered, including the cases without priority, with relative preemptive priority, and with absolute preemptive priority. For the selected classes, a unified scheme of Markov process representation is described, based on the length of one queue, the difference between the queue lengths, and a phase variable. The main approaches to obtaining stationary performance measures are indicated: the probability generating function method and the matrix-geometric method.