The M^X/M/c queue with state-dependent control at idle time and catastrophes

TL;DR

This paper analyzes a complex queueing model with state-dependent controls, catastrophes, and resurrection, providing insights into its long-term behavior and transition probabilities.

Contribution

It introduces a detailed study of an M^X/M/c queue with state-dependent controls, catastrophes, and resurrection, including new results on recurrence, equilibrium, and transition probabilities.

Findings

Recurrence and equilibrium distributions are characterized.

Laplace transform of transition probabilities is derived.

Results apply to queues with catastrophes and resurrection mechanisms.

Abstract

IIn this paper, we consider an M^X/M/c queue with state-dependent control at idle time and catastrophes. Properties of the queues which terminate when the servers become idle are firstly studied. Recurrence, equilibrium distribution and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these results and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we can obtain the Laplace transform of the transition probability for the absorptive M^X/M/c queue.