Time-dependent behaviour of an M/M/3 heterogeneous server queueing system with multiple vacations subject to system disaster

Abstract

This research paper investigates the dynamic behaviour of a heterogeneous three-server queuing model with multiple vacation. The model also accounts for the possibility that a disaster could occur during busy periods or on vacation, in which case the restoration process would begin immediately. The time-dependent probabilities of system size are presented in the work with explicit equations computed in terms of modified Bessel functions, employing generating functions. To support the theoretical conclusions, numerical examples are given.

Keywords

• transient analysis, three-server, multiple vacation, disaster.