Transient Analysis of an M / M /2 Heterogeneous Server Queueing System with Multiple Working Vacations Subject to System Disaster

This research study investigates the transient behavior of a heterogeneous two-server queuing model that incorporates multiple vacation periods. The model also accounts for the potential for a disaster to occur during busy times and vacations, in which case the restoration process would begin immediately. In the work, generating functions are used to define the time-dependent probabilities of system size in terms of modified Bessel functions. The theoretical results have been supported by numerical instances.