Time-Dependent Analytical and Computational Study of an M/M/1 Queue with Disaster Failure and Multiple Working Vacations

An M/M/1 working vacation (WV) queueing model with disaster failure is considered to examine time-dependent behavior. When the system is in busy mode, it can fail such that all the customers in the system are flushed out and never returns; such type of failure is known as disaster failure. The server is allowed to go for a WV after each busy period for a random duration of time. In the duration of WV, the server reduces the service rate rather than halting the service. After completing the vacation period, the server can take any number of vacation until he found some customers waiting in the queue; this vacation policy is known as multiple vacation policy. The transient analytical formulae for the queue size distributions are formulated by solving Chapman-Kolmogorov equations using continued fractions, modified Bessel function and probability generating function methods. Moreover, various queueing performance measures are given, and real-time performance is evaluated by computing the performance measures numerically.