Performance analysis of vacation interruption queue with balking and reneging

Abstract

This paper presents a comprehensive study of an infinite buffer M/M/1 queue with variant working vacations subjected to Bernoulli schedule vacation interruption wherein the customers balk with a probability. The server commences a working vacation as soon as the system becomes empty and resumes a regular busy period by interrupting the working vacation with probability 1 − p if the system is non-empty at a service completion instant or continues the vacation with probability p. The customers may renege due to slow service rate during the working vacation. The inter-arrival times, service times (both during regular busy period and working vacation periods), vacation times and reneging times are mutually independent and exponentially distributed. We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size for different server states. Various performance measures and the monotonicity on some performance measures with respect to K are discussed, and a cost optimization problem through quadratic fit search method has been considered. The stochastic decomposition structures of the mean queue length and mean waiting time are verified. Mathematics Subject Classification (2000) 60K25 · 68M20 · 90B22