An M^[X]/G(a,b)/1 queueing system with unreliable server, stand-by server, restricted arrivals, variant threshold policy for vacations

Abstract

We studied the behaviour of an M[X]/G(a, b)/1 queueing system with unreliable server, stand-by server, restricted admissibility and variant threshold policy for vacations in this paper. The stand-by server is utilised only during main server's repair period. At the moment of main server's busy completion or repair completion, if the number of customers in the queue is less than 'a', the main server avails type-I vacation repeatedly until the queue length reaches at least 'a'. While getting back from vacation of type-I, if the queue has its length of value as at least 'a' then the server performs the type-II vacation continuously, until it reaches at least N(a < b ≤ N). When both types of vacation gets completed, and the length queue is at least 'N', then the server starts service to the batch of 'b' customers. The PGF of queue size and some important performance measures are derived. An extensive numerical result is illustrated.