A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption

This paper deals with a M/M/c queueing system waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the is emptied, servers wait for while before synchronously going on during which services are offered lower rate. We obtain steady-state probabilities of using matrix-geometric method. In addition, we derive important performance measures model. Moreover, construct cost model apply direct search method get optimum service rates both regular periods at lowest cost. Finally, numerical results provided.