this paper analyzes an m/m/2 queueing system with two heterogeneous servers. both servers goes on vacation when there is no customers waiting for service after this server 1 is always available but the other goes on vacation whenever server 2 is idle. the vacationing server however, returns to serve at a low rate as an arrival finds the other server busy. the system is analyzed in the steady st...

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 ...

In this paper, a meta-heuristic method, the Bat Algorithm, based on the echolocation behavior of bats is used to determine the optimum service rate of a queue problem. A finite buffer M/M/1 queue with N policy, multiple working vacations and Bernoulli schedule vacation interruption is considered. Under the two customers' impatient situations, balking and reneging, the...

In this paper we deal with an M/G/1 vacation system with the sojourn time (wait plus service) limit and two typical vacation rules, i.e. multiple and single vacation rules. Using the level crossing approach, explicit expressions for the steady-state distributions of the virtual waiting times are obtained in vacation systems with exponential and constant service times, a general vacation time, a...

Consider an M/M/1 retrial queue with collisions and working vacation interruption under N-policy. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decompo...