Analysis Of M/M/1/WV Queueing System With Vacation Interruption N-Policy

An M/M/1 working vacation queue with vacation interruption-N policy is considered in this paper. A new vacation policy, namely the vacation interruption-N policy is introduced into the M/M/1 working vacation queue. Based on the new vacation policy, the Bernoulli feedback mechanism is also introduced into the customer's service process, and we further study the M/M/1 working vacation queue with Bernoulli feedback and vacation interruption N—policy. Employing QBD process, matrix geometric solution method, generating function technique and Laplace-Stieltjes transformation, some queueing characteristics of the system are discussed:1)using quasi birth and death process and matrix-geometric solution method, we indicate the expressions of the steady-state distributions for the queue length.2)using generating function technique and Laplace-Stieltjes transformation, we discuss the expressions of the sojourn time of a customer in the stationary state. and obtain the LST of the expressions of the sojourn time.3)discussing the stochastic decomposition structures of stationary queue length and stationary sojourn time, and obtaining the expressions of the stochastic decomposition structures of stationary queue length and stationary sojourn time.4) discussing the exceptional case when N=1 or p=1, and point out: the results obtained by this paper can be directly deduced some of the existing results.