The Discrete Time Geo /G /1 Queue with Negative Customers and Multiple Working Vacations

In this article, we study the discrete time Geo /G/1 queue with negative customers and multiple working vacations. Under the RCH disciple, the arrival of a negative customer does not receive service and removes the positive customer who is being served. Using embedded Markov chain and matrix analytic approach, we derive the probability generating function (PGF) and mean of the stationary queue length at the departure epoch. From the process of the proof and the results, we also obtain the probabilities that the server is in idle, working vacation, and regular busy period, respectively. Finally, we discuss numerical results.