A single-server discrete-time queue with correlated positive and negative customer arrivals

An MMBP/Geo/1 queue with correlated positive and negative customer arrivals is studied. In the infinite-capacity queueing system, positive customers and negative customers are generated by a Bernoulli bursty source with two correlated geometrically distributed periods. I.e., positive and negative customers arrive to the system according to two different geometrical arrival processes. Under the late arrival scheme (LAS), two removal disciplines caused by negative customers are investigated in the paper. In individual removal scheme, a negative customer removes a positive customer in service if any, while in disaster model, a negative customer removes all positive customers in the system if any. The negative customer arrival has no effect on the system if it finds the system empty. We analyze the Markov chains underlying the queueing systems and evaluate the performance of two systems based on generating functions technique. Some explicit solutions of the system, such as the average buffer content and the stationary probabilities are obtained. Finally, the effect of several parameters on the system performance is shown numerically.