Behavior Analysis of an M/M/1 vacation Queue in Random Environment. Issue 4 (4th July 2021) - Ammar, Sherif
ABSTRACT: This study examines an M/M/1 vacation queue in a random environment. This system is considered a classical M / M / 1 queueing system in which customers are served one by one in the operative phase i, i = 1, 2, …, n, and the arrival and service rates are λ i and μ i ., respectively. The system starts the vacation phase when it is empty and there are no customers to which to provide the service. Furthermore, the system moves to some operating phase i with probability q i, i = 1, 2, …, n at the end of the vacation phase. Based on the generating function technique, we derived the transient probabilities and some performance measures. The steady-state analysis is also discussed. Finally, the effectiveness of the proposed system parameters on the behaviour of the system is illustrated with some numerical examples.