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Analyzing of a finite buffer queue with finite number of vacation policy and correlated arrivals

This paper analyses a MAP/G/1/N queue having finite number of vacations. The server takes a finite number (say J ≥ 0) of vacations whenever the system becomes empty at service completion epoch. If no clients are found by the end of the Jth vacation, the server does not go for vacation and stays in the system (called dormant period) until one client arrives. The number of vacations being finite and the server can utilise vacation periods for any other jobs. This is obvious that J = 1 and J → 1 lead to single and multiple vacation models, respectively. This research work mainly focuses more generalised vacation policy and different use cases. The following results have been obtained: 1) the distributions of clients in the queue at various epochs; 2) the Laplace-Stieltjes transform of the actual waiting-time distribution in the queue of a client under the FCFS discipline. The numerical data and graphs are presented to establish the analytical result.