This paper considers an infinite buffer renewal input queue with multiple working vacation policy wherein customers are served by a single server according to general bulk service （a,b）-rule （1 ≤ a ≤ b）. If the ...This paper considers an infinite buffer renewal input queue with multiple working vacation policy wherein customers are served by a single server according to general bulk service （a,b）-rule （1 ≤ a ≤ b）. If the number of waiting customers in the system at a service completion epoch （during a normal busy period） is lower than ＇a＇, then the server starts a vacation. During a vacation if the number of waiting customers reaches the minimum threshold size ＇a＇, then the server starts serving this batch with a lower rate than that of the normal busy period. After completion of a batch service during working vacation, if the server finds less than takes another vacation, otherwise the server rate. The maximum allowed size of a batch a＇ customers accumulated in the system, then the server continues to serve the available batch with that lower in service is ＇b＇. The authors derive both queue-length and system-length distributions at pre-arrival epoch using both embedded Markov chain approach and the roots method. The arbitrary epoch probabilities are obtained using the classical argument based on renewal theory. Several performance measures like average queue and system-length, mean waiting-time, cost and profit optimization are studied and numerically computed.展开更多
文摘This paper considers an infinite buffer renewal input queue with multiple working vacation policy wherein customers are served by a single server according to general bulk service （a,b）-rule （1 ≤ a ≤ b）. If the number of waiting customers in the system at a service completion epoch （during a normal busy period） is lower than ＇a＇, then the server starts a vacation. During a vacation if the number of waiting customers reaches the minimum threshold size ＇a＇, then the server starts serving this batch with a lower rate than that of the normal busy period. After completion of a batch service during working vacation, if the server finds less than takes another vacation, otherwise the server rate. The maximum allowed size of a batch a＇ customers accumulated in the system, then the server continues to serve the available batch with that lower in service is ＇b＇. The authors derive both queue-length and system-length distributions at pre-arrival epoch using both embedded Markov chain approach and the roots method. The arbitrary epoch probabilities are obtained using the classical argument based on renewal theory. Several performance measures like average queue and system-length, mean waiting-time, cost and profit optimization are studied and numerically computed.
