It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.

No abstract

No abstract

No abstract

This paper presents an approximation formula for the overflow probability for GI/GI/c(N) queues in terms of a queue-length distribution for the corresponding GI/GI/c(\infty ) queues, where N is the total capacity of the system. The approximation is based on the conservation law, and on assumptions which might be acceptable if N \gg c. The authors' approximation formula is numerically examined for various phase-type GI/GI/c(N) queues and the results show that the approximation is very good for practical parameter settings. The authors' approximation stands merely on a stationarity assumption. Therefore, it is also expected to be good for G/G/c(N) queues with a large N.overflow probability, loss probability, G/G/c(N), finite queue, approximation, conservation law