The Interrelationship Between N-policy M/G/1/K and F-policy G/M/1/K Queues with Startup Time

Abstract

This paper studies the interrelationship between the N-policy M/G/1/K queue and the F-policy G/M/1/K queue. The N-policy queuing problem investigates the most common issue of controlling service. The F-policy queuing problem deals with the most common issue of controlling arrivals. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to develop the solution algorithm for the N-policy M/G/1/K queue with startup time. We have demonstrated that the N-policy M/G/1/K queue with startup time has been effectively used to derive the solution algorithm to the F-policy G/M/1/K queue with startup time. The interrelationship between the N-policy and the F-policy queueing problems are illustrated analytically for 3-stage Erlang (service or interarrival) time distribution.