This paper deals with the optimal control of a finite capacity G/M/1 queueing system combined the F-policy and an exponential startup time before start allowing customers in the system. The F-policy queueing problem investigates the most common issue of controlling arrival to a queueing system. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distribution of the number of customers in the system. We illustrate a recursive method by presenting three simple examples for exponential, 3-stage Erlang, and deterministic interarrival time distributions, respectively. A cost model is developed to determine the optimal management F-policy at minimum cost. We use an efficient Maple computer program to determine the optimal operating F-policy and some system performance measures. Sensitivity analysis is also studied. (c) 2007 Elsevier Inc. All rights reserved
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.
This paper studies Optimal NT policies for a k-phase service M/G/1 system with Bernoulli vacation schedule. The system contains an unreliable server with a breakdown period and delaying period. The server determines to start service by the policy: the server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the completion period. There are k phases of service in the system. After the completion of k phases service, the server may take a short vacation or may remain in the system to serve the next unit, which is defined by Bernoulli vacation schedule. Moreover, we assume the server fails according to a Poisson process whose repair time follows a general distribution. In final, we analyze the system characteristics for each scheme and obtained the optimal NT threshold to minimize the cost function.
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