Search

Abstract: This paper considers an infinite buffer queueing system in which servers follow a multi-threshold vacation policy. With such a policy, at a service completion instant, if the number of customers in the system is less than a prefixed threshold value, part of servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the vacation completion instant, they return to the system for serving the customers. Some practical production and inventory systems or call centers could be modeled as this Markovian queue with a multi-threshold vacation policy. Using the Markovian process model, we obtain the exact closed-form expression of rate matrix and the stationary distribution of the number of customers in the system. A cost model is developed to search the joint optimal values of the thresholds of vacation policy and service rate of each server, which minimizes the long-term average cost. Some numerical results are presented to illustrate the optimization procedures. [Copyright &y& Elsevier]

Abstract: This paper studies the vacation policy of an M/G/1 queueing system with an unreliable server and startup. After all the customers are served in the queue exhaustively, the server deactivates and takes at most J vacations of constant time length T repeatedly until at least one customer is found waiting in the queue upon returning from a vacation. If at least one customer presents in the system when the server returns from a vacation, then the server reactivates and requires a startup time before providing the service. On the other hand, if no customers arrive by the end of the J th vacation, the server remains dormant in the system until at least one customer arrives. We will call the policy modified T vacation policy. Furthermore, it is assumed that the server breaks down according to a Poisson process and his repair time has a general distribution. We analyze the system characteristics for this model. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the optimal control of a batch arrival, bulk service queueing system under N-policy. If the number of customers in the system at a service completion is larger than some integer r, then the server starts processing a group of r customers. If, on the other hand, it is smaller than r, then the server idles and waits for the line to grow up to some integer N, (N ≥ r). System characteristics are obtained by means of the embedded Markov chain and semiregenerative techniques, then the expected total cost per unit of time is developed for this model. Finally, a search procedure is presented to determine the optimal thresholds r and N that yield the minimum cost. [Copyright &y& Elsevier]