Repairable M/G/1 Queuing System With Variable Service Speed

Lots have been done concerning repairable M/G/1 queuing systems and many important results have been gotten .In this paper we make a further research about this system. By setting a N-threshold in the queuing we considered repairable M/G(M/G)/1 queuing systems with two service speeds changing according the number of the customers in the system. We separately make a particular deep discussion to different disciplines of the service speed change. In the chapter two we discussed that the server would first use speed-1 to serve customers when the system entered the busy state from the empty state, but when the server found the number of customers in the system exceeded the thresh-N during serving, after finishing the service of current customer it would use speed-2 to serve the next customer till there is no customer. By the method of supplementary variable, L-transition and constructing Vector Markov, we attained the distribution of the queue length, the distribution of wait-time, the distribution of stay-time, the utility and etc. In the last part of this chapter, we discussed the optimal N* for thresh N which minimizing the cost function and we illustrate the cost function behaves for various parameter selections by a numerical study. In the chapter 3, we discussed the repairable M/G(M/G)/1 queuing systems whose discipline of speed change is that if the number exceeds the threshold N at the moment of a customer leaving the system the speed-2 should be used to serve the next customer otherwise the speed-1 should be used. In the chapter 4, we make an extension to the model of the chapter-2. The service speed change is instant, that is say, during the service using speed-1 to serve, if the number exceeds the threshold N, then the server should immediately use speed-2 not speed-1 to serve current customer and the next till entered the empty state. We especially point out that the classical M/G/1 queuing model and the M/G/1 queuing with N-policy are the particular cases of model discussed in chapter-4.