The Queuing Systems With Repairabie Deteriorate Service Station

In recent years, repairable queuing system has been widespread concern and achieved certain results, the service station repair non new repairable queuing system is an extension of the repairable queueing system. In the modern society of science and technology advance quickly, the service system is intend to provide customers with convenient and efficient services and the best economic benefit and service station repair non new should be considered a service failure happens when the maintenance cost, the replacement of new service cost and maintenance service station service rate and fault rate change caused a series of changes. This paper is the simulation of these factors, to provide a scientific and effective basis for the queuing system in practical application.First, we consider the system of M/M/1 queue of ‘not as good as new’ with repairable service station. Assuming that the service station after repair is ‘not as good as new’ and the life distribution obeys the exponential one, by using the Markov process method and the matrix-geometric solution method, Some performance measures of the system such as the expected number of the customers in the system or in the queue and numerical results are also obtained. and by MATLAB calculation, paper gives some numerical analysis for the results.Second, we investigate an M/M/2/N queue system of ‘not as good as new’ with repairable service station. In the same model, Using quasi birth and death process and matrix-geometric solution method derive the equilibrium condition of the system and the steady-state probability vectors. Furthermore, we get stationary indices, such as steady-state availability and steady-state fault frequency, and by MATLAB calculation,paper gives some numerical analysis for the results.Finally, we deals with an M/M/1 queue, and is controlled by Bernoulli, which each customer to receive a service with a certain probability(feedback probability) ? from the new row in the tail waiting for another service or leaving the system with probability1-? and no longer back. Using QBD process and matrix-geometric solution, we obtain the steady-state distributions, for the number of customer in system and prove the result of stochastic decomposition of the queue length and gain the mean of the system size,and byMATLAB calculation, paper gives some numerical analysis for the results.