Abstract
In this paper, we present analysis for an M/M/R/N queueing systemwith balking, reneging and server breakdowns. The server is subjectto breakdowns with different Poisson breakdown rates $\alpha_0 $ and$\alpha$ for the empty period of the system and the nonempty periodof the system, respectively. When the server breaks down, it will berepaired immediately by a repair facility attended by $R$ repairmen.The repair times of the servers are assumed to follow a negativeexponential distribution with different repair rates $\beta_0$ and$\beta$ corresponding to whether the server breaks down in the emptyperiod of the system and the nonempty period of the system. We studynot only some queueing problems of the system, but also somereliability problems of the servers. By using the partitioned blockmatrix method, we solved the steady-state probability equationsiteratively and derived the steady-state probabilities in a matrixform. Some performance measures of queueing and reliability areobtained. A cost model is developed to determine the optimum numberof servers while the system availability is maintained at a certainlevel. The cost analysis is also investigated by numerical results.
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