Queue Of Server Breakdowns And Vacations With Balking And Reneging

The repairable queue and the vacation queue are extension and development of classical queuing theory and have widespread application in communications system ,management system and transportation system. the phenomena of the customers'balking and reneging offen happens in our real life. Thus, the study on the repairable queuing system and the vacation queuing system with balking and reneging has important theoretical significance and actual application value.In this paper, we consider the queuing models with server breakdowns and the phenomena of balking and reneging, as well as the model with vacation.Firstly, we investigate a finite waiting room repairable queuing system with balking, reneging and partial server breakdowns, in which there are two types servers ,one is completely reliable and another is unreliable. By Markov process method, we develop the steady-state probability equations, and obtain the simple and obvious iterative formulas of the steady-State probability vectors by using a method of blocking matrix. Then we obtain some performance measures of the system and make numerical analysis by using Matlab software.Secondly, we study a finite waiting room repairable queuing system with balking and reneging, in which two servers have different service rate, failure rate and repair rate. Using Markov process method, we develop the steady-state probability equations, and derive the iterative formulas of the steady-State probability vectors .we obtain some performance measures of the system and reliability indices of two unreliable servers.Finally, we study a finite waiting room vacation queuing system with balking and reneging, in which two servers have different service rate and carry on synchronous multiple vacations. By Markov process method, we develop the steady-state probability equations and derive matric solutions of the steady-state probability vectors. Meantime, by computing inverse matrices of some blocking matrices, we obtain the close-form precise expression of steady-state probability and some performance measures of the system. Furthermore, we give the precise close-form expressions of condition waiting time distribution and condition mean time of the arrival customers who finally accept service when two heterogeneous servers are busy.