Two Heterogeneous Servers Of Repairable Queuing System With Fixing Await And Customers Balking

Two-server queuing system is one of the simplest models in multi-sever queuing system. It has played great important role in manufactures and our actual life. This model becomes more concrete and practical, especially brings in some conditions. So it owns its application value and significance in some certain degree.The whole work based on M/M/2repairing queuing system, using a consistent theoretical basis-that is matrix geometric solution. But the innovation of this paper lies in fixing await, customer balking and choosing. It makes the model more practical and general. The model is thought to be a application of QBD process, the paper doesn’t say more about theoretical proof except normal return condition.In this paper, we first discuss two heterogeneous servers of M/(Em, M)/2repairable queuing system with fixing await and customer balking. We describe the model assumptions explicitly, give its state space, state transition matrix, show the infinitesimal generator, and prove its normal return condition. Then we calculate the steady distribution and index of the model by using matrix geometric solution of QBD process.Furthermore, by using the method of recursion, we extend Erlang distribution to Generalized Erlang distribution, Hyperexponential distribution and PH distribution. For extension models, we give the modification of matrix T, for this part, we don’t repeat again.At last, we do some numerical simulation via MATLAB, give the approximate solution of steady distribution. We also compare the4models of their sensitivity and some reasonable suggestions are given.