On Optimization of a Coxian Queueing Model with Two Phases

Abstract

In this study we have obtained stochastic equation systems of a Coxian queueing model with two phases where arrival stream of this model is according to the exponential distribution with λ parameter. The service time of any customer at server i (i=1,2) is exponential with parameter μ_i. In addition we have obtained state probabilities of this queueing model at any given t moment.Furthermore performance measures of this queueing system are calculated. Various queueing systems are found for some values of α probability and service parameters: if α=1and µ_1=µ_2taken then M/E_2/1/ 0 queueing model is obtained, for α=1it is shown that service time of a customer is according to hypoexponential, if α=0 is taken we have M/ M/1/ 0 queueing system. Lately,an application of this queueing model is done. The optimal value of the mean customer number in the system is found. Finally, optimal ordering according to the loss probability is obtained by changing the service parameters .A numerical example is given on the subject