Open Journal of Optimization > Vol.4 No.3, September 2015

Vedat Sağlam¹, Murat Sağır¹, Erdinç Yücesoy¹, Müjgan Zobu²

¹Department of Statistics, Ondokuz May?s University, Samsun, Turkey.
²Department of Statistics, Amasya University, Amasya, Turkey.

We analyze a Coxian stochastic queueing model with three phases. The Kolmogorov equations of this model are constructed, and limit probabilities and the stationary probabilities of customer numbers in the system are found. The performance measures of this model are obtained and in addition the optimal order of service parameters is given with a theorem by obtaining the loss probabilities of customers in the system. That is, putting the greatest service parameter at first phase and the second greatest service parameter at second phase and the smallest service parameter at third phase makes the loss probability and means waiting time minimum. We also give the loss probability in terms of mean waiting time in the system. is the transition probability from j-th phase to  phase . In this manner while and this system turns into queueing model and while the system turns into Cox(2) queueing model. In addition, loss probabilities are graphically given in a 3D graph for corresponding system parameters and phase transient probabilities. Finally it is shown with a numeric example that this theorem holds.

Stochastic Coxian Queueing Model, Loss Probability, Limiting Distribution, Optimization, Kolmogorov Equations

Sağlam, V. , Sağır, M. , Yücesoy, E. and Zobu, M. (2015) On Optimal Ordering of Service Parameters of a Coxian Queueing Model with Three Phases. Open Journal of Optimization, 4, 61-68. doi: 10.4236/ojop.2015.43008.