On Optimization of a Coxian Queueing Model with Two Phases
Applied and Computational Mathematics
Volume 3, Issue 2, April 2014, Pages: 43-47
Received: Jan. 30, 2014;
Published: Mar. 20, 2014
Views 3548 Downloads 196
Vedat Sağlam, Department of Statistics, Faculty of Science and Arts, OndokuzMayıs University, Kurupelit, Turkey
Merve Uğurlu, Department of Statistics, Faculty of Science and Arts, OndokuzMayıs University, Kurupelit, Turkey
Erdinç Yücesoy, Department of Statistics, Faculty of Science and Arts, OndokuzMayıs University, Kurupelit, Turkey
Müjgan Zobu, Department of Statistics, Faculty of Science and Arts, Amasya University, Amasya, Turkey
Murat Sağır, Department of Statistics, Faculty of Science and Arts, OndokuzMayıs University, Kurupelit, Turkey
Follow on us
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
Coxian Model, Differential Equations, Loss Probability, Limiting Distribution, Optimal Ordering
To cite this article
On Optimization of a Coxian Queueing Model with Two Phases, Applied and Computational Mathematics.
Vol. 3, No. 2,
2014, pp. 43-47.
D.R. Cox, "A use of complex probabilities in the theory of stochastic processes. Proc. Camb. Phil. Soc.,"313-19, 1955.
W. J. Stewart, "Probability, Markov Chains, Queues, Simulation, New Jersey,"2009.
F.Neuts, "Probability distributions of phase type, in Liber Amicorum Professor Emeritus H.Florin, Department of Mathematics", University of Louvain, Louvain, Belgium 173-206.
U. N. Bhat, "An Introduction to Queuing Theory," Boston, 2008.
R.Marie, "Calculating Equilibrim Probabilities for (((λ(n))⁄C_k )⁄1)⁄N Queues," ACM Sigmetrics Performance Evaluation Review, Vol. 9, No.2, 1980.
M. Zobu, V. Sağlam, M. Sağır, E. Yücesoy and T. Zaman"The Simulation and Minimization of Loss Probability in theTandem Queueing with Two Heterogeneous Channels," Mathematical Problems in Engineering, vol. 2013,Article ID 529010, 4, pages, 2013.
M.Zobu "Using Sequential Analysis for Hypothesis Tests in The Phase-Type Distribution Queueing Systems," Ph.D. Thesis, OndokuzMayis University, Samsun, Turkey, 2013.
D. Gross, C.M. Harris, "Fundamentals of Queuing Theory," Third Edition, John Wiley & Sons, New York, 1998.