一个不同到达率及负顾客的离散工作休假排队

doi:10.6040/j.issn.1671-9352.0.2014.328

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 1-6.doi: 10.6040/j.issn.1671-9352.0.2014.328

A discrete time working vacations queuing system with different arrival rates and negative customers

LIU Zai-ming, YU Sen-lin

School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China

Received:2014-07-10 Revised:2015-01-06 Online:2015-06-20 Published:2015-07-31

Abstract

Abstract: A multiple working vacations Geo/Geo/1 queuing system with negative customers was proposed and studied in this paper. For this model, the positive customers have different arrival rates in the normal busy period and working vacation period. The quantities including the transition probability matrix of the queuing system, the equilibrium distribution of the queue length, the mean number of customers, the stochastic decomposition and the busy period analysis were obtained by using the matrix-analytical method of quasi birth-death chains. The cost function and two numerical examples were given to provide a basis for optimal design and illustrate the impact of parameters on the queue length.

Key words: matrix-geometric solution, different arrival rates, working vacations, negative customers

CLC Number:

O226

LIU Zai-ming, YU Sen-lin. A discrete time working vacations queuing system with different arrival rates and negative customers[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 1-6.

References

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