Infinite capacity multi-server queue with second optional service channel

Jau Chuan Ke*, Chia-Huang Wu, W.l. Pearn


研究成果: Conference article同行評審


This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with probability (1-θ), or at the completion of the FES may immediately require a SOS with probability θ (0 ≤ θ ≤ 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to determine the optimal values of the number of servers and the two service rates, simultaneously, at the minimal total expected cost per unit time. Quasi-Newton method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided in which several system performance measures are calculated based on assumed numerical values of the system parameters.

期刊Journal of Physics: Conference Series
出版狀態Published - 1 1月 2013
事件1st International Conference on Mathematical Modelling in Physical Sciences, IC-MSQUARE 2012 - Budapest, Hungary
持續時間: 3 9月 20127 9月 2012


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