Infinite capacity multi-server queue with second optional service channel

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

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish
Article number012115
JournalJournal of Physics: Conference Series
Issue number1
StatePublished - 1 Jan 2013
Event1st International Conference on Mathematical Modelling in Physical Sciences, IC-MSQUARE 2012 - Budapest, Hungary
Duration: 3 Sep 20127 Sep 2012


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