Analysis of an infinite multi-server queue with an optional service

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 a probability (1 - θ), or the completion of the FES may immediately require a SOS with a 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 simultaneously determine the optimal values of the number of servers and the two service rates at the minimal total expected cost per unit time. Quasi-Newton method and Particle Swarm Optimization (PSO) method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided from which several system performance measures are calculated based on the assumed numerical values of the system parameters.

Original languageEnglish
Pages (from-to)216-225
Number of pages10
JournalComputers and Industrial Engineering
Issue number2
StatePublished - 17 Apr 2013


  • First essential channel
  • Linear progressing algorithm
  • Particle Swarm Optimization
  • Quasi-Newton method
  • Second optional channel

Fingerprint Dive into the research topics of 'Analysis of an infinite multi-server queue with an optional service'. Together they form a unique fingerprint.

Cite this