Computation and optimization of a working breakdown queue with second optional service. (3rd April 2018)

• Record Type: Journal Article
• Authors: Yang, Dong-Yuh; Chen, Yi-Hsuan
• Is Part Of: Journal of industrial and production engineering. Volume 35:Number 3(2018)
• Page Start: 181
• Page End: 188
• Publication Date: 2018-04-03
• Subjects: Genetic algorithm -- matrix-geometric method -- optimization -- second optional service; Industrial engineering -- Periodicals; Production engineering -- Periodicals; 620
• DOI: 10.1080/21681015.2018.1439113
• Languages: English
• ISSNs: 2168-1015

Abstract

Abstract: This paper considers an M/M/1 queue with second optional service, in which the server is subject to working breakdowns and repairs. All arriving customers require the first essential service, whereas only a portion of them require a second optional service. In case where the server may break down while providing the first (essential) or second (optional) service, the server continues operation at a reduced level rather than ceasing service entirely. The stability condition for this queue is derived in explicit form. The matrix-geometric method is used to compute the stationary probability distribution of the system size and various system performance measures. The genetic algorithm is applied to a cost optimization problem with the aim of optimizing service rates by minimizing the expected cost per unit time. Finally, a numerical example is presented for illustrative purposes.