M/M/c balking retrial queue with vacation. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Ke, Jau-Chuan; Chang, Fu-Min; Liu, Tzu-Hsin
• Is Part Of: Quality technology & quantitative management. Volume 16:Issue 1(2019)
• Page Start: 54
• Page End: 66
• Publication Date: 2019-01-02
• Subjects: Retrial queueing -- vacation -- balking -- matrix-analytical method -- optimization; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2017.1365280
• Languages: English
• ISSNs: 1684-3703

Abstract

Abstract: This paper deals with an M/M/c balking retrial queue with vacation. Both single and multiple vacation policies are analysed. This system is investigated as a quasi-birth-and-death process. Using the matrix-geometric method, we derive the useful formulae for computing the rate matrix and stationary probabilities. Various system performance measures are further developed in the matrix-form expressions. We construct a cost function to determine the optimum value of servers and the optimum mean service rate subject to the stability condition at minimum cost. Quasi-Newton method, Nelder–Mead simplex method and simulated annealing method are employed to perform the optimization tasks. Under optimum operating conditions, we provide the numerical results for a comparison of vacation policies. An application example is given to illustrate the system's potential applicability.