M/M/c balking retrial queue with vacation

• Published in: Quality technology & quantitative management Vol. 16; no. 1; pp. 54 - 66
• Main Authors: Ke, Jau-Chuan, Chang, Fu-Min, Liu, Tzu-Hsin
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 02.01.2019
• Subjects: balking; matrix-analytical method; optimization; Retrial queueing; vacation
• ISSN: 1684-3703; 1684-3703
• DOI: 10.1080/16843703.2017.1365280

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.