TY - JOUR

T1 - Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns

AU - Yang, Dong Yuh

AU - Wu, Chia-Huang

PY - 2015/1/1

Y1 - 2015/1/1

N2 - This paper investigates the N-policy M/M/1 queueing system with working vacation and server breakdowns. As soon as the system becomes empty, the server begins a working vacation. The server works at a lower service rate rather than completely stopping service during a vacation period. The server may break down with different breakdown rates during the idle, working vacation, and normal busy periods. It is assumed that service times, vacation times, and repair times are all exponentially distributed. We analyze this queueing model as a quasi-birth-death process. Furthermore, the equilibrium condition of the system is derived for the steady state. Using the matrix-geometric method, we find the matrix-form expressions for the stationary probability distribution of the number of customers in the system and system performance measures. The expected cost function per unit time is constructed to determine the optimal values of the system decision variables, including the threshold N and mean service rates. We employ the particle swarm optimization algorithm to solve the optimization problem. Finally, numerical results are provided, and an application example is given to demonstrate the applicability of the queueing model.

AB - This paper investigates the N-policy M/M/1 queueing system with working vacation and server breakdowns. As soon as the system becomes empty, the server begins a working vacation. The server works at a lower service rate rather than completely stopping service during a vacation period. The server may break down with different breakdown rates during the idle, working vacation, and normal busy periods. It is assumed that service times, vacation times, and repair times are all exponentially distributed. We analyze this queueing model as a quasi-birth-death process. Furthermore, the equilibrium condition of the system is derived for the steady state. Using the matrix-geometric method, we find the matrix-form expressions for the stationary probability distribution of the number of customers in the system and system performance measures. The expected cost function per unit time is constructed to determine the optimal values of the system decision variables, including the threshold N and mean service rates. We employ the particle swarm optimization algorithm to solve the optimization problem. Finally, numerical results are provided, and an application example is given to demonstrate the applicability of the queueing model.

KW - Matrix-geometric method

KW - N-policy

KW - Particle swarm optimization

KW - Quasi-birth-death process

KW - Working vacation

UR - http://www.scopus.com/inward/record.url?scp=84923226578&partnerID=8YFLogxK

U2 - 10.1016/j.cie.2015.01.017

DO - 10.1016/j.cie.2015.01.017

M3 - Article

AN - SCOPUS:84923226578

SN - 0360-8352

VL - 82

SP - 151

EP - 158

JO - Computers and Industrial Engineering

JF - Computers and Industrial Engineering

ER -