A two-stage service policy for an M/G/1 queueing system

Abstract

Abstract We introduce the P M;˝ service policy, as a generalized two-stage service policy ofthe P M policy of Bae et al. (2002) for an M=G=1 queueing system. By using the levelcrossing theory and solving the corresponding integral equations, we obtain the explicitexpression for the stationary distribution of the workload in the system.Keywords: M=G=1 queue, P M;˝ service policy, stationary distribution. 1. Introduction Bae et al. (2002) introduced the P M service policy for an M=G=1 queueing system; whena customer arrives, the server starts to work with service speed 1, that is, the workload of theserver starts to decrease by one per unit time, until the workload in the system exceeds thethreshold >0. As soon as this occurs, the server increases his/her service speed to M1instantaneously, and the decrease in the workload becomes Mper unit time until the systembecomes empty. Under this policy, Bae et al. (2002) obtained the stationary distribution ofthe workload process. After assigning the corresponding costs, Kim et al. (2006) showed theexistence of the optimal service speed Mwhich minimizes the long-run average cost per unittime. Recently, Kim et al. (2011) derived the long-run average cost per unit time under theP