An SMDP model for a multiclass multi-server queueing control problem considering conversion times

¹ Department of Industrial Engineering, School of Mechanical Engineering, Dongguan University of Technology, Songshan Lake District, Dongguan 523808, Guangdong Province, China.
stephen1998@gmail.com; yanxh@dgut.edu.cn; lishuai@dgut.edu.cn
² Department of Industrial Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China.
na-li03@sjtu.edu.cn
³ School of Mechanical Engineering, Dongguan University of Technology, Songshan Lake District, Dongguan 523808, Guangdong Province, P.R. China.
guojw@dgut.edu.cn

Received: 29 September 2013
Accepted: 27 March 2014

Abstract

We address a queueing control problem considering service times and conversion times following normal distributions. We formulate the multi-server queueing control problem by constructing a semi-Markov decision process (SMDP) model. The mechanism of state transitions is developed through mathematical derivation of the transition probabilities and transition times. We also study the property of the queueing control system and show that optimizing the objective function of the addressed queueing control problem is equivalent to maximizing the time-average reward.