Discrete-Time Geo(X)/G/1 Queue with Geometrically Working Vacations and Vacation Interruption

作者：Gao Shan^*; Yin Chuancun

来源：Quality Technology and Quantitative Management, 2013, 10(4): 423-442.

• Batch arrival
• discrete-time queue
• vacation interruption
• working vacation

This paper treats a discrete-time batch arrival queue with geometrically working vacations and vacation interruption. The main purpose of this paper is to present a performance analysis of this system. For this purpose, we first derive the probability generating PGF) of the stationary system length at the departure epochs based on the embedded Markov chain technique. Next, we present the stationary distributions of the system lengths as well as some performance measures at random epochs by using the supplementary variable method. Thirdly, still based on the supplementary variable method we give a distribution for the number of the customers at the beginning of a busy period and give a stochastic decomposition formula for the PGF of the stationary system length at the departure epochs. Additionally, we investigate the relation between our discrete-time system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on some crucial performance characteristics of the system.

• 出版日期2013-12
• 单位阜阳师范学院