A new approach for analyzing the M/M/1 queue with multiple working vacations
ZHANG Hong-bo1, ZHENG Qun-zhen1, SHI Ding-hua2
1. School of Mathematics and Statistics, Henan Institute of Education, Zhengzhou 450046, China
2. College of Sciences, Shanghai University, Shanghai, 200444, China
Abstract A new approach to model the M/M/1 queue with multiple working vacations is provided. By the GI/M/1 type Markov process and matrix analytic method, the explicit expression for the stationary queue length distribution is given firstly. Furthermore, the probability of the exact number of vacations that the sever has taken is also obtained. The more accurate descriptions for the status of the server are new results for the queue model.
ZHANG Hong-bo, ZHENG Qun-zhen, SHI Ding-hua. A new approach for analyzing the M/M/1 queue with multiple working vacations. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 50-56.
