Analysis of queuing system with multiple working vacation
1.School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing 100876, China; 2.Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
Abstract：The working vacation queuing system with negative customers and vacation interruption was considered. The server works with low service rate rather than completely stops during vacation period, and this kind of incomplete vacation strategy is called working vacation. Because the real life queuing model might meet many interference factors, a negative customers queuing model was proposed. In the system, customers are either positive or negative. Negative customers remove positive customers one by one only at the end of line if there is positive customer. When a negative customer arrives, if there is no positive customer in system, the negative customer will disappear. Negative customers do not accept service. Another vacation policy of vacation interruption was introduced. By quasi birth and death process and matrixgeometric solution method, the stationary queue length was obtained. The stochastic decomposition of queue length in stationary state was proved to achieve the distributions for additional queue length. According to numerical examples, the proposed model can represent some practical problems reasonably.
2014, Vol. 35 
