The Queuing System With The Impatient Customers And Working Vacation

In 2002, Servi and Finn introduced working vacation policy, which plays an important role in the performance analysis of gateway router in optical networks. In this paper, we consider the queuing system with impatient customers and working vacations. The server takes working vacation once the busy period ends and the server works at a lower rate rather than completely stops and the customers who are waiting for service during the working vacation maybe leave the system with impatience. We derive some performance measures of the system about the queuing model with impatient customers and working vacations . The main contents are as follows:Firstly, we study the M/M/1 queuing model with impatient customers and single working vacation . We obain the steady-state balance equations by the Markov process theory. Some performance measures of the system such as the mean queue sizes in the busy period and the working vacation period were derived by balance equations and probability generating functions. The effects of the two service rates on the system performance measures are investigated by numerical experiment.Secondly, we study the M/M/1 queuing model with impatient customers and multiple working vacation . Some performance measures of the system such as the mean queue sizes in the busy period and the working vacation period are derived by balance equations and probability generating functions. The effects of the two service rates on the system performance measures are investigated by numerical experiment.Finally, we study the M/M/C queuing model with impatient customers and multiple working vacation . We obain the steady-state balance equations by the Markov process theory. When C=2 some performance measures of the system such as the mean queue sizes in the busy period and the working vacation period are derived by balance equations and probability generating functions.