On a retrial queue with abandoned customers and multi-optional vacations. Issue 3 (3rd July 2018) - Gao, Shan; Liu, Bin; Wang, Jinting
Abstract: This paper treats an M/G/1 retrial queue with abandoned customers and multi-optional vacations. If the server is found busy upon a new arrival, the customer being served could be abandoned by the server with some probability. Once the system is empty after a service completion, the server takes the first essential vacation (FEV) immediately. At the end of the FEV, if the system is still empty, the server will take another optional vacation depending on the server's choice; whereas, if the server finds a nonempty system, it will wait for a new arrival or a repeated customer from the orbit. The sufficient and necessary condition for the system to be stable is provided by using the embedded Markov chain technique. Moreover, the steady-state analysis is carried out via the supplementary variable method. The Laplace-Stieltjes transform of the sojourn time distribution is also provided. Finally, numerical examples with cost optimization analysis are given.