Abstract:

An M／M／1／N queuing system was considered with negative  customers and a single working vacation. The server works at a lower rate rather  than completel y stops service during the vacation period. Negative customers remove positive customers only one by one at the head (if present). When a negative customer arrives, if the system is empty, it will disappear. Negative customers need no services.  The matrix form solution of the steadystate probability is derive d  by the Markfov process method and the matrix solution method. Some performance  measures of the system such as the expected number of customers the system or  in the queue and the loss probability of the customer are also presented. Finally the effects of the parameters of the system are investigated, such as the va cati on service rate μ_vand the vacation rate θon the expected waiting  queue length and the loss probability of customers by numerical examples.

Key words: queuing system; steady-state probability; matrix solution method; negative customers; single working vacation