Retrial Queues With Finite Source

Queueing systems based on customers' retrial behavior are stepped from the study of telephone service problems.Due to its reasonable assumptions as well as widely applied background in modern telecommunication networks,computer systems, telephone switching systems and supply chain management,retrial queuing systems have attracted the extensive attention of numerous experts and scholars in the recent twenty years.The finite source retrial queueing system is a kind of very important queuing system.It assumes that the source generating customers is finite.Every source generates a customer with a certain generating rate when it's free.The finite retrial queuing is especially suitable to model the star-like local area networks,telephone communicating networks and local area networks with non-persistent CSMA/CD protocol.Besides,the queuing models with server repairable are paid more and more attention on.Because in the reality,the server will have a breakdown after it have worked a certain time.It is common in communicating systems and telephone banking systems.If we combine the finite source retrial queue with server repairable, the model will be more challenging,and with more reality and applied backgrounds. The retrial queue models with second optional service appear in our daily life frequently,it draw people's attention widely recently.It's widely used in call center and telephone banking system.Because customers in these systems will probably request a extra service.According to practical background,this paper establishes and resolves two finite retrial queue models,that is,M/G/1//K finite source retrial queue with second optional service,M/G/1//K finite source retrial queue with server breakdowns and repairable. Using a supplementary variable method,we get some indexes for both queuing and reliability measures of interest,such as the mean queue length in retrial orbit, availability,waiting time,busy period and the reliability function of the system.