Repairable Retrial Queues Under Individual Removal Policy

Queuing 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 modem 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 negative customer is a kind of particular customer,which can be viewed as an improper manipulation or disaster of system and may kill the positive customer in the queue.In the retrial queuing system,the combination of the negative customer and queuing system is a new research area,which study customers' retrial behavior as well as signal interference in telecommunication networks and the influence of virus in computer networks.In addition,retrial queuing system with priority subscribers has been attached great importance to the researchers.In the telecommunication system,electrical and computer systems,some customers have to obtain priority service.Therefore,the study of this kind of queuing system is based on important applied background.According to practical background,this paper establishes and resolves three retrial queue models,that is,repairable M^k/G/1 batch arrival retrial queue with negative customers,an M/G/1 retrial queue with second optional service and negative customers,and a repairable M₁,M₂ /G₁,G₂ /1 retrial queues with priority customers and Negative arrivals.Furthermore,we analyze two kinds of server breakdowns:one is the normal breakdowns,that is the server fails at an fixed rate;The other is abnormal breakdowns,that is,the server fails immediately after an arrival of negative customer 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,failure frequency and the reliability function of the system.