SINGLE LINE QUEUE WITH RECURRENT REPEATED DEMANDS

We analyze a model queueing system in which customers cannot be in con tinuous contact with the server, but must call in to request service. If the server is free, the customer enters service immediately, but if the server is occupied, the unsatisfied customer must break contact a nd reapply for service later. There are two types of customer present who may reapply. First transit customers who arrive from outside accor ding to a Poisson process and if they find the server busy they join a source of unsatisfied customers, called the orbit, who according to a n exponential distribution reapply for service till they find the serv er free and leave the system on completion of service. Secondly there are a number of recurrent customers present who reapply for service ac cording to a different exponential distribution and immediately go bac k in to the orbit after each completion of service. We assume a genera l service time distribution and calculate several characterstic quanti ties of the system for both the constant rate of reapplying for servic e and for the case when customers are discouraged and reduce their rat e of demand as more customers join the orbit.