Retrial Queue with Threshold Recovery, Geometric Arrivals and Finite Capacity

The present investigation deals with the performance prediction of finite Markovian retrial queues with unreliable server. The arrivals of the customers follow geometric distribution while the service pattern follows exponential distribution. The customers are served in two stages i.e. first essential service (FES) which is compulsory for all the arriving customers and second optional service (SOS) which depends on the customer’s demand. The customer occupies the server if it is idle, otherwise he is forced to join the orbit and retry for the service later with the retrial rateθ . The server is unreliable and can breakdown during any stage of service. The broken down server is sent for repair and after repair it becomes as good as before failure. The repair process follows threshold recovery according to which the repair starts when a minimum number of customers say L (≥1) has been accumulated in the system. Various performance measures like expected queue length, availability, throughput etc. have been obtained in terms of transient probabilities. Furthermore, sensitivity analysis has been done to examine the effect of different parameters on various performance indices.