Queuing System with Feedback and Reneging Due to Impatient Customers and Urgent Call

Abstract

This paper deals with queuing model having M-service channels in series in which feedback is permitted from each server of the model to all its previous service channels including the same server also. Reneging characteristics due to impatient behaviour of the customer and urgent call have been incorporated in the queue-model. Input process and service rates follow Poisson and exponential probability distributions respectively where the queue discipline is SIRO. After the description of the queue-model, we write its differential equations in transient form, reduce these equations independent of time and solve the reduced equations either by iterative method or by mathematical induction. Mean queue lengths are derived for infinite capacity when queue discipline is FIFO. This model finds its applications in administrative setups.