An exact solution to a class of queueing systems with multipurpose counters

This paper considers a queueing system with a multipurpose counter. The service mechanism consists of three stages, I, II and III; performed in sequence by two servers. Stage I and III of service are performed by a single server and therefore, when stage I customers are served, stage III customers are blocked and vice versa. Exact numerical solutions are obtained for the finite waiting room case using a Markovian network model and various measures of performance such as average system time, average number of customers in the system, blocking probabilities etc, are evaluated.