Performance analysis of a queuing system with facilities requiring post-processing

This paper considers a queuing system in which a fixed number of identical facilities (servers) are employed one at a time for providing individual customer service at the single service station with unit capacity and each facility undergoes a post-processing after serving its own customer. Customers arrive in a Poisson process, and the customer service time and the facility post-processing time distributions are all exponential. For the queuing system, two different cases, the loss system (finite buffer capacity) and the delay system (infinite buffer capacity), will be analyzed separately to exploit their approximate computation algorithms for the associated long-run system state distributions. The algorithms are then tested for efficiency and effectiveness with various numerical problems.