The Impact of Class Clustering on a System with a Global FCFS Service Discipline

This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server with exponential service times. The system adopts a "global FCFS" service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. "Class clustering", i.e., the fact that customers of any given type may (or may not) have a tendency to "arrive back-to-back", is a concept that we believe is often neglected in literature. As it is clear that customers of different types hinder each other more as they tend to arrive in the system more clustered according to class, the major aim of this paper is to estimate the impact of the degree of class clustering on the system performance. In this paper both classes of customers have an own "cluster parameter". The motivation of our work are systems where this kind of blocking is encountered, such as input-queueing network switches, security checkpoints or road splits.