Multiple class G-Networks

ABSTRACT Queueing network theory and applications is a branch of operations research of direct relevance to computer and communication network system performance. The search for new classes of queueing networks having analytical solutions has been an ongoing subject of research for close to a century. Recently a new class of queueing networks with “positive and negative customers” has been introduced in (Gelenbe 1991) and shown to have product form. In the present paper we consider a family of such networks with a single class of negative customers and multiple class positive customers. We call these networks “generalized (G) networks”. We show that when they have exponential service times, Poisson external customer arrivals, Markovian customer movements between queues, and three types of service center (FIFO, Processor Sharing, and LCFS with Preemptive Resume Priority), they possess a simple product form solution in stationary state. Such systems can be used to model neural networks (as in (Gelenbe and Batty in this book), as well as (Gelenbe 1989, 1990).