G-Networks: A Survey of Results, a Solver and an Application

Abstract

In this paper, we first present a brief survey of the main theoretical results providing product forms for networks of queues with positive and negative customers and with signals (G-networks). Then we present a graphical tool for solving a G-network model in steady state, i.e. for finding the steady-state probabilities of the number of positive customers in a G-network. The user will draw a G-network on the screen and input the parameters of each queue (mean service time, arrival rates, routing probabilities, etc.). Then the solver will provide the user with the solution of the system of non-linear traffic equations, and the stationary distribution of queue length, and performance measures such as sojourn times, mean number of customers in the system. Finally we show how these theoretical results and the tool we describe can be used to obtain an analytical solution to a problem which until now has resisted to such a treatment: the performance evaluation of receiver initiated load balancing algorithms in distributed systems.