Measures of the Potential for Load Sharing in Distributed Computing Systems

In this paper we are concerned with the problem of determining the potential for load balancing in a distributed computing system. We define a precise measure, called the number of sharable jobs, of this potential in terms of the number of jobs that can usefully be transferred across sites in the system. Properties of this measure are derived, including a general formula for its probability distribution, independent of any particular queuing discipline. A normalized version of the number of sharable jobs, called the job sharing coefficient , is defined. From the general formula, the probability distribution of the number of sharable jobs is computed for three important queuing models and exact expressions are derived in two cases. For queuing models in which an exact expression for the probability distribution of the number of sharable jobs is difficult to obtain, two methods are presented for numerical computation of this distribution. The job sharing coefficient is plotted against traffic intensity for various values of system parameters. Both of these measures are shown to be useful analytic tools for understanding the characteristics of load sharing in distributed systems. They can also aid in the design of such systems.