Institution: Stanford University, Department of Computer Science

Title: Balanced computer systems.

Author: Price, Thomas G.

Date: April 1974

Abstract: We use the central server model to extend Buzen's results on balance and bottlenecks. We develop two measures which appear to be useful for evaluating and improving computer system performance. The first measure, called the balance index, is useful for balancing requests to the peripheral processors. The second quantity, called the sensitivity index, indicates which processing rates have the most effect on overall system performance. We define the capacity of a central server model as the maximum throughput as we vary the peripheral processor probabilities. We show that the reciprocal of the CPU utilization is a convex function of the peripheral processor probabilities and that a necessary and sufficient condition for the peripheral processor probabilities to achieve capacity is that the balance indexes are equal for all peripheral processors. We give a method to calculate capacity using classical optimization techniques. Finally, we consider the problem of balancing the processing rates of the processors. Two conditions for "balance" are derived. The first condition maximizes our uncertainty about the next state of the system. This condition has several desirable properties concerning throughput, utilizations, overlap, and resistance to changes in job mix. The second condition is based on obtaining the most throughput for a given cost.

http://i.stanford.edu/pub/cstr/reports/cs/tr/74/435/CS-TR-74-435.pdf