Characterizing The Load of A Single-Server System

The load of a computer is an important metric and is useful in many applications, such as balancing load across heterogeneous computers. In this paper, a new metric for characterizing the load of a uniprocessor computer is studied. This metric is defined as a ratio of the average waiting time experienced by computing jobs to the average idle time of the processor. The definition of the new load metric is based on two important observations: 1) the average idle time between serving consecutive computing tasks shrinks as the load becomes heavier; 2) the average waiting time experienced by computing jobs increases as the load becomes heavier. The new load metric aims to being able to compare different load status of a single-server system— the typical abstraction of a uniprocessor computer. The validity of comparing two different load status using the new load metric is subject to the satisfaction of certain conditions. These conditions are that relations of stochastic ordering need to be satisfied between the two processes of physical observations under different load status, e.g. the process of idle time and the processes of waiting time. When these conditions are not fully satisfied, the new load metric only serves as the firstmoment approximation to the status of operations of a single-server system. Numerical analysis on the effectiveness of the new load metric has been conducted by simulating operations of a single-server system under different types of job arrivals, the new load metric has been demonstrated to have the ability of characterizing the status of operations of the system, and the limitations on its ability have also been demonstrated. The ability of the new load metric in characterizing different load status is also compared to the ability of the traditional load metric— the average utilization, by comparing their effectiveness on serving as job assignment criteria for balancing load across multiple uni-processor systems with different service capabilities. The preliminary results suggest that the new load metric serves balancing the load more evenly across multiple systems than the average utilization. Jun Liu Computer Science Department University of North Dakota Grand Forks, ND 58202 [email protected]