Abstract

this paper, we will give a short review of Amdahl's law, and order statistics, and provide some examples of what realistic speedups to expect. In particular, we will look at Uniform, Exponential, and Power-tail distributions in detail. Then we will examine the much more difficult problem where the number of tasks exceeds the number of processors. In this case the tasks must queue up for service. This is equivalent to Mean time to drain of a G/C queue with no new arrivals, and in Reliability Theory, to Mean time to failure, with hot and cold backup. We will also present some examples of this. We also give a description of how to treat jobs where the tasks come from different distributions, and show how longest task time can be computed if the distributions are all exponential (but with different parameters). In this case, if k exceeds C,

Citations