Stochastic Convexity of Sums of I.I.D. Non-Negative Random Variables with Applications

Abstract

We present some monotonicity and convexity properties for the sequence of partial sums associated with a sequence of non- negative independent identically distributed random variables. These results are applied to a system of parallel queues with Bernoulli routing, and are useful in establishing a performance comparison between two scheduling strategies in multi-processor systems.