Am. Makowski et Tk. Philips, STOCHASTIC CONVEXITY OF SUMS OF IID NONNEGATIVE RANDOM-VARIABLES WITHAPPLICATIONS, Journal of Applied Probability, 29(1), 1992, pp. 156-167
We present some monotonicity and convexity properties for the sequence
of partial sums associated with a sequence of non-negative independen
t 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 strate
gies in multiprocessor systems.