Departure Processes from GI/GI/∞ and GI/GI/c/c with Bursty Arrivals

Abstract

When the random variable has a completely monotone density function, we call it bursty (BRST) random variable. At first, we prove that the entropy of inter-arrival time is smaller than or equal to the entropy of inter-departure time in an infinite-server system GI/GI/∞ having general renewal arrivals. On the basis of that result, we prove that a BRST/GI/∞ having bursty arrivals and the associated loss system BRST/GI/c/c have the following paradoxical behavior: In the BRST/GI/∞, the stationary number of customers as well as the inter-departure time become stochastically less variable, as the service time becomes stochastically more variable. Also for the loss system BRST/GI/c/c, the blocking probability decreases and the inter-departure time becomes stochastically less variable, as the service time becomes stochastically more variable.