M/G/ oo with Batch Arrivals

Abstract

Let po(n) be the distribution of the number N(oo) in the system at ergodicity for systems with an infinite number of servers, batch arrivals with general batch size distribution and general holding times. This distribution is of impotance to a variety of studies in congestion theory, inventory theory and storage systems. To obtain this distribution, a more general problem is addressed . In this problem, each epoch of a Poisson process gives rise to an independent stochastic function on the lattice of integers, which may be viewed as a stochastic impulse response. A continuum analogue to the lattice process is also provided.