M/G/∞ with batch arrivals

  • Authors:

  • J Keilson;A Seidmann

  • Affiliations:

  • GTE Laboratories and Massachusetts Institute of Technology, Cambridge, MA, USA;University of Rochester, Rochester, NY, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 1988

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Abstract

Let p"~(n) be the distribution of the number N(~) 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 importance to a variety of studies in congestion theory, inventory 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 stochastic impulse response. A continuum analogue to the lattice process is also provided.