M/G/∞ with batch arrivals

• Published in: Operations research letters Vol. 7; no. 5; pp. 219 - 222
• Main Authors: Keilson, J, Seidmann, A
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 1988; Elsevier
• Subjects: Applied sciences; batch arrivals; Exact sciences and technology; M/G; Operational research and scientific management; Operational research. Management science; queues; Queuing theory. Traffic theory; batch arrivals; M/G; queues; Storage; Batch mode; Arrival process; Probabilistic model; Poisson distribution; Queue; Traffic congestion
• ISSN: 0167-6377; 1872-7468
• DOI: 10.1016/0167-6377(88)90034-X

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.