Abstract
The paper reviews various aspects, mostly mathematical, concerning the output or departure process of a general queueing system G/G/s/N with general arrival process, mutually independent service times, s servers (1 ≦ s ≦ ∞), and waiting room of size N (0 ≦ N ≦ ∞), subject to the assumption of being in a stable stationary condition. Known explicit results for the distribution of the stationary inter-departure intervals {Dn} for both infinite and finite-server systems are given, with some discussion on the use of reversibility in Markovian systems. Some detailed results for certain modified single-server M/G/1 systems are also available. Most of the known second-order properties of {Dn} depend on knowing that the system has either Poisson arrivals or exponential service times. The related stationary point process for which {Dn} is the stationary sequence of the corresponding Palm–Khinchin distribution is introduced and some of its second-order properties described. The final topic discussed concerns identifiability, and questions of characterizations of queueing systems in terms of the output process being a renewal process, or uncorrelated, or infinitely divisible.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference79 articles.
1. References added in proof but not mentioned in the text.
2. On some properties of simply connected dependent streams (In Russian);Yarovitskii;Ukrain. Mat. Z.,1962
3. Yarovitskii N. V. (1961) On the outgoing flow of a unilinear service system with losses (Ukrainian). Dop. Akad. Nauk Ukrain. RSR 1961, 1251–1254.
4. The departure process from the GI/G/1 Queue
5. Some applications of probability generating functionals to the study of input-output streams;Vere-Jones;J. R. Statist. Soc.,1968
Cited by
113 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献