Abstract
The matrix-geometric work of Neuts could be viewed as a matrix variant of M/M/1. A 2 × 2 matrix counterpart of Neuts for M/M/∞ is introduced, the stability conditions are identified, and the ergodic solution is solved analytically in terms of the ten parameters that define it. For several cases of interest, system properties can be found from simple analytical expressions or after easy numerical evaluation of Kummer functions. When the matrix of service rates is singular, a qualitatively different solution is derived. Applications to telecommunications include some retrial models and an M/M/∞ queue with Markov-modulated input.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference18 articles.
1. On the fundamental problem of telephone traffic theory and the influence of repeated calls;Cohen;Philips Telecomm. Rev.,1957
2. Jonin G. L. and Sedol J. J. (1970b) Telephone systems with repeated calls. Proc. 6th Internat. Telecommunication Congress , pp. 435/1–435/5.
3. Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts
Cited by
34 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