Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-03T08:42:13.941Z Has data issue: false hasContentIssue false

Fixed Point Approximations for Retrial Networks

Published online by Cambridge University Press:  27 July 2009

Glen K. Takahara
Affiliation:
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada K7L 3N6

Abstract

Fixed point approximations for blocking probabilities arising from a link independence assumption and a light retrial rate limit are derived for circuitswitched network models that incorporate caller retrials. This approximation is a generalization of the well-known reduced load approximation for loss networks, which retains much of the versatility of this approximation.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Brockmeyer, E., Halstrom, H.L., & Jensen, A. (1948). The life and works of A. K. Erlang. Copenhagen: Academy of Technical Sciences.Google Scholar
2.Burman, D.Y., Lehoczky, J.P., & Lim, Y. (1984). Insensitivity of blocking probabilities in a circuit switching network. Journal of Applied Probability 21: 850859.CrossRefGoogle Scholar
3.Cohen, J.W. (1957). Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommunication Review 18(2): 49100.Google Scholar
4.Falin, G.I. (1980). Switching systems with allowance for repeated calls. Problems of Information Transmission 16: 145151.Google Scholar
5.Falin, G.I. (1990). A survey of retrial queues. Queueing Systems 7: 127168.CrossRefGoogle Scholar
6.Hunt, P.J. (1990). Limit theorems for stochastic loss networks. Ph.D. dissertation, University of Cambridge.Google Scholar
7.Hunt, P.J. (1992). Loss networks under diverse routing, 1: The symmetric star network. Technical Report, University of Cambridge.Google Scholar
8.Kelly, F.P. (1986). Blocking probabilities in large circuit-switched networks. Advances in Applied Probability 18: 473505.CrossRefGoogle Scholar
9.Kelly, F.P. (1991). Loss networks. Annals of Applied Probability 1: 319378.CrossRefGoogle Scholar
10.Krupp, R.S. (1982). Stabilization of alternate routing networks. In IEEE International Communications Conference. New York: IEEE.Google Scholar
11.Louth, G.M. (1990). Stochastic networks: Complexity, dependence and routing. Ph.D. dissertation, University of Cambridge.Google Scholar
12.Takahara, G.K. (1994). Incorporating retrials into L-symmetric networks. Technical Report 605, Carnegie Mellon University.Google Scholar
13.Takahara, G.K. (1994). Incorporating retrials into models of large circuit-switched networks. Ph.D. dissertation, Carnegie Mellon University.Google Scholar
14.Takahara, G.K. (1995). Asymptotic analysis of star networks with retrials using martingales. Advances in Applied Probability (preprint).Google Scholar
15.Valiant, L.G. (1979). The complexity of computing the permanent. Theoretical Computer Science 8: 189201.CrossRefGoogle Scholar
16.Valiant, L.G. (1979). The complexity of enumeration and reliability problems. SIAM Journal on Scientific Computing 8: 410421.CrossRefGoogle Scholar
17.Whitt, W. (1985). Blocking when service is required from several facilities simultaneously. AT&T Technical Journal 64 18071856.Google Scholar
18.Yang, T. & Templeton, J.G.C. (1987). A survey on retrial queues. Queueing Systems 2: 203233.CrossRefGoogle Scholar
19.Zelinskey, A.M. & Kornishev, Y.N. (1978). Two models of a system with repeated calls. Elektrosvyaz 1: 6063.Google Scholar
20.Ziedins, I.B. & Kelly, F.P. (1989). Limit theorems for loss networks with diverse routing. Advances in Applied Probability 21: 804830.CrossRefGoogle Scholar