Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-14T12:10:57.044Z Has data issue: false hasContentIssue false
  • English
  • Français

Least Busy Alternative Routing in Queueing and Loss Networks

Published online by Cambridge University Press:  27 July 2009

P. J. Hunt  and
C. N. Laws
P. J. Hunt
Affiliation:
Statistical Laboratory University of Cambridge, 16 Mill Lane Cambridge, CB2 1SB, United Kingdom
C. N. Laws
Affiliation:
Statistical Laboratory University of Cambridge, 16 Mill Lane Cambridge, CB2 1SB, United Kingdom
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is divided into two distinct parts: the first considers a loss network, the second a queueing network. In each case, we consider a fully connected network consisting of a large number of links (queues) and operating under a dynamic routing policy known as least busy alternative routing. Using weak convergence results, we can examine the behavior of the networks as the number of links (queues) increases to infinity. We find that, despite the models having similarities and being amenable to the same analytical tools, they exhibit important differences in character.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 4 , October 1992 , pp. 439 - 456
Copyright
Copyright © Cambridge University Press 1992

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

Ackerley, R.G. (1987). Hysteresis-type behaviour in networks with extensive overflow. British Telecom Technology Journal 5: 42–50.Google Scholar
Akinpelu, J.M. (1984). The overflow performance of engineered networks with nonhierarchical and hierarchical routing. AT&T Technical Journal 63: 1261–1281.Google Scholar
Crametz, J.-P. & Hunt, P.J. (1991). A limit result respecting graph structure for a fully connected loss network with alternative routing. Annals of Applied Probability 1: 436–444.CrossRefGoogle Scholar
Foschini, G.J. (1982). Equilibria for diffusion models of pairs of communicating computers – Symmetric case. IEEE Transactions on Information Theory 28: 273–284.CrossRefGoogle Scholar
Gibbens, R.J., Hunt, P.J., & Kelly, F.P. (1990). Bistability in communication networks. In Grimmett, G.R. & Welsh, D.J.A. (eds.), Disorder in physical systems. Oxford: Oxford University Press, pp. 113–128.Google Scholar
Gibbens, R.J. & Kelly, F.P. (1990). Dynamic routing in fully connected networks. IMA Journal of Mathematical Control & Information 7: 77–111.CrossRefGoogle Scholar
Hunt, P.J. (1990). Limit theorems for stochastic loss networks. Ph.D. thesis, Statistical Laboratory, University of Cambridge, Cambridge.Google Scholar
Hunt, P.J. & Laws, C.N. (1992). Asymptotically optimal loss network control (to appear in Mathematics of Operations Research).Google Scholar
Hunt, P.J., Laws, C.N., & Pitsilis, E. (1992). Asymptotically optimal queueing network control (in preparation).Google Scholar
Kelly, F.P. (1991). Loss networks. Annals of Applied Probability 1: 319–378.CrossRefGoogle Scholar
Kelly, F.P. & Laws, C.N. (1992). Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling (to appear in Queueing Systems).CrossRefGoogle Scholar
Krupp, R.S. (1982). Stabilization of alternate routing networks. IEEE International Communications Conference, Paper 31.2. New York: IEEE.Google Scholar
Marbukh, V.V. (1981). Asymptotic investigation of a complete communications network with a large number of points and bypass routes. Problemy Peredaci Informacii 16: 89–95.Google Scholar
Marbukh, V.V. (1983). Investigations of a fully connected channel switching network with many nodes and alternative routes. Avtomatika i Telemekhanika 12: 86–94.Google Scholar
Mitra, D., Gibbens, R.J., & Huang, B.D. (1991). Analysis and optimal design of aggregated-least-busy-alternative routing on symmetric loss networks with trunk reservations. In Jensen, A. & Iversen, V.B. (eds.), Proceedings of 13th International Teletraffic Congress. Amsterdam: Elsevier North-Holland, pp. 477–482.Google Scholar
Nakagome, Y. & Mori, H. (1973). Flexible routing in the global communication network. Proceedings of 7th International Teletraffic Congress, Paper 426. Amsterdam: Elsevier North-Holland.Google Scholar
Reiman, M.I. (1984). Open queueing networks in heavy traffic. Mathematics of Operations Research 9: 441–458.CrossRefGoogle Scholar