Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-14T06:40:10.944Z Has data issue: false hasContentIssue false
  • English
  • Français

Applying POS(i) rules to communication problems

Part of: Markov processes Theory of data

Published online by Cambridge University Press:  14 July 2016

K. S. Chong  and
K. Lam
K. S. Chong*
Affiliation:
University of Hong Kong
K. Lam*
Affiliation:
Hong Kong Baptist University and University of Hong Kong
*
∗Postal address: Department of Statistics, The University of Hong Kong, Pokfulam Road, Hong Kong. Email address: kschong@hp735.sta.cuhk.edu.hk.
∗∗Postal address: Department of Finance and Decision Sciences, Hong Kong Baptist University.
Get access Rights & Permissions [Opens in a new window]

Abstract

A spectrum of self-organizing rules including the move-to-front rule and the transposition rule are applied to the communication problem. The stationary distributions under these rules are obtained. Cost comparison between them is considered. In the special case of three paths, it is shown that the transposition rule always outperforms the move-to-front rule.

Keywords

Markov chain modelslinear searchcomparison of search costscommunication networks

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 68P10: Searching and sorting
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 762 - 769
Copyright
Copyright © Applied Probability Trust 1998 

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

Allen, B., and Munro, I. (1978). Self-organizing binary search trees. J. Assoc. Comput. Mach. 25, 526–535.CrossRefGoogle Scholar
Ash, G. R., Kafker, A. H., and Krishnan, K. R. (1981). Servicing and real-time control of networks with dynamic routing. Bell System Tech. J. 60, 1821–1845.CrossRefGoogle Scholar
Bitner, J. R. (1979). Heuristics that dynamically organize data structures. SIAM J. Comput. 8, 82–110.CrossRefGoogle Scholar
Chong, K. S., and Lam, K. (1997). Cost comparison of a spectrum of self-organizing rules. J. Appl. Prob. 34, 583–592.CrossRefGoogle Scholar
Gonnet, G. H., Munro, J. I., and Suwanda, H. (1981). Exegesis of self-organizing linear search. SIAM J. Computing 10, 613–637.CrossRefGoogle Scholar
Heggestad, H. M. (1980). A flexible routing algorithm for the future Defense Switched Network. Proc IEEE Natl. Telecomm. Conf., 74.3.1–74.3.5.Google Scholar
Hendricks, W. J. (1972). The stationary distribution of an interesting Markov chain. J. Appl. Prob. 9, 231–233.CrossRefGoogle Scholar
Hendricks, W. J. (1976). An account of self-organizing systems. SIAM J. Computing 5, 715–723.CrossRefGoogle Scholar
Lam, K. (1984). Comparison of self-organizing linear search rules. J. Appl. Prob. 21, 763–776.CrossRefGoogle Scholar
Lam, K., Siu, M. K., and Yu, C. T. (1981). A general counter scheme. Theoret. Computer Sci. 16, 271–278.CrossRefGoogle Scholar
McCabe, J. (1965). On serial files with relocatable records. Operat. Res. 13, 609–618.CrossRefGoogle Scholar
Meketon, M. S., and Topkis, D. M. (1983). Adaptive routing for damaged networks. Proc. IEEE Mil. Comm. Conf., 282–288.CrossRefGoogle Scholar
Rivest, R. (1976). On self-organizing sequential search heuristics. Comm. ACM 19, 63–67.CrossRefGoogle Scholar
Sleator, D. D., and Tarjan, R. E. (1985). Amortized efficiency of list update and paging rules. Comm. ACM 28, 202–208.CrossRefGoogle Scholar
Tenenbaum, A. M., and Nemes, R. M. (1982). Two spectra of self-organizing sequential search algorithms. SIAM J. Computing 11, 557–566.CrossRefGoogle Scholar
Topkis, D. M. (1986). Reordering heuristics for routing in communications networks. J. Appl. Prob. 23, 130–143.CrossRefGoogle Scholar