Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- Part I Probability theory
- Part II Stochastic processes
- Part III Physics of networks
- 15 General characteristics of graphs
- 16 The Shortest Path Problem
- 17 The effciency of multicast
- 18 The hopcount to an anycast group
- Appendix A Stochastic matrices
- Appendix B Algebraic graph theory
- Appendix C Solutions of problems
- Bibliography
- Index
18 - The hopcount to an anycast group
from Part III - Physics of networks
Published online by Cambridge University Press: 22 February 2010
- Frontmatter
- Contents
- Preface
- 1 Introduction
- Part I Probability theory
- Part II Stochastic processes
- Part III Physics of networks
- 15 General characteristics of graphs
- 16 The Shortest Path Problem
- 17 The effciency of multicast
- 18 The hopcount to an anycast group
- Appendix A Stochastic matrices
- Appendix B Algebraic graph theory
- Appendix C Solutions of problems
- Bibliography
- Index
Summary
In this chapter, the probability density function of the number of hops to the most nearby member of the anycast group consisting of m members (e.g. servers) is analyzed. The results are applied to compute a performance measure η of the effciency of anycast over unicast and to the server placement problem. The server placement problem asks for the number of (replicated) servers m needed such that any user in the network is not more than j hops away from a server of the anycast group with a certain prescribed probability. As in Chapter 17 on multicast, two types of shortest path trees are investigated: the regular k-ary tree and the irregular uniform recursive tree treated in Chapter 16. Since these two extreme cases of trees indicate that the performance measure η ≈ 1 − alogm where the real number a depends on the details of the tree, it is believed that for trees in real networks (as the Internet) a same logarithmic law applies. An order calculus on exponentially growing trees further supplies evidence for the conjecture that η ≈ 1 alogm for small m.
Introduction
IPv6 possesses a new address type, anycast, that is not supported in IPv4. The anycast address is syntactically identical to a unicast address. However, when a set of interfaces is specified by the same unicast address, that unicast address is called an anycast address. The advantage of anycast is that a group of interfaces at different locations is treated as one single address. For example, the information on servers is often duplicated over several secondary servers at different locations for reasons of robustness and accessibility.
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- Performance Analysis of Communications Networks and Systems , pp. 417 - 434Publisher: Cambridge University PressPrint publication year: 2006