Network routing

Abstract

How should flows through a network be organized, so that the network responds sensibly to failures and overloads? The question is currently of considerable technological importance in connection with the development of computer and telecommunication networks, while in various other forms it has a long history in the fields of physics and economics. In all of these areas there is interest in how simple, local rules, often involving random actions, can produce coherent and purposeful behaviour at the macroscopic level. This paper describes some examples from these various fields, and indicates how analogies with fundamental concepts such as energy and price can provide powerful insights into the design of routing schemes for communication networks.

The Routing Continuum from Shortest-Path to All-Path: A Unifying Theory

“…Using this formulation, we obtain a surprising result: as we vary the trade-off parameter , the routing graphs induced by the optimal flow solutions span from the shortest-path routing to multi-path routing with increasing path lengths to the potential-based ("all-path") routing -this entire (finite) sequence of routing graphs is referred to as the routing continuum. Our theory therefore subsumes the earlier 1 and 2 network flow optimization results [16], [30] as two extreme points in the entire routing continuum.…”

“…(1) states that if In the next two subsections we will use two well-known results [16], [30] to illustrate that certain common routing strategies, namely, shortest path routing and potential-based, "allpath" routing, can be derived by minimizing the (weighted)…”

“…This formulation is inspired by the earlier results where it has been shown that shortest path routing can be derived from network flow optimization with 1 norm [30], whereas potential-based, "all-path" routing can be derived from network flow optimization with 2 -norm objective [16], [19]. Intuitively, the mixed 1 / 2 -norm objective can be interpreted as a tradeoff between the latency and energy dissipation of paths used for routing (collectively, the paths form a routing graph): shorter paths lead to better routing with low latency, while diffusing traffic along more paths generally reduces energy dissipation.…”

“…For instance, in modern IP-based data networks, shortest path routing is most commonly used. In traditional telecommunication networks, dynamic alternative routing strategies that employ paths that are longer than shortest paths have been also proposed to reduce call blocking probabilities (see, e.g., [1], [16]). In wireless networks, due to the unstable channel characteristics, using a single "shortest" path (e.g., with link quality as link weights) for routing is often not the best choice; routing strategies that go beyond shortest path routing (see, e.g., [4], [15], [18], [25] and references therein) using multiple paths are often more effective.…”

Distributed Optimization in Transportation and Logistics Networks

“…Compared with the traditional centralized approach, this has the advantage of less computational load and communication overhead, and robustness against network breakdown. The Dynamic Alternative Routing of British Telecom was an early successful example [17]. Also, in computer science, many algorithmic solutions have been proposed to distribute computational load among computers connected in a network, but they are usually more heuristic.…”