Partially Optimal Routing

Abstract

Most large-scale communication networks, such as the Internet, consist of interconnected administrative domains. While source (or selfish) routing, where transmission follows the least cost path for each source, is reasonable across domains, service providers typically engage in traffic engineering to improve operating performance within their own network. Motivated by this observation, we develop and analyze a model of partially optimal routing, where optimal routing within subnetworks is overlaid with selfish routing across domains. We demonstrate that optimal routing within a subnetwork does not necessarily improve the performance of the overall network. In particular, when Braess' paradox occurs in the network, partially optimal routing may lead to worse overall network performance. We provide bounds on the worst-case loss of efficiency that can occur due to partially optimal routing. For example, when all congestion costs can be represented by affine latency functions and all administrative domains have a single entry and exit point, the worst-case loss of efficiency is no worse than 25% relative to the optimal solution. In the presence of administrative domains incorporating multiple entry and/or exit points, however, the performance of partially optimal routing can be arbitrarily inefficient even with linear latencies. We also provide conditions for traffic engineering to be individually optimal for service providers. *This work was partially supported by research grants from the Okawa Foundation and the National Science Foundation. We thank Nicolas Stier-Moses for helpful discussions on the proof of Lemma 4.

A geometric approach to the price of anarchy in nonatomic congestion games

“…As an example to illustrate this, we sketch two extensions: a different type of social cost function, and general side constraints on the utilization rates. Let us also mention that the proof-by-picture idea put forward in Section 3 has recently been used by others to derive bounds on the price of anarchy in a variety of noncooperative games (e.g., Yang and Huang, 2005;Farzad et al, 2006;Acemoglu et al, 2007;Harks, 2007).…”

Inter-domain traffic engineering as bi-level network flow optimization

“…Moreover, recent measurements also show fast-changing patterns for inter-domain traffic [16]; inter-domain TE and pricing solutions need to be flexible enough to adapt to such dynamically changing traffic patterns. Another challenge in this context is the counter-productive effects of intra-domain and inter-domain TE policies if they are not designed with careful consideration of their interaction with each other [17], [18]. This paper focuses on the design of cooperative mechanisms between ISPs, or the constituent autonomous systems (ASes) or "domains" managed by them, towards attaining optimal TE objectives in the overall Internet.…”

“…Promising benefits of cooperative TE have driven research community to develop signaling protocols to mediate such negotiation and distributed decision making [30], [31]. Among existing work, [32], [33], [18] are the most closely related to the decomposable network flow optimization based perspective that we adopt for cooperative inter-domain TE. These approaches, like the one we envision, do not require the individual ISPs to reveal their intra-domain topology or state directly, but only in the form of transit/forwarding costs.…”

“…A symbiotic optimization based inter-domain TE approach is discussed in [33], but no formal analysis is presented on the optimality of the approach. The authors in [18] study flow equilibrium efficiency with optimal routing at the intra-domain level and selfish (non-cooperative) routing across domains. [18] shows that Braess' paradox may exist in this case, in that optimal intra-domain routing need not necessarily improve overall network performance, and show that the worst case inefficiency is bounded by 25%.…”

“…The authors in [18] study flow equilibrium efficiency with optimal routing at the intra-domain level and selfish (non-cooperative) routing across domains. [18] shows that Braess' paradox may exist in this case, in that optimal intra-domain routing need not necessarily improve overall network performance, and show that the worst case inefficiency is bounded by 25%. There is a growing body of literature in non-cooperative inter-domain routing and pricing questions [34], [35], [36], [37], [41], [42].…”