On the Stability of Interdomain Inbound Trafﬁc Engineering

In the Internet, ISPs adopt local routing polices to choose routes to achieve objectives such as reducing cost, increasing revenue, reducing latency, and avoiding congestion. Recently, systematic models (e.g., [3]) are proposed to study the stability of path-vector, policy-based interdomain routing. Gao and Rexford [2] prove the surprising result that the constraints on local routing policies due to business considerations can guarantee stability. Although the preceding stability results are surprisingly pleasant and elegant, practice poses further challenges in analyzing interdomain routing stability. First, the previous studies focus on a specific interdomain route selection algorithm (e.g., the BGP-based greedy route selection algorithm such as SPVP [3]). As a result, factors such as route dampening, which are present in routing practice, are not easily allowed in previous analysis. Although conceptually such factors might not change the conclusions of previous analysis, an analytical framework is still missing. Second, the previous studies focus on local policies which rank only the egress routes; that is, they assume that the local ranking of egress routes at each autonomous system is independent of the inbound traffic pattern of the AS. This independence is justified when the inbound traffic of an AS is relatively constant. However, in practice, the local policies of ASes may involve both the egress routes and the pattern of inbound traffic, introducing unexpected interaction. Specifically, an AS may rank egress routes depending on the pattern of inbound traffic. If this happens, we say that the local policy of the AS is inbound-traffic-dependent, or inbound-dependent for short. One way such inbounddependent route selection can happen is that the operator of the AS observes traffic demand, and manually reconfigures the local preference values. Such inbound-dependent route selection can also be implemented automatically, with a traffic engineering algorithm based on an estimated traffic demand matrix. In this paper, we analyze the stability of interdomain routing under the general model that the local preference of an AS depends on not only its egress routes to the destinations but also its inbound traffic pattern. Furthermore, instead of studying a specific route selection algorithm, we study a large class of route selection algorithms which are characterized by their asymptotic behaviors. Specifically, we first show that the common route selection algorithms can lead to instability due to trafficroute mis-association This instability happens even when all constraints on interdomain routing imposed by business considerations [2] are satisfied, and just a single AS is using such an algorithm. As a remedy, an AS should adopt a route selection algorithm which estimates inbound traffic in such a way that the estimated inbound traffic is truly the result of the chosen egress route. We then analyze the stability of a network where ASes run any reasonable route selection algorithms which we call rational route selection algorithms. The definition of a rational route selection algorithm depends only on the asymptotic behavior of the algorithm. Conducting stability analysis based on the general notion of rational route selection algorithms allows us to prove the stability of a heterogeneous network where different ASes can run different route selection algorithms, so long all of the algorithms are rational. Since the notion of a rational route selection algorithm is defined by its asymptotic behavior, if variations to a route selection algorithm do not change its asymptotic behavior (e.g., non-persistent route dampening), the route selection algorithm is still rational, and thus the stability result still holds.