A duality model of TCP and queue management algorithms

We propose a duality model of end-to-end congestion control and apply it to understanding the equilibrium properties of TCP and active queue management schemes. The basic idea is to regard source rates as primal variables and congestion measures as dual variables, and congestion control as a distributed primal-dual algorithm over the Internet to maximize aggregate utility subject to capacity constraints. The primal iteration is carried out by TCP algorithms such as Reno or Vegas, and the dual iteration is carried out by queue management algorithms such as DropTail, RED or REM. We present these algorithms and their generalizations, derive their utility functions, and study their interaction

Network equilibrium of heterogeneous congestion control protocols

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the resulting equilibrium may no longer be interpreted as a solution to the standard utility maximization problem. We prove the existence of equilibrium under mild assumptions. Then we show that multi-protocol networks whose equilibria are locally non-unique or infinite in number can only form a set of measure zero. Multiple locally unique equilibria can arise in two ways. First, unlike in the single-protocol case, the set of bottleneck links can be non-unique with heterogeneous protocols even when the routing matrix has full row rank. The equilibria associated with different sets of bottleneck links are necessarily distinct. Second, even when there is a unique set of bottleneck links, network equilibrium can still be non-unique, but is always finite and odd in number. They cannot all be locally stable unless it is globally unique. Finally, we provide various sufficient conditions for global uniqueness. Numerical examples are used throughout the paper to illustrate these results

Cross-Border Trade: A Two-Stage Equilibrium Model of the Florence Regulatory Forum Proposals

Cross-Border Trade: A Two-Stage Equilibrium Model of the Florence Regulatory Forum Proposal

Atomic Routing Games on Maximum Congestion

We study atomic routing congestion games in which each player chooses a path in the network from its strategy set (a collection of paths) with the objective to minimize the maximum congestion along any edge on its selected path. The social cost is the global maximum congestion on any edge in the network. We show that for arbitrary routing games, the price of stability is 1, and the price of anarchy, PoA, is bounded by κ − 1 ≤ PoA ≤ c(κ 2 + log 2 n), where κ is the length of the longest cycle in the network, n is the size of the network and c is a constant. Further, any best response dynamic converges to a Nash equilibrium. Our bounds show that for maximum congestion games, the topology of the network, in particular the length of cycles, plays an important role in determining the quality of the Nash equilibria. A fundamental issue in the management of large scale communication networks is to route the packet traffic so as to optimize the network performance. Our measure of network performance is the worst bottleneck (most used link) in the system. The model we use for network traffic is that of finite, unsplittable packets (atomic flow), and each packet’s path is controlled independentl