An Optimal Distributed Routing Algorithm using Dual Decomposition Techniques

Abstract

We consider the routing problem in wireline, packet-switched communication net- works. We cast our optimal routing problem in a multicommodity network flow optimization frame- work. Our cost function is related to the congestion in the network, and is a function of the flows on the links of the network. The optimization is over the set of flows in the links corresponding to the various destinations of the incoming traffic. We separately address the single commodity and the multicommodity versions of the routing problem. We consider the dual problems, and using dual decomposition techniques, we provide primal-dual algorithms that converge to the optimal solutions of the problems. Our algorithms, which are subgradient algorithms to solve the corresponding dual problems, can be implemented in a distributed manner by the nodes of the network. For online, adap- tive implementations of our algorithms, the nodes in the network need to utilize 'locally available information' like estimates of queue lengths on outgoing links. We show convergence to the optimal routing solutions for synchronous versions of the algorithms, with perfect (noiseless) estimates of the queueing delays. Every node of the network controls the flows on the outgoing links using the distributed algorithms. For both the single commodity and multicommodity cases, we show that our algorithm converges to a loop-free optimal solution. Our optimal solutions also have the attractive property of being multipath routing solutions. 1. Introduction. We consider in this paper the routing problem in wireline, packet-switched communication networks. Such a network can be represented by a directed graph G = (N , L), where N denotes the set of nodes and L the set of directed links of the network. For such a network we are given a set of origin-destination (OD) node pairs, with a certain incoming traffic rate (in packets per sec) associated with each OD pair. The arriving packets at the origin node have to be transported by the network to the corresponding destination node of the OD pair. The routing objective is to establish a packet traffic flow pattern so that packets are directed to their respective destinations while, at the same time, minimizing congestion in the network. A typical framework for accomplishing the same involves setting up an optimization problem, with the cost being related to the network-wide congestion and the constraints being the natural flow conservation relations in the network. For large-scale networks which are of interest to us, it is desired that the routing solution be implementable in a decentralized manner by the nodes of the network.