Joint Network-and-Server Congestion in Multi-Source Traffic Allocation: A Convex Formulation and Price-Based Decentralization

TL;DR

This paper formulates a convex optimization model for multi-source, multi-node traffic rate allocation considering rate-dependent access delays and load-dependent queueing delays, and proposes a decentralized pricing algorithm for optimal traffic distribution.

Contribution

It introduces a convex formulation for joint network and server congestion management and develops a distributed, price-based algorithm ensuring convergence to the global optimum.

Findings

The optimization problem is convex and admits a global optimal solution.

The decentralized algorithm converges to the centralized optimal solution.

Numerical results demonstrate effective joint congestion control and trade-offs.

Abstract

This paper studies an important rate allocation problem that arises in many networked and distributed systems: steady-state traffic rate allocation from multiple sources to multiple service nodes when both (i) the access-path delay on each source-node route is rate-dependent (capacity-constrained) and convex, and (ii) each service node (also capacity-constrained) experiences a load-dependent queueing delay driven by aggregate load from all sources. We show that the resulting flow-weighted end-to-end delay minimization is a convex program, yielding a global system-optimal solution characterized by KKT conditions that equalize total marginal costs (a path marginal access term plus a node congestion price) across all utilized routes. This condition admits a Wardrop-type interpretation: for each source, all utilized options equalize total marginal cost, while any option with strictly larger total marginal cost receives no flow. Building on this structure, we develop a lightweight distributed pricing-based algorithm in which each service node locally computes and broadcasts a scalar congestion price from its observed aggregate load, while each source updates its traffic split by solving a small separable convex allocation problem under the advertised prices. Numerical illustrations demonstrate convergence of the distributed iteration to the centralized optimum and highlight the trade-offs induced by jointly modeling access and service congestion.