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

2026-02-03

AI Summary

This study addresses the steady-state rate allocation problem for multi-source traffic subject to both network path delays and server queuing delays. By formulating end-to-end delay minimization as a convex optimization problem, the work jointly models network and service congestion for the first time and derives a globally optimal solution that admits a Wardrop equilibrium interpretation via the KKT conditions. Furthermore, a lightweight distributed iterative algorithm based on marginal cost pricing is proposed to achieve efficient traffic allocation. Numerical experiments demonstrate that the algorithm converges to the centralized optimum and effectively reveals the trade-off between network and service congestion.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• congestion
• rate allocation
• convex optimization
• queueing delay
• networked systems

Innovation

• convex optimization
• congestion pricing
• distributed algorithm
• Wardrop equilibrium
• multi-source traffic allocation