Distributed Decisions on Optimal Load Balancing in Loss Networks

TL;DR

This paper develops a mathematical framework for load balancing in loss networks, analyzing both centralized optimization and decentralized user behaviors, and evaluates the efficiency loss due to selfish routing decisions.

Contribution

It introduces a polynomial-time algorithm for system-wide optimal load balancing and characterizes Nash equilibria in decentralized settings, including efficiency analysis.

Findings

Centralized algorithm achieves system optimum in polynomial time.

Decentralized users reach Nash equilibrium through distributed decisions.

Selfish behaviors cause non-monotonic efficiency loss, sometimes with extreme values.

Abstract

When multiple users share a common link in direct transmission, packet loss and network collision may occur due to the simultaneous arrival of traffics at the source node. To tackle this problem, users may resort to an indirect path: the packet flows are first relayed through a sidelink to another source node, then transmitted to the destination. This behavior brings the problems of packet routing or load balancing: (1) how to maximize the total traffic in a collaborative way; (2) how self-interested users choose routing strategies to minimize their individual packet loss independently. In this work, we propose a generalized mathematical framework to tackle the packet and load balancing issue in loss networks. In centralized scenarios with a planner, we provide a polynomial-time algorithm to compute the system optimum point where the total traffic rate is maximized. Conversely, in decentralized settings with autonomous users making distributed decisions, the system converges to an equilibrium where no user can reduce their loss probability through unilateral deviation. We thereby provide a full characterization of Nash equilibrium and examine the efficiency loss stemming from selfish behaviors, both theoretically and empirically. In general, the performance degradation caused by selfish behaviors is not catastrophic; however, this gap is not monotonic and can have extreme values in certain specific scenarios.