Tight Load Balancing via Randomized Local Search

We consider the following balls-into-bins process with $n$ bins and $m$ balls: each ball is equipped with a mutually independent exponential clock of rate 1. Whenever a ball's clock rings, the ball samples a random bin and moves there if the number of balls in the sampled bin is smaller than in its current bin. This simple process models a typical load balancing problem where users (balls) seek a selfish improvement of their assignment to resources (bins). From a game theoretic perspective, this is a randomized approach to the well-known Koutsoupias-Papadimitriou model, while it is known as randomized local search (RLS) in load balancing literature. Up to now, the best bound on the expected time to reach perfect balance was $O\left({(\ln n)}^2+\ln(n)\cdot n^2/m\right)$ due to Ganesh, Lilienthal, Manjunath, Proutiere, and Simatos (Load balancing via random local search in closed and open systems, Queueing Systems, 2012). We improve this to an asymptotically tight $O\left(\ln(n)+n^2/m\right)$. Our analysis is based on the crucial observation that performing "destructive moves" (reversals of RLS moves) cannot decrease the balancing time. This allows us to simplify problem instances and to ignore "inconvenient moves" in the analysis.Comment: 24 pages, 3 figures, preliminary version appeared in proceedings of 2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS'17

Distributed Decisions on Optimal Load Balancing in Loss Networks

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.Comment: 6 pages, WiOPT workshop RAWNE

Load Balancing via Random Local Search in Closed and Open systems

In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch server independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner.Comment: Accepted to Sigmetrics 201

Stochastic Optimization of Service Provision with Selfish Users

We develop a computationally efficient technique to solve a fairly general distributed service provision problem with selfish users and imperfect information. In particular, in a context in which the service capacity of the existing infrastructure can be partially adapted to the user load by activating just some of the service units, we aim at finding the configuration of active service units that achieves the best trade-off between maintenance (e.g.\ energetic) costs for the provider and user satisfaction. The core of our technique resides in the implementation of a belief-propagation (BP) algorithm to evaluate the cost configurations. Numerical results confirm the effectiveness of our approach.Comment: paper presented at NETSTAT Workshop, Budapest - June 201