6,612 research outputs found

    Tight Load Balancing via Randomized Local Search

    Full text link
    We consider the following balls-into-bins process with nn bins and mm 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((lnn)2+ln(n)n2/m)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(ln(n)+n2/m)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

    Load Balancing via Random Local Search in Closed and Open systems

    Full text link
    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

    Locally Optimal Load Balancing

    Full text link
    This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree Δ\Delta, and each node has up to LL units of load. The task is to distribute the load more evenly so that the loads of adjacent nodes differ by at most 11. If the graph is a path (Δ=2\Delta = 2), it is easy to solve the fractional version of the problem in O(L)O(L) communication rounds, independently of the number of nodes. We show that this is tight, and we show that it is possible to solve also the discrete version of the problem in O(L)O(L) rounds in paths. For the general case (Δ>2\Delta > 2), we show that fractional load balancing can be solved in poly(L,Δ)\operatorname{poly}(L,\Delta) rounds and discrete load balancing in f(L,Δ)f(L,\Delta) rounds for some function ff, independently of the number of nodes.Comment: 19 pages, 11 figure

    Makespan Minimization via Posted Prices

    Full text link
    We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms

    Asymptotically Optimal Load Balancing Topologies

    Full text link
    We consider a system of NN servers inter-connected by some underlying graph topology GNG_N. Tasks arrive at the various servers as independent Poisson processes of rate λ\lambda. Each incoming task is irrevocably assigned to whichever server has the smallest number of tasks among the one where it appears and its neighbors in GNG_N. Tasks have unit-mean exponential service times and leave the system upon service completion. The above model has been extensively investigated in the case GNG_N is a clique. Since the servers are exchangeable in that case, the queue length process is quite tractable, and it has been proved that for any λ<1\lambda < 1, the fraction of servers with two or more tasks vanishes in the limit as NN \to \infty. For an arbitrary graph GNG_N, the lack of exchangeability severely complicates the analysis, and the queue length process tends to be worse than for a clique. Accordingly, a graph GNG_N is said to be NN-optimal or N\sqrt{N}-optimal when the occupancy process on GNG_N is equivalent to that on a clique on an NN-scale or N\sqrt{N}-scale, respectively. We prove that if GNG_N is an Erd\H{o}s-R\'enyi random graph with average degree d(N)d(N), then it is with high probability NN-optimal and N\sqrt{N}-optimal if d(N)d(N) \to \infty and d(N)/(Nlog(N))d(N) / (\sqrt{N} \log(N)) \to \infty as NN \to \infty, respectively. This demonstrates that optimality can be maintained at NN-scale and N\sqrt{N}-scale while reducing the number of connections by nearly a factor NN and N/log(N)\sqrt{N} / \log(N) compared to a clique, provided the topology is suitably random. It is further shown that if GNG_N contains Θ(N)\Theta(N) bounded-degree nodes, then it cannot be NN-optimal. In addition, we establish that an arbitrary graph GNG_N is NN-optimal when its minimum degree is No(N)N - o(N), and may not be NN-optimal even when its minimum degree is cN+o(N)c N + o(N) for any 0<c<1/20 < c < 1/2.Comment: A few relevant results from arXiv:1612.00723 are included for convenienc
    corecore