Bipartite graph structures for efficient balancing of heterogeneous loads

Abstract

This paper considers large scale distributed content service platforms, such as peer-to-peer video-on-demand systems. Such systems feature two basic resources, namely storage and bandwidth. Their efficiency critically depends on two factors: (i) content replication within servers, and (ii) how incoming service requests are matched to servers holding requested content. To inform the corresponding design choices, we make the following contributions.We first show that, for underloaded systems, so-called proportional content placement with a simple greedy strategy for matching requests to servers ensures full system efficiency provided storage size grows logarithmically with the system size. However, for constant storage size, this strategy undergoes a phase transition with severe loss of efficiency as system load approaches criticality.To better understand the role of the matching strategy in this performance degradation, we characterize the asymptotic system efficiency under an optimal matching policy. Our analysis shows that -in contrast to greedy matchingoptimal matching incurs an inefficiency that is exponentially small in the server storage size, even at critical system loads. It further allows a characterization of content replication policies that minimize the inefficiency. These optimal policies, which differ markedly from proportional placement, have a simple structure which makes them implementable in practice.On the methodological side, our analysis of matching performance uses the theory of local weak limits of random graphs, and highlights a novel characterization of matching numbers in bipartite graphs, which may both be of independent interest.

Bypassing correlation decay for matchings with an application to XORSAT

“…Adapting the proof of Lemma 3 allows us to get the first part of the following proposition. The second part of the proposition does not follow directly from our analysis and its proof relies on König-Hall min-max Theorem and can be found in [10] (see Theorem 1).…”

Serving content with unknown demand

“…Our model of content delivery systems shares several features with recent models and analyses for content placement and request scheduling in multi-server queueing systems [10,11,15,18]. All these works either assume known demand statistics, or a low-dimensional regime (thus permiting "easy" learning).…”

Optimal Content Replication and Request Matching in Large Caching Systems

“…Next, we turn our attention to the dynamics of the system which are determined by the matching policy in use. In earlier works, e.g., [4], [5] a maximum matching scheme has been considered to match incoming requests to servers. However, in the maximum matching scheme, the service of ongoing requests may be interrupted to incorporate a newly arrived request.…”

“…A replication policy in which the number of replicas is proportional to the arrival rate of the contents was proposed and analyzed in conjunction with the maximum matching algorithm which is different from the setting in our paper. In [5] a similar loss model was considered. However, the objective was to maximize the utilization of the resources as opposed to maximization of throughput.…”