Impact of fairness and heterogeneity on delays in large-scale centralized content delivery systems
Queueing Systems(2016)
摘要
We consider multiclass queueing systems where the per class service rates depend on the network state, fairness criterion, and is constrained to be in a symmetric polymatroid capacity region. We develop new comparison results leading to explicit bounds on the mean service time under various fairness criteria and possibly heterogeneous loads. We then study large-scale systems with a growing number of service classes n (for example, files), m = ⌈bn⌉ heterogenous servers with total service rate ξ m , and polymatroid capacity resulting from a random bipartite graph 𝒢^(n) modeling service availability (for example, placement of files across servers). This models, for example, content delivery systems supporting pooling of server resources, i.e., parallel servicing of a download request from multiple servers. For an appropriate asymptotic regime, we show that the system’s capacity region is uniformly close to a symmetric polymatroid—heterogeneity in servers’ capacity and file placement disappears. Combining our comparison results and the asymptotic ‘symmetry’ in large systems, we show that large randomly configured systems with a logarithmic number of file copies are robust to substantial load and server heterogeneities for a class of fairness criteria. If each class can be served by c_n=ω (log n) servers, the load per class does not exceed θ _n=o( min (n/log n, c_n)) , mean service requirement of a job is ν , and average server utilization is bounded by γ <1 , then for each constant δ >1 , the conditional expectation of delay of a typical job with respect to the σ -algebra generated by 𝒢^(n) satisfies the following: lim _n→∞ P( E[D^(n)|𝒢^(n)] ≤δν/ξ c_n1/γlog( 1/1-γ) ) = 1.
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关键词
Delays,Fairness,Heterogeneity,Robustness,Queueing,Asymptotic symmetry,Content delivery systems
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