Impact of fairness and heterogeneity on delays in large-scale centralized content delivery systems

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), \(m = \left\lceil {bn} \right\rceil \) heterogenous servers with total service rate \(\xi m\), and polymatroid capacity resulting from a random bipartite graph \({\mathcal {G}}^{(n)}\) 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 \(c_n=\omega (\log n)\) servers, the load per class does not exceed \(\theta _n=o\left( \min (\frac{n}{\log n}, c_n)\right) \), mean service requirement of a job is \(\nu \), and average server utilization is bounded by \(\gamma <1\), then for each constant \(\delta >1\), the conditional expectation of delay of a typical job with respect to the \(\sigma \)-algebra generated by \({\mathcal {G}}^{(n)}\) satisfies the following: