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Learning traffic correlations in multi-class queueing systems by sampling workloads

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Martin Zubeldia, Georgia Institute of Technology

We consider a service system consisting of parallel single server queues of infinite capacity. Work of different classes arrives as correlated Gaussian processes with known drifts but unknown covariances, and it is deterministically routed to the different queues according to some routing matrix. In this setting we show that, under some conditions, the covariance matrix of the arrival processes can be directly recovered from the large deviations behavior of the queue lengths. Also, we show that in some cases this covariance matrix cannot be directly recovered this way, as there is an inherent loss of information produced by the dynamics of the queues. Finally, we show how this can be used to quickly learn an optimal routing matrix with respect to some utility function.