Randomized longest-queue-first scheduling for large-scale buffered systems. (English) Zbl 1335.90015

Summary: We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling (LQF) algorithm by establishing new mean-field limit theorems as the number of buffers \(n \to \infty\). We achieve this by allowing the number of sampled buffers \(d = d(n)\) to depend on the number of buffers \(n\), which yields an asymptotic ‘decoupling’ of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of \(n\) and \(d(n)\). To the best of the authors’ knowledge, this is the first derivation of diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized LQF algorithm emulates the LQF algorithm, yet is computationally more attractive. The analysis of the system performance as a function of \(d(n)\) is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized LQF scheduling algorithm.


90B22 Queues and service in operations research
90B36 Stochastic scheduling theory in operations research
Full Text: DOI arXiv Euclid


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