Prakirt Raj Jhunjhunwala
Abstract
This paper studies the heavy-traffic joint distribution of queue lengths of an input-queued switch operating under the MaxWeight scheduling policy. Input-queued switch acts as a representative of SPNs that do not satisfy the so-called complete resource pooling (CRP) condition, and consequently exhibit a multidimensional state space collapse. Except in special cases, only mean queue lengths of such non-CRP systems have been obtained in the literature. In this paper, we develop the transform method to study the steady state distribution of non-CRP systems. The key challenge is in solving an implicit functional equation involving the Laplace transform of the heavy-traffic limiting distribution. We then consider the general n - n input-queued switch that has n2 queues. Under a conjecture on uniqueness of the solution of the functional equation, we obtain an exact joint distribution of the heavy-traffic limiting queue-lengths in terms of a nonlinear transformation of 2n iid exponentials.
- D. Hurtado-Lange and S. T. Maguluri. Heavy-traffic analysis of queueing systems with no complete resource pooling. Under Review at Mathematics of Operations Research, Preprint arXiv:1904.10096, 2019.Google Scholar
- D. Hurtado-Lange and S. T. Maguluri. Transform methods for heavy-traffic analysis. Stochastic Systems, 10(4):275--309, 2020.Google ScholarCross Ref
- P. Jhunjhunwala and S. T. Maguluri. Heavy traffic distribution of queueing systems without resource pooling. Preprint arXiv:2206.06504, 2022.Google Scholar
- P. R. Jhunjhunwala and S. T. Maguluri. Low-complexity switch scheduling algorithms: Delay optimality in heavy traffic. IEEE/ACM Transactions on Networking, 2021.Google Scholar
- G. S. Litvinchuk and A. Nechaev. A generalized carleman boundary value problem. Matematicheskii Sbornik, 124(1):30--54, 1970.Google Scholar
- S. T. Maguluri and R. Srikant. Heavy traffic queue length behavior in a switch under the maxweight algorithm. Stochastic Systems, 6(1):211--250, 2016.Google ScholarCross Ref
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