Prakirt Raj Jhunjhunwala
Abstract
This paper studies the Heavy Traffic (HT) joint distribution of queue lengths in an Input-queued switch (IQ switch) operating under the MaxWeight scheduling policy. IQ switchserve as representative of SPNs that do not satisfy the socalled Complete Resource Pooling (CRP) condition, and consequently exhibit a multidimensional State Space Collapse (SSC). Except in special cases, only mean queue lengths of such non-CRP systems is known in the literature. In this paper, we develop the Transform method to study the joint distribution of queue lengths in non-CRP systems. The key challenge is in solving an implicit functional equation involving the Laplace transform of the HT limiting distribution. For the general n x n IQ 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 HT limiting queue-lengths in terms of a non-linear combination of 2n iid exponentials.
- D. A. Hurtado Lange and S. T. Maguluri. Heavy-traffic analysis of queueing systems with no complete resource pooling. Mathematics of Operations Research, 47(4):3129--3155, 2022.Google Scholar
Digital Library
- P. Jhunjhunwala and S. T. Maguluri. Heavy traffic distribution of queueing systems without resource pooling. Preprint arXiv:2206.06504, 2022.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
Index Terms
- Heavy Traffic Joint Queue Length Distribution withoutResource Pooling
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