Optimal heavy-traffic queue length scaling in an incompletely saturated switch

Maguluri, Siva Theja; Burle, Sai Kiran; Srikant, R.

doi:10.1007/s11134-017-9562-x

Cited by 24 publications

(35 citation statements)

References 21 publications

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“…For the first case, we assume that the interval (t 0 , t 1 ) is jump-free. 9 We consider two subcases. If t 0 = 0, then…”

Section: B7mentioning

confidence: 99%

“…Robust delay stability via Lyapunov functions. Lyapunov functions are a powerful tool for the stability analysis of queueing networks, [19,4,9] e.g., in throughput optimality proofs for the MW policy [19,14]. The references [10,12] provided a sufficient condition for delay stability based on a class of piecewise linear Lyapunov functions, and used it to derive a sharp characterization of delay stability for a special class of networks, namely networks with disjoint schedules.…”

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confidence: 99%

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Jumping Fluid Models and Delay Stability of Max-Weight Dynamics under Heavy-Tailed Traffic

Sharifnassab¹,

Tsitsiklis²

2021

Preprint

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“…For the first case, we assume that the interval (t 0 , t 1 ) is jump-free. 9 We consider two subcases. If t 0 = 0, then…”

Section: B7mentioning

confidence: 99%

mentioning

confidence: 99%

Jumping Fluid Models and Delay Stability of Max-Weight Dynamics under Heavy-Tailed Traffic

Sharifnassab¹,

Tsitsiklis²

2021

Preprint

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“…Then, using the Kingman bound for single server queue in Lemma 1, we get (7). Similarly lower bounding the total queue length for output port (column) j, i q (ǫ) ij (t) by a single server queue, we get (8). Taking the heavy traffic limits using the fact that γ…”

Section: Universal Lower Boundmentioning

confidence: 99%

Optimal Heavy-Traffic Queue Length Scaling in an Incompletely Saturated Switch

Maguluri

Burle

Srikant

2016

SIGMETRICS Perform. Eval. Rev.

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We consider an input queued switch operating under the MaxWeight scheduling algorithm. This system is interesting to study because it is a model for Internet routers and data center networks. Recently, it was shown that the MaxWeight algorithm has optimal heavy-traffic queue length scaling when all ports are uniformly saturated. Here we consider the case when an arbitrary number of ports are saturated (which we call the incompletely saturated case), and each port is allowed to saturate at a different rate. We use a recently developed drift technique to show that the heavy-traffic queue length under the MaxWeight scheduling algorithm has optimal scaling with respect to the switch size even in these cases.

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Heavy Traffic Queue Length Behaviour in a Switch under Markovian Arrivals

Mou¹,

Maguluri²

2020

Preprint

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The paper studies the input queued switch that is a good model for data center networks, operating under the MaxWeight algorithm. The heavy-traffic scaled mean queue length was characterized in Maguluri et al. (2018), Maguluri and Srikant (2016) when the arrivals are i.i.d.. This paper characterizes the heavy-traffic scaled mean sum queue length under Markov modulated arrivals in the heavy-traffic limit, and shows that it is within a factor of less than 2 from a universal lower bound. Moreover, the paper obtains lower and upper bounds, that are applicable in all traffic regimes, and they become tight in heavy-traffic regime.The paper obtains these results by generalizing the drift method that was developed in Eryilmaz and Srikant (2012), Maguluri and Srikant (2016) to the case of Markovian arrivals. The paper illustrates this generalization by first obtaining the heavy-traffic mean queue length in a single server queue under Markovian arrivals. The paper also illustrates the generalization of the transform method Hurtado-Lange and Maguluri (2018) to obtain the queue length distribution in a single server queue under Markovian arrivals. The key ideas are the use of geometric mixing of finite-state Markov chains, and studying the drift of a test function over a time window that depends on the heavy-traffic parameter.

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Optimal heavy-traffic queue length scaling in an incompletely saturated switch

Cited by 24 publications

References 21 publications

Jumping Fluid Models and Delay Stability of Max-Weight Dynamics under Heavy-Tailed Traffic

Jumping Fluid Models and Delay Stability of Max-Weight Dynamics under Heavy-Tailed Traffic

Optimal Heavy-Traffic Queue Length Scaling in an Incompletely Saturated Switch

Heavy Traffic Queue Length Behaviour in a Switch under Markovian Arrivals

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