Delay Stability of Back-Pressure Policies in the Presence of Heavy-Tailed Traffic

Markakis, Mihalis G.; Modiano, Eytan; Tsitsiklis, John N.

doi:10.1109/tnet.2015.2448107

Cited by 12 publications

(11 citation statements)

References 21 publications

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“…As mentioned in the Introduction, the companion paper [47] studies the same setting as this section. However, while the present section, and the paper in general, is methodologically oriented -to introduce analytical tools that facilitate a delay analysis under heavy-tailed traffic -the companion paper is more geared towards applications.…”

Section: Delay Analysis Of the Back-pressure Policy Under Heavytailedmentioning

confidence: 99%

“…To illustrate the use of the above analytical tools, we borrow an example from the companion paper [47]: consider the multi-hop network of Figure 5, which includes the heavy-tailed flow 1 and the exponential-type flows 2 and 3. The source of flow 1 is node 2 and the source of flows 2 and 3 is node 1.…”

Section: Theoremmentioning

confidence: 99%

“…All links can transmit simultaneously at unit rate and the Back-Pressure policy is applied. Figure 5: An example from [47]: the heavy-tailed flow 1 enters the network at node 2 and exits at node 3. The light-tailed flow 2 enters the network at node 1 and exits at node 3.…”

Section: Theoremmentioning

confidence: 99%

“…The more interesting question concerns flow 3, which serves as cross-traffic to flow 2, and which turns out to have a nontrivial delay stability region as the results of [47] prove. More specifically, if λ 3 < 2 + λ 1 − 2λ 2 /3, then traffic flow 3 is delay stable and its aggregate queue length in steady state is exponential-type.…”

Section: Theoremmentioning

confidence: 99%

“…The companion paper [47] uses technical results derived here (more specifically, Theorems 4 and 5 in Section 4) to study how the network topology, the routing constraints, and the link capacities affect the delay performance of multihop switched queueing networks with heavy-tailed traffic under Back-Pressure-type policies.…”

Section: Introductionmentioning

confidence: 99%

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Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations

2018

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We consider switched queueing networks with a mix of heavy-tailed (i.e., arrival processes with infinite variance) and exponential-type traffic and study the delay performance of the MaxWeight policy, known for its throughput optimality and asymptotic delay optimality properties. Our focus is on the impact of heavy-tailed traffic on exponential-type queues/flows, which may manifest itself in the form of subtle rate-dependent phenomena. We introduce a novel class of Lyapunov functions (piecewise linear and nonincreasing in the length of heavy-tailed queues) whose drift analysis, combined with results in [31], can provide exponentially decaying upper bounds to queue-length tail asymptotics despite the presence of heavy tails. To facilitate a drift analysis we employ fluid approximations, proving that if a continuous and piecewise linear function is also a "Lyapunov function" for the fluid model, then the same function is a "Lyapunov function" for the original stochastic system. Furthermore, we use fluid approximations and renewal theory in order to prove delay instability results, i.e., infinite expected delays in steady state. We illustrate the benefits of the proposed approach in two ways: (i) analytically, by studying the delay stability regions of single-hop switched queueing networks with disjoint schedules, providing a precise characterization of these regions for certain queues and inner and outer bounds for the rest. As a side result, we prove monotonicity properties for the service rates of different schedules that, in turn, allow us to identify "critical configurations" towards which the state of the system is driven, and which determine to a large extent delay stability; (ii) computationally, through a Bottleneck Identification algorithm, which identifies (some) delay unstable queues/flows in complex switched queueing networks by solving the fluid model from certain initial conditions.

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Section: Delay Analysis Of the Back-pressure Policy Under Heavytailedmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations

2018

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On Scheduling Policies With Heavy-Tailed Dynamics in Wireless Queueing Systems

et al. 2020

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This paper takes a system view and studies a wireless queueing system where heavy-tailness may occur both at the traffic arrival and in the form of the multiuser interference. With the rapid development of AI technologies, this heavy-tailed traffic model has become more prevalent in the current network system, such as the file or data size used in the deep learning algorithm. We first re-visit the standard asymmetric queueing system with a mix of heavy-tailed and light-tailed traffic, but under a new variable-rate service model that not only better models the dynamics of the wireless medium but also includes the previous models as special cases. We then focus on the scheduling problem when heavy-tailed interference disrupts the serving link. The performance of queueing policies is investigated during an ON/OFF renewal channel process with heavy-tailed OFF periods, and the expected queue length and the throughput characteristic is studied under the priority as well as max-weight scheduling policies. The results show that the expected queue length of the heavy queue cannot be maintained as finite even under the most favorable priority policy. On the other hand, a priority policy can guarantee the finiteness of an expected queue length for the light queue, but the system is not throughput optimal any longer. It is further shown that no benefit can be provided by the max-weight scheduling policy to the light queue for the queue length behavior in a steady-state, though the system is always throughput optimal.

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Reinforcement Learning for Optimal Control of Queueing Systems

Liu

Xie

Modiano

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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With the rapid advance of information technology, network systems have become increasingly complex and hence the underlying system dynamics are often unknown or difficult to characterize. Finding a good network control policy is of significant importance to achieve desirable network performance (e.g., high throughput or low delay). In this work, we consider using model-based reinforcement learning (RL) to learn the optimal control policy for queueing networks so that the average job delay (or equivalently the average queue backlog) is minimized. Traditional approaches in RL, however, cannot handle the unbounded state spaces of the network control problem. To overcome this difficulty, we propose a new algorithm, called Reinforcement Learning for Queueing Networks (RL-QN), which applies model-based RL methods over a finite subset of the state space, while applying a known stabilizing policy for the rest of the states. We establish that the average queue backlog under RL-QN with an appropriately constructed subset can be arbitrarily close to the optimal result. We evaluate RL-QN in dynamic server allocation, routing and switching problems. Simulation results show that RL-QN minimizes the average queue backlog effectively.

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Delay Stability of Back-Pressure Policies in the Presence of Heavy-Tailed Traffic

Cited by 12 publications

References 21 publications

Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations

Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations

On Scheduling Policies With Heavy-Tailed Dynamics in Wireless Queueing Systems

Reinforcement Learning for Optimal Control of Queueing Systems

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