Large Deviations for the Stationary Measure of Networks Under Proportional Fair Allocations

Jonckheere, Matthieu; López, Sergio I.

doi:10.1287/moor.2013.0605

Cited by 7 publications

(7 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The stability of proportional fairness in Massoulié networks was first shown by De Veciana et al (1999); an important generalization of this stability analysis is given in Massoulié (2007). Further progress on the stability and large deviations behavior of proportional fairness can be found in Jonckheere and López (2014). Heavy traffic analysis of proportional fair policies can be found in Kang et al (2009), Yao (2012), andVlasiou et al (2014).…”

Section: J |mentioning

confidence: 97%

Proportional Switching in First-in, First-out Networks

Bramson

D’Auria

Walton³

2017

Operations Research

View full text Add to dashboard Cite

We consider a family of discrete time multihop switched queueing networks where each packet moves along a fixed route. In this setting, BackPressure is the canonical choice of scheduling policy; this policy has the virtues of possessing a maximal stability region and not requiring explicit knowledge of traffic arrival rates. BackPressure has certain structural weaknesses because implementation requires information about each route, and queueing delays can grow super-linearly with route length. For large networks, where packets over many routes are processed by a queue, or where packets over a route are processed by many queues, these limitations can be prohibitive.In this article, we introduce a scheduling policy for FIFO networks, the Proportional Scheduler, which is based on the proportional fairness criterion. We show that, like BackPressure, the Proportional Scheduler has a maximal stability region and does not require explicit knowledge of traffic arrival rates. The Proportional Scheduler has the advantage that information about the network's route structure is not required for scheduling, which substantially improves the policy's performance for large networks. For instance, packets can be routed with only next-hop information and new nodes can be added to the network with only knowledge of the scheduling constraints.

show abstract

Section: J |mentioning

confidence: 97%

Proportional Switching in First-in, First-out Networks

Bramson

D’Auria

Walton³

2017

Operations Research

View full text Add to dashboard Cite

show abstract

“…Stability results on proportional fairness can be found in [10,23]. Further progress on the large deviations and heavy traffic behavior of proportional fairness can be found in Jonckheere and López [18] and Vlasiou, Zhang, Zwart [37]. The paper generalizes the MaxWeight policies by allowing for resource sharing similar to that found in Bandwidth Sharing Networks.…”

Section: Introductionmentioning

confidence: 94%

Concave switching in single-hop and multihop networks

Walton

2015

Queueing Syst

View full text Add to dashboard Cite

Switched queueing networks model wireless networks, input-queued switches, and numerous other networked communications systems. We consider an (α, g)-switch policy; these policies provide a generalization of the MaxWeight policies of Tassiulas and Ephremides (IEEE Trans Autom Control 37(12): 1992) and the weighted α-fair with allocations of Mo and Walrand (IEEE/ACM Trans Netw 8(5): [556][557][558][559][560][561][562][563][564][565][566][567] 2000) which are typically applied to Bandwidth Sharing Networks (Massoulié and Roberts in IEEE/ACM Trans Netw 10(3):320-328, 2002). For single-hop switch networks, we prove the maximum stability property for this class of randomized policies. Thus these policies have the same first-order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies. For multihop networks with fixed routing, we consider a policy called the Proportional Scheduler (or (1, log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue at each node for every route destination, which typically grows rapidly with a network's size. However, the Proportional Scheduler only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing, each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights; only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, 123 266 Queueing Syst (2015) 81: while maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.

show abstract

“…Notice in the first equality, we include the term j = j r 0 . Since applying convention (17) we have, log((xjrσ * j (qj))/(qj ār)) = log 1 = 0.…”

Section: Second Proofmentioning

confidence: 99%

“…Stability proofs for these systems can be found in Bonald and Massoulié [3] and Massoulié [22]. Further progress on the large deviations and heavy traffic behaviour of proportional fairness can be found in Jonckheere, Lopez [17] and Vlasiou, Zhang, Zwart [37]. To the knowledge of this author, discussions applying these models to switch networks are first made by Shah and Wischik [32] and Zhong [38] for the weighted α-fair bandwidth allocation policies of Mo and Walrand [25].…”

Section: Introductionmentioning

confidence: 99%

Concave switching in single and multihop networks

Walton

2014

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a (α, g)-switch policy which combines the MaxWeight policies with bandwidth sharing networks -a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies.For multihop networks with fixed routing, we consider the Proportional Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue for every route-destination, which typically grows rapidly with a network's size. However, this proportionally fair policy only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights, only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, whilst maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.

show abstract

Large Deviations for the Stationary Measure of Networks Under Proportional Fair Allocations

Cited by 7 publications

References 19 publications

Proportional Switching in First-in, First-out Networks

Proportional Switching in First-in, First-out Networks

Concave switching in single-hop and multihop networks

Concave switching in single and multihop networks

Contact Info

Product

Resources

About