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Concave switching in single and multihop networks
 In Proc. ACM International Conference on Measurement and Modeling of Computer Systems (SIGMETRICS
, 2014
"... Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For singlehop networks, we consider a (α, g)switch policy which combines the MaxWeight policies with bandwidth sharing networks – a further well studied model of Internet ..."
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Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For singlehop 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 routedestination, 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 perlink 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. 1
StoreForward and its implications for Proportional Scheduling
"... Abstract — The Proportional Scheduler was recently proposed as a scheduling algorithm for multihop switch networks. For these networks, the BackPressure scheduler is the classical benchmark. For networks with fixed routing, the Proportional Scheduler is maximum stable, myopic and, furthermore, will ..."
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Abstract — The Proportional Scheduler was recently proposed as a scheduling algorithm for multihop switch networks. For these networks, the BackPressure scheduler is the classical benchmark. For networks with fixed routing, the Proportional Scheduler is maximum stable, myopic and, furthermore, will alleviate certain scaling issued found in BackPressure for large networks. Nonetheless, the equilibrium and delay properties of the Proportional Scheduler has not been fully characterized. In this article, we postulate on the equilibrium behaviour of the Proportional Scheduler though the analysis of an analogous rule called the StoreForward allocation. It has been shown that StoreForward has asymptotically allocates according to the Proportional Scheduler. Further, for StoreForward networks, numerous equilibrium quantities are explicitly calculable. For FIFO networks under StoreForward, we calculate the policies stationary distribution and endtoend route delay. We discuss network topologies when the stationary distribution is productform, a phenomenon which we call product form resource pooling. We extend this product form notion to independent set scheduling on perfect graphs, where we show that nonneighbouring queues are statistically independent. Finally, we analyse the large deviations behaviour of the equilibrium distribution of StoreForward networks in order to construct Lyapunov functions for FIFO switch networks. I.
Applied Probability Trust (17 February 2015) A COMPARATIVE ANALYSIS OF THE SUCCESSIVE LUMPING AND THE LATTICE PATH COUNTING ALGORITHMS
"... This article provides a comparison of the successive lumping (SL) methodology developed in [19] with the popular lattice path counting [24] in obtaining rate matrices for queueing models, satisfying the specific quasi birth and death structure as in [21], [22]. The two methodologies are compared bot ..."
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This article provides a comparison of the successive lumping (SL) methodology developed in [19] with the popular lattice path counting [24] in obtaining rate matrices for queueing models, satisfying the specific quasi birth and death structure as in [21], [22]. The two methodologies are compared both in terms of applicability requirements and numerical complexity by analyzing their performance for the same classical queueing models considered in [21]. The main findings are: i) When both methods are applicable the SL based algorithms outperform the lattice path counting algorithm (LPCA). ii) There are important classes of problems (e.g., models with (level) nonhomogenous rates or with finite state spaces) for which the SL methodology is applicable and for which the LPCA cannot be used. iii) Another main advantage of successive lumping algorithms over lattice path counting is that the former includes a method to compute the steady state distribution using this rate matrix.