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A queueing analysis of maxmin fairness, proportional fairness and balanced fairness. Queueing Systems: Theory and Applications
, 2006
"... We compare the performance of three usual allocations, namely maxmin fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processorsharing queues. The vector of service rates ..."
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Cited by 36 (7 self)
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We compare the performance of three usual allocations, namely maxmin fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processorsharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of maxmin fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.
Structural properties of proportional fairness: Stability and insensitivity
 Annals of Applied Probability
"... In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel– Legendre transform of the network capacity region. We use this characterization to prove stability (i.e., ergodicity) of network dynamics under proporti ..."
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Cited by 26 (4 self)
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In this article we provide a novel characterization of the proportionally fair bandwidth allocation of network capacities, in terms of the Fenchel– Legendre transform of the network capacity region. We use this characterization to prove stability (i.e., ergodicity) of network dynamics under proportionally fair sharing, by exhibiting a suitable Lyapunov function. Our stability result extends previously known results to a more general model including Markovian users routing. In particular, it implies that the stability condition previously known under exponential service time distributions remains valid under socalled phasetype service time distributions. We then exhibit a modification of proportional fairness, which coincides with it in some asymptotic sense, is reversible (and thus insensitive), and has explicit stationary distribution. Finally we show that the stationary distributions under modified proportional fairness and balanced fairness, a sharing criterion proposed because of its insensitivity properties, admit the same large deviations characteristics. These results show that proportional fairness is an attractive bandwidth allocation criterion, combining the desirable properties of ease of implementation with performance and insensitivity.
State space collapse and diffusion approximation for a network operating under a fair bandwidthsharing policy, in preparation
, 2004
"... We consider a connectionlevel model of Internet congestion control, introduced by Massoulié and Roberts [36], that represents the randomly varying number of flows present in a network. Here bandwidth is shared fairly amongst elastic document transfers according to a weighted αfair bandwidth sharin ..."
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Cited by 20 (7 self)
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We consider a connectionlevel model of Internet congestion control, introduced by Massoulié and Roberts [36], that represents the randomly varying number of flows present in a network. Here bandwidth is shared fairly amongst elastic document transfers according to a weighted αfair bandwidth sharing policy introduced by Mo and Walrand [37] (α ∈ (0,∞)). Assuming Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. A fluid model (or functional law of large numbers approximation) for this stochastic model was derived and analyzed in a prior work [29] by two of the authors. Here we use the long time behavior of the solutions of this fluid model established in [29] to derive a property called multiplicative state space collapse, which loosely speaking shows that in diffusion scale the flow count process for the stochastic model can be approximately recovered as a continuous lifting of the workload process. Under weighted proportional fair sharing of bandwidth (α = 1) and a mild
A survey on Discriminatory Processor Sharing.
 Queueing Systems
, 2006
"... The Discriminatory Processor Sharing (DPS) model is a multiclass generalization of the egalitarian Processor Sharing model. In the DPS model all jobs present in the system are served simultaneously at rates controlled by a vector of weights {gk> 0; k = 1,..., K}. If there are Nk jobs of class k pre ..."
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Cited by 14 (5 self)
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The Discriminatory Processor Sharing (DPS) model is a multiclass generalization of the egalitarian Processor Sharing model. In the DPS model all jobs present in the system are served simultaneously at rates controlled by a vector of weights {gk> 0; k = 1,..., K}. If there are Nk jobs of class k present in the system, k = 1,..., K, each classk job is served at rate gk/�K j=1 gjNj. The present article provides an overview of the analytical results for the DPS model. In particular, we focus on response times and numbers of jobs in the system.
Computational aspects of balanced fairness
 In Proceedings of 18th International Teletraffic Congress
, 2003
"... Flow level behaviour of data networks depends on the allocation of link capacities between competing flows. It has been recently shown that there exist allocations with the property that the stationary distribution of the number of flows in progress on different routes depends only on the traffic lo ..."
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Cited by 11 (7 self)
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Flow level behaviour of data networks depends on the allocation of link capacities between competing flows. It has been recently shown that there exist allocations with the property that the stationary distribution of the number of flows in progress on different routes depends only on the traffic loads on these routes and is insensitive to any detailed traffic characteristics. Balanced fairness refers to the most efficient of such allocations. In this paper we develop a general recursive algorithm for efficiently calculating the corresponding performance metrics like flow throughput. Several examples are worked out using this algorithm including the practically interesting case of tree networks. 1
On performance bounds for balanced fairness
 Performance Evaluation
, 2004
"... While Erlang’s formula has helped engineers to dimension telephone networks for over eighty years, such a threeway “performance demand capacity ” relationship is still lacking for data networks. It may be argued that the enduring success of Erlang’s formula is essentially due to its simplicity: t ..."
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Cited by 8 (1 self)
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While Erlang’s formula has helped engineers to dimension telephone networks for over eighty years, such a threeway “performance demand capacity ” relationship is still lacking for data networks. It may be argued that the enduring success of Erlang’s formula is essentially due to its simplicity: the call blocking rate does not depend on the distribution of call duration but on overall demand only. In this paper, we consider data networks and characterize those capacity allocations which have the same insensitivity property, in the sense that performance of data transfers does not depend on precise traffic characteristics such as the distribution of data volume but on overall demand only. We introduce the notion of “balanced fairness ” and prove some key properties satisfied by this insensitive allocation. It is shown notably that the performance of balanced fairness is always better than that obtained if flows are transmitted in a “storeandforward ” fashion, allowing simple formula applying to the latter to be used as a conservative evaluation for network design and provisioning purposes. 1
Performance of wireless ad hoc networks under balanced fairness
 In Proceedings of Networking 2004
, 2004
"... Abstract. Balanced fairness is a new resource sharing concept recently introduced by Bonald and Proutière. We extend the use of this notion to wireless networks where the link capacities at the flow level are not fixed but depend on the scheduling of transmission rights to interfering nodes on a fas ..."
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Cited by 7 (5 self)
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Abstract. Balanced fairness is a new resource sharing concept recently introduced by Bonald and Proutière. We extend the use of this notion to wireless networks where the link capacities at the flow level are not fixed but depend on the scheduling of transmission rights to interfering nodes on a faster time scale. The balance requirement together with the requirement of maximal use of the network’s resources jointly determine both a unique statedependent scheduling and bandwidth sharing between the contending flows. The flow level performance under the resulting scheme is insensitive to detailed traffic characteristics, e.g., flow size distribution. The theoretical and computational framework is formulated and illustrated by two examples for which the performance in terms of average flow throughputs in a dynamic system is explicitly worked out. 1
Dimensioning high speed IP access networks
 In: 18th International Teletraffic Congress. (2003
, 2003
"... This paper discusses the definition of simple dimensioning rules for high speed IP access networks carrying data traffic. We notably provide formulas relating capacity, demand and performance allowing dimensioning for a target quality of service expressed in terms of useful perflow throughput. Thes ..."
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Cited by 7 (0 self)
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This paper discusses the definition of simple dimensioning rules for high speed IP access networks carrying data traffic. We notably provide formulas relating capacity, demand and performance allowing dimensioning for a target quality of service expressed in terms of useful perflow throughput. These formulas derive from a data traffic model equivalent of the Engset model for telephone access networks. Performance is shown to be largely independent of precise traffic characteristics. The key dimensioning parameter is offered traffic defined as the average data rate a user would generate in the absence of congestion. 1.
Proportional fairness and its relationship with multiclass queueing networks
, 2009
"... We consider multiclass singleserver queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the ..."
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Cited by 6 (3 self)
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We consider multiclass singleserver queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multiclass queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that the stationary throughput of a multiclass singleserver queueing network converges to a proportionally fair allocation. This work combines classical queueing networks with more recent work on stochastic flow level models and proportional fairness. One could view these seemingly different models as the same system described at different levels of granularity: a microscopic, queueing level description; a macroscopic, flow level description and a teleological, optimization description. 1. Introduction. In