Thomas Bonald

Analytic evaluation of RED performance

End-to-end congestion control mechanisms such as those in TCP are not enough to prevent congestion collapse in the Internet, and they must be supplemented by control mechanisms inside the network. The IRTF has singled out random early detection (RED) as one queue management scheme recommended for rapid deployment throughout the Internet. However, RED is not a thoroughly understood scheme-witness for example how the recommended parameter setting, or even the various benefits RED is claimed to provide, have changed over the past few years. In this paper, we describe simple analytic models for RED, and use these models to quantify the benefits (or lack thereof) brought about by RED. In particular, we examine the impact of RED on the loss and delay suffered by bursty and less bursty traffic (such as TCP and UDP traffic, respectively). We find that: (i) RED does eliminate the higher loss bias against bursty traffic observed with tail drop, but not by decreasing the loss rate of bursty traffic, rather by increasing that of non bursty traffic; (ii) the number of consecutive packet drops is higher with RED than tail drop, suggesting RED might not help as anticipated with the global synchronization of TCP flows; (iii) RED can be used to control the average queueing delay in routers and hence the end to end delay, but increases the jitter of non bursty streams. Thus, applications that generate smooth traffic, such as interactive audio applications, will suffer higher loss rates and require large playout buffers, thereby negating at least in part the lower mean delay brought about by RED.

Wireless downlink data channels: user performance and cell dimensioning

We consider wireless downlink data channels where the transmission power of each base station is time-shared between a dynamic number of active users as in CDMA/HDR systems. We derive analytical results relating user performance, in terms of blocking probability and data throughput, to cell size and traffic density. These results are used to address a number of practically interesting issues, including the trade-off between cell coverage and cell capacity and the choice of efficient scheduling and admission control schemes.

Epidemic live streaming: optimal performance trade-offs

Several peer-to-peer systems for live streaming have been recently deployed (e.g. CoolStreaming, PPLive, SopCast). These all rely on distributed, epidemic-style dissemination mechanisms. Despite their popularity, the fundamental performance trade-offs of such mechanisms are still poorly understood. In this paper we propose several results that contribute to the understanding of such trade-offs. Specifically, we prove that the so-called random peer, latest useful chunk mechanism can achieve dissemination at an optimal rate and within an optimal delay, up to an additive constant term. This qualitative result suggests that epidemic live streaming algorithms can achieve near-unbeatable rates and delays. Using mean-field approximations, we also derive recursive formulas for the diffusion function of two schemes referred to as latest blind chunk, random peer and latest blind chunk, random useful peer. Finally, we provide simulation results that validate the above theoretical results and allow us to compare the performance of various practically interesting diffusion schemes terms of delay, rate, and control overhead. In particular, we identify several peer/chunk selection algorithms that achieve near-optimal performance trade-offs. Moreover, we show that the control overhead needed to implement these algorithms may be reduced by restricting the neighborhood of each peer without substantial performance degradation.

A queueing analysis of max-min fairness, proportional fairness and balanced fairness

We compare the performance of three usual allocations, namely max-min 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 processor-sharing 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 max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.

Insensitive Bandwidth Sharing in Data Networks

We represent a data network as a set of links shared by a dynamic number of competing flows. These flows are generated within sessions and correspond to the transfer of a random volume of data on a pre-defined network route. The evolution of the stochastic process describing the number of flows on all routes, which determines the performance of the data transfers, depends on how link capacity is allocated between competing flows. We use some key properties of Whittle queueing networks to characterize the class of allocations which are insensitive in the sense that the stationary distribution of this stochastic process does not depend on any traffic characteristics (session structure, data volume distribution) except the traffic intensity on each route. We show in particular that this insensitivity property does not hold in general for well-known allocations such as max-min fairness or proportional fairness. These results are ilustrated by several examples on a number of network topologies.

Insensitivity in processor-sharing networks

We consider an open network of processor-sharing nodes with state-dependent service capacities, i.e., the speed of each node may depend on the number of customers at any node. We demonstrate that the stationary distribution of the network state is insensitive to the distribution of service times if and only if the service capacities are balanced, i.e., the considered network is a Whittle network. The stationary distribution then has a closed-form expression and the expected sojourn time of a customer at any node is proportional to its required quantity of service. These results are extended to the cases of closed networks and state-dependent arrival rates and routing. Two simple examples illustrate the practical interest of these results in the context of communication networks.

Congestion at flow level and the impact of user behaviour

So-called elastic flows, corresponding to document transfers of various types, constitute the bulk of Internet traffic. This paper presents models of a single bottleneck link handling elastic traffic, accounting for random flow arrivals. The transport protocol and packet scheduling are taken into account approximately by assuming perfectly realized bandwidth sharing objectives.We refer to the demand as the product of the flow arrival rate and the average flow size. It is shown that per-flow throughput performance is generally satisfactory as long as demand is only slightly less than capacity. In overload, on the other hand, some flows must be abandoned. A fraction of link bandwidth is then wasted and performance critically depends on user behaviour. The models are useful in appraising the effectiveness of proposed schemes for Internet service differentiation.

Statistical performance guarantees for streaming flows using expedited forwarding

We suggest that satisfactory statistical performance guarantees for streaming flows can be fulfilled when their packets receive expedited forwarding in non-preemptive priority queues. This relies on the conjecture that jitter remains negligible in the network such that performance measures can be bounded by assuming flows constitute Poisson arrival processes of maximum transfer unit (MTU) sized packets. We provide analytical and simulation evidence in support of this conjecture and show how it leads to simple engineering rules for both constant and variable rate streaming traffic.

How mobility impacts the flow-level performance of wireless data systems

The potential for exploiting rate variations to increase the capacity of wireless systems by opportunistic scheduling has been extensively studied at packet level. In the present paper, we examine how slower, mobility-induced rate variations impact performance at flow level, accounting for the random number of flows sharing the transmission resource. We identify two limit regimes, termed fluid and quasistationary, where the rate variations occur on an infinitely fast and an infinitely slow time scale, respectively. Using stochastic comparison techniques, we show that these limit regimes provide simple performance bounds that only depend on easily calculated load factors. Additionally, we prove that for a broad class of fading processes, performance varies monotically with the speed of the rate variations. These results are illustrated through numerical experiments, showing that the fluid and quasistationary bounds are remarkably tight in certain usual cases

On performance bounds for the integration of elastic and adaptive streaming flows

We consider a network model where bandwidth is fairly shared by a dynamic number of elastic and adaptive streaming flows. Elastic flows correspond to data transfers while adaptive streaming flows correspond to audio/video applications with variable rate codecs. In particular, the former are characterized by a fixed size (in bits) while the latter are characterized by a fixed duration. This flow-level model turns out to be intractable in general. In this paper, we give performance bounds for both elastic and streaming traffic by means of sample-path arguments. These bounds present the practical interest of being insensitive to traffic characteristics like the distributions of elastic flow size and streaming flow duration.