Section: New Results

Design and Performance Analysis of Wireless Networks

Participants : François Baccelli, Bartłomiej Błaszczyszyn, Chung Shue Chen, Miodrag Jovanović, Holger Paul Keeler, Mir Omid Haji Mirsadeghi, Frédéric Morlot, Tien Viet Nguyen.

CDMA/UMTS, Wireless LANs, ad hoc networks, IEEE 802.11, mesh networks, cognitive radio, Hiperlan, CSMA, TCP, MAC protocols, exponential back-off protocols, signal to interference ratio, coverage, capacity, transport capacity, admission and congestion control.

This axis bears on the analysis and the design of wireless access communication networks. Our contributions are organized in terms of network classes: cellular networks, wireless LANs and MANETs, VANETs. We also have a section on generic results that regard more general wireless networks. We are interested both in macroscopic models, which are particularly important for economic planning and in models allowing the definition and the optimization of protocols. Our approach combines several tools, queueing theory, point processes, stochastic geometry, random graphs, distributed control algorithms, self organization protocols.

Cellular Networks

The activity on cellular networks has several complementary facets ranging from performance evaluation to protocol design. The work is mainly based on strong collaborations with Alcatel-Lucent and Orange Labs.

Effect of Opportunistic Scheduling on the Quality of Service Perceived by the Users in OFDMA Cellular Networks

Our objective in [17] is to analyze the impact of fading and opportunistic scheduling on the quality of service perceived by the users in an Orthogonal Frequency Division Multiple Access (OFDMA) cellular network. To this end, assuming Markovian arrivals and departures of customers that transmit some given data volumes, as well as some temporal channel variability (fading), we study the mean throughput that the network offers to users in the long run of the system. Explicit formulas are obtained in the case of allocation policies, which may or may-not take advantage of the fading, called respectively opportunistic and non-opportunistic. The main practical results of the present work are the following. Firstly we evaluate for the non-opportunist allocation the degradation due to fading compared to Additive White Gaussian Noise (AWGN) (that is, a decrease of at least 13% of the throughput). Secondly, we evaluate the gain induced by the opportunistic allocation. In particular, when the traffic demand per cell exceeds some value (about 2 Mbits/s in our numerical example), the gain induced by opportunism compensates the degradation induced by fading compared to AWGN. Partial results were presented at ComNet in 2009  [61] .

Impact of propagation-loss model on the geometry and performance of cellular networks

Impact of Shadowing on QoS

Shadowing is believed to degrade the quality of service in wireless cellular networks. In [18] we discovered a more subtle reality. Increasing variance of the lognormal shadowing tends to “separate” the strongest (serving BS) signal from all other signals — a phenomenon observed for heavy-tailed distributions and called “single big jump principle”. In consequence, in some cases, an increase of the variance of the shadowing can significantly reduce the mean interference factor and improve some QoS metrics in interference limited systems. We exemplify this phenomenon, similar to stochastic resonance and related to the “single big jump principle” of the heavy-tailed log-nornal distribution, studying the blocking probability in regular, hexagonal networks in a semi-analytic manner, using a spatial version of the Erlang's loss formula combined with Kaufman-Roberts algorithm.

Using Poisson processes to model lattice cellular networks

In [51] we mathematically proved that a large spatially homogeneous (arbitrary, including hexagonal) network is perceived by a typical user as an equivalent (infinite) Poisson network, provided shadowing is strong enough. This justifies an almost ubiquitous Poisson assumption made in the stochastic-analytic approach to study of the quality of user-service in cellular networks.

Linear-Regression Estimation of the Propagation-Loss Parameters Using Mobiles' Measurements

In [35] we proposed a new linear-regression model for the estimation of the path-loss exponent and the parameters of the shadowing from the propagation-loss data collected by the mobiles with respect to their serving base stations. The model is based on the aforementioned Poisson convergence result.

Quality of Real-Time Streaming in Wireless Cellular Networks

In [50] we present a new stochastic service model with service capacity sharing and interruptions, meant to be useful for the performance evaluation and dimensioning of wireless cellular networks offering real-time streaming, like e.g. mobile TV. Our general model takes into account Markovian, multi-class process of call arrivals, arbitrary streaming time distribution, and allows for a general service (outage) policy saying which users are temporarily denied the service due to insufficient service capacity. Using Palm theory formalism, we develop expressions for several important characteristics of this model, including mean time spent in outage and mean number of outage incidents for a typical user of a given class. We also propose some natural class of least-effort-served-first service policies, for which the aforementioned expressions can be efficiently evaluated on the basis of the Fourier analysis of Poisson process. Last but not least, we show how our model can be used to analyse the quality of real-time streaming in 3GPP Long Term Evolution (LTE) cellular networks. We identify and evaluate an optimal and a fair service policy, the latter being suggested by LTE implementations, as well as propose some intermediate policies which allow to solve the optimality/fairness trade-off caused by unequal user radio-channel conditions.

Theoretically Feasible QoS in a MIMO Cellular Network Compared to the Practical LTE Performance

Our goal in [39] is to build a global analytical approach for the evaluation of the quality of service perceived by the users in wireless cellular networks which is calibrated in some reference cases. To do so, a model accounting for interference in a MIMO cellular system is firstly described. An explicit expression of users bit-rates theoretically feasible from the information theory point of view is then deduced. The comparison between these bit-rates and practical LTE performance permits to obtain the progress margins for potential evolution of the technology. Moreover, it leads to an analytical approximate expression of the system performance which is calibrated with the practical one. This expression is the keystone of a global analytical approach for the evaluation of the QoS perceived by the users in the long run of users arrivals and departures in the network. We illustrate our approach by calculating the users QoS as function of the cell radius in different mobility and interference cancellation scenarios.

Self-Optimization of Radio Resources in Cellular Networks

In [19] , we surveyed the mathematical and algorithmic tools for the self-optimization of mobile cellular networks based on Gibbs' sampler. This technique allows for the joint optimization of radio resources in heterogeneous cellular networks made of a juxtaposition of macro and small cells. It can be implemented in a distributed way and nevertheless achieves minimal system-wide potential delay. Results show that it is effective in both throughput and energy efficiency.

Three patents were filed on this line of thought under the Inria/Alcatel–Lucent joint laboratory.

Coverage in Cellular Networks

Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In a collaboration with H. Dhillon, J. Andrews and R. Ganti [UT Austin, USA] [20] , we developed a model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting Signal-to-Interference-plus-Noise-Ratio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derived an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access. One interesting observation for interference-limited open access networks is that at a given SINR, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same SINR threshold.

Mobile Ad Hoc Networks

A MANET is made of mobile nodes which are at the same time terminals and routers, connected by wireless links, the union of which forms an arbitrary topology. The nodes are free to move randomly and organize themselves arbitrarily. Important issues in such a scenario are connectivity, medium access (MAC), routing and stability. This year, we worked on a game theoretic view of Spatial Aloha in collaboration with E. Altman and M.K. Hanawal [Inria MAESTRO] [22] This line of though is currently continued with Chandramani Singh. We also compared the performance of spatial Aloha to CSMA.

Improvement of CSMA/CA's Spatial Reuse

The most popular medium access mechanism for such ad hoc networks is CSMA/CA with RTS/CTS. In CSMA-like mechanisms, spatial reuse is achieved by implementing energy based guard zones. In a collaboration with Qualcomm [12] , we considered the problem of simultaneously scheduling the maximum number of links that can achieve a given signal to interference ratio (SIR). Using tools from stochastic geometry, we studied and maximized the medium access probability of a typical link. Our contributions are two-fold: (i) We showed that a simple modification to the RTS/CTS mechanism, viz., changing the receiver yield decision from an energy-level guard zone to an SIR guard zone, leads to performance gains; and (ii) We showed that this combined with a simple modification to the transmit power level – setting it to be inversely proportional to the square root of the link gain – leads to significant improvements in network throughput. Further, this simple power-level choice is no worse than a factor of two away from optimal over the class of all "local" power level selection strategies for fading channels, and further is optimal in the non-fading case. The analysis relies on an extension of the Matérn hard core point process which allows us to quantify both these SIR guard zones and this power control mechanism.

Comparison of the maximal spatial throughput of Aloha and CSMA in Wireless multihop Ad-Hoc Networks

In [46] this paper we compare the spatial throughput of Aloha and Carrier Sense Multiple Access (CSMA) in Wireless multihop Ad-Hoc Networks. In other words we evaluate the gain offered by carrier sensing (CSMA) over the pure statiscal collision avoidance which is the basis of Aloha. We use a Signal-to-Interference-and-Noise Ratio (SINR) model where a transmission is assumed to be successful when the SINR is larger than a given threshold. Regarding channel conditions, we consider both standard Rayleigh and negligible fading. For slotted and non-slotted Aloha, we use analytical models as well as simulations to study the density of successful transmissions in the network. As it is very difficult to build precise models for CSMA, we use only simulations to compute the performances of this protocol. We compare the two Aloha versions and CSMA on a fair basis, i.e. when they are optimized to maximize the density of successful transmissions. For slotted Aloha, the key optimization parameter is the medium access probability, for non-slotted Aloha we tune the mean back-off time, whereas for CSMA it is the carrier sense threshold that is adjusted. Our study shows that CSMA always outperforms slotted Aloha, which in turn outperforms its non-slotted version.

Stochastic Analytic Evaluation of End-to-End Performance of Linear Nearest Neighbour Routing in MANETs with Aloha

Planar Poisson models with the Aloha medium access scheme have already proved to be very useful in studies of mobile ad-hoc networks (MANETs). However, it seems difficult to quantitatively study the performances of end-to-end routing in these models. In order to tackle this problem, in [52] , we study a linear stationary route embedded in an independent planar field of interfering nodes. We consider this route as an idealization of a "typical" route in a MANET obtained by some routing mechanism. Such a decoupling allows us to obtain many numerically tractable expressions for local and mean end-to-end delays and the speed of packet progression, assuming slotted Aloha MAC and the Signal-to-Interference-and-Noise Ratio (SINR) capture condition, with the usual power-law path loss model and Rayleigh fading. These expressions show how the network performance depends on the tuning of Aloha and routing parameters and on the external noise level. In particular we show a need for a well-tuned lattice structure of fixed relaying nodes, which helps to relay packets on long random routes in the presence of a non-negligible noise. We also consider a Poisson-line MANET model, in which nodes are located on roads forming a Poisson-line process. In this case our linear route is rigorously (in the sense of Palm theory) the typical route in this Poisson-line MANET.

Vehicular Ad-Hoc Networks (VANETs)

Vehicular Ad Hoc NETworks (VANETs) are special cases of MANETs where the network is formed between vehicles. VANETs are today the most promising civilian application for MANETs and they are likely to revolutionize our traveling habits by increasing safety on the road while providing value added services.

Point-to-Point, Emergency and Broadcast Communications

Our aim in [36] is to analyze the Aloha medium access (MAC) scheme in one-dimensional, linear networks, which might be an appropriate assumption for VANETs. The locations of the vehicles are assumed to follow a homegeneous Poisson point process. Assuming powerlaw mean path-loss and independent point-to-point fading we study performance metrics based on the signal-over-interference and noise ratio (SINR). In contrast to previous studies where the receivers are at a fixed distance from the transmitter, we assume here that the receivers are the nearest neighbors of the transmitters in the Poisson process and in a given direction. We derive closed formulas for the capture probability and for the density of progress of a packet sent by a given node. We compute the mean delay to send a packet transmitted at each slot until successful reception. We also evaluate an upper bound to discover the neighborhood within a given space interval. We show that we can include noise in the previous models.

Cognitive Radio Networks

We wrote a survey [26] on the probabilistic framework which can be used to model and analyze cognitive radio networks using various classes of MAC protocols (including carrier sensing based multiple access schemes and Aloha schemes). For each model, analytical results were derived for important performance metrics. This leads to a quantification of the interplay between primary and secondary users in such networks.