arXiv subjects

Fabrice Guillemin

Publications and source records attributed to Fabrice Guillemin.

At least 37 records · Page 2Linked to original sources

arXiv2019

Contribution to the design and the implementation of a Cloud Radio Access Network

This dissertation paper presents the main contributions to the design and the implementation of a Cloud-RAN solution. We concretely address the two main challenges of Cloud-RAN systems: real-time processing of radio signals and reduced fronthaul capacity. We propose a multi-threading model to achieve latency reduction of critical RAN functions as well as an adapted functional split for optimizing the transmission of radio signals. We model the performance of the proposed solution by means of stochastic service systems which reflect the behavior of high performance computing architectures based on parallel processing and yield dimensioning rules for the required computing capacity. Finally, we validate the accuracy of the theoretical proposals by a Cloud-RAN testbed implemented on the basis of open source solutions, namely Open Air Interface (OAI).

cs.NI↗

arXiv2019

Automating the deployment of 5G Network Slices with ONAP

Open Network Automation Platform (ONAP) is a carrier grade platform for automatically deploying and managing Virtualized Network Functions. In this paper, we address the deployment of network slices in order to come up with a model that is compatible with ONAP. We analyze various types of network slice ontology presented in the framework of 5G standardization bodies and we propose an ONAP-compatible model on the basis of which we illustrate the design, onboarding, instantiation and distribution of a network slice. We concretely define and deploy a network slice implementing a private and customized mobile core network. The achieved results not only make true NFV and 5G promises, notably those referring to on-demand networks, service customization and time-to-market acceleration, but they open the door to the deployment of private tailored cloud-native 5G networks.

cs.NI↗

arXiv2019

Inversion formula with hypergeometric polynomials and its application to an integral equation

For any complex parameters $x$ and $ν$, we provide a new class of linear inversion formulas $T = A(x,ν) \cdot S \Leftrightarrow S = B(x,ν) \cdot T$ between sequences $S = (S_n)_{n \in \mathbb{N}^*}$ and $T = (T_n)_{n \in \mathbb{N}^*}$, where the infinite lower-triangular matrix $A(x,ν)$ and its inverse $B(x,ν)$ involve Hypergeometric polynomials $F(\cdot)$, namely $$ \left\{ \begin{array}{ll} A_{n,k}(x,ν) = \displaystyle (-1)^k\binom{n}{k}F(k-n,-nν;-n;x), \\ B_{n,k}(x,ν) = \displaystyle (-1)^k\binom{n}{k}F(k-n,kν;k;x) \end{array} \right. $$ for $1 \leqslant k \leqslant n$. Functional relations between the ordinary (resp. exponential) generating functions of the related sequences $S$ and $T$ are also given. These new inversion formulas have been initially motivated by the resolution of an integral equation recently appeared in the field of Queuing Theory; we apply them to the full resolution of this integral equation. Finally, matrices involving generalized Laguerre polynomials polynomials are discussed as specific cases of our general inversion scheme.

math.CA↗

arXiv2019

A Processor-Sharing model for the Performance of Virtualized Network Functions

The parallel execution of requests in a Cloud Computing platform, as for Virtualized Network Functions, is modeled by an $M^{[X]}/M/1$ Processor-Sharing (PS) system, where each request is seen as a batch of unit jobs. The performance of such paralleled system can then be measured by the quantiles of the batch sojourn time distribution. In this paper, we address the evaluation of this distribution for the $M^{[X]}/M/1$-PS queue with batch arrivals and geometrically distributed batch size. General results on the residual busy period (after a tagged batch arrival time) and the number of unit jobs served during this residual busy period are first derived. This enables us to provide an approximation for the distribution tail of the batch sojourn time whose accuracy is confirmed by simulation.

cs.PF↗

arXiv2019

On the sojourn of an arbitrary customer in an $M/M/1$ Processor Sharing Queue

In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system revealed in an earlier study, we compute the distributions of these two quantities and prove that they are equal in distribution. We moreover derive the asymptotic behavior of this common distribution. The knowledge of the number of departures seen by a tagged customer allows us to test the validity of an approximation, which consists of assuming that the tagged customer is randomly served among those customers in the residual busy period of the queue following the arrival of the tagged customer. A numerical evidence shows that this approximation is reasonable for moderate values of the number of departures, given that the asymptotic behaviors of the distributions are very different even if the exponential decay rates are equal.

cs.PF↗

arXiv2019

Higher aggregation of gNodeBs in Cloud-RAN architectures via parallel computing

In this paper, we address the virtualization and the centralization of real-time network functions, notably in the framework of Cloud RAN (C-RAN). We thoroughly analyze the required fronthaul capacity for the deployment of the proposed C-RAN architecture. We are specifically interested in the performance of the software based channel coding function. We develop a dynamic multi-threading approach to achieve parallel computing on a multi-core platform. Measurements from an OAI-based testbed show important gains in terms of latency; this enables the increase of the distance between the radio elements and the virtualized RAN functions and thus a higher aggregation of gNodeBs in edge data centers, referred to as Central Offices (COs).

cs.NI↗

arXiv2017

Allocation Schemes of Ressources with Downgrading

We consider a server with large capacity delivering video files encoded in various resolutions. We assume that the system is under saturation in the sense that the total demand exceeds the server capacity $C$. In such a case, requests may be rejected. For the policies considered in this paper, instead of rejecting a video request, it is downgraded. When the occupancy of the server is above some value $C_0{<}C$, the server delivers the video at a minimal bit rate. The quantity $C_0$ is the bit rate adaptation threshold. For these policies, request blocking is thus replaced by bit rate adaptation. Under the assumptions of Poisson request arrivals and exponential service times, we show that, by rescaling the system, a process associated to the occupancy of the server converges to some limiting process whose invariant distribution is computed by a Wiener-Hopf technique. This allows us to derive an asymptotic expression of the key performance measure of such a policy, the equilibrium probability that a request is transmitted without downgrading. Numerical applications of these results are presented.

cs.NI↗

arXiv2016

Analysis of an offloading scheme for data centers in the framework of fog computing

In the context of fog computing, we consider a simple case when data centers are installed at the edge of the network and assume that if a request arrives at an overloaded data center, then it is forwarded to a neighboring data center with some probability. Data centers are assumed to have a large number of servers and that traffic at some of them is causing saturation. In this case the other data centers may help to cope with this saturation regime by accepting some of the rejected requests. Our aim is to qualitatively estimate the gain achieved via cooperation between neighboring data centers. After proving some convergence results, related to the scaling limits of loss systems, for the process describing the number of free servers at both data centers, we show that the performance of the system can be expressed in terms of the invariant distribution of a random walk in the quarter plane. By using and developing existing results in the technical literature, explicit formulas for the blocking rates of such a system are derived.

cs.NI↗

arXiv2016

Analysis of a trunk reservation policy in the framework of fog computing

We analyze in this paper a system composed of two data centers with limited capacity in terms of servers. When one request for a single server is blocked at the first data center, this request is forwarded to the second one. To protect the single server requests originally assigned to the second data center, a trunk reservation policy is introduced (i.e., a redirected request is accepted only if there is a sufficient number of free servers at the second data center). After rescaling the system by assuming that there are many servers in both data centers and high request arrival rates, we are led to analyze a random walk in the quarter plane, which has the particularity of having non constant reflecting conditions on one boundary of the quarter plane. Contrary to usual reflected random walks, to compute the stationary distribution of the presented random walk, we have to determine three unknown functions, one polynomial and two infinite generating functions. We show that the coefficients of the polynomial are solutions to a linear system. After solving this linear system, we are able to compute the two other unknown functions and the blocking probabilities at both data centers. Numerical experiments are eventually performed to estimate the gain achieved by the trunk reservation policy.

cs.NI↗

arXiv2014

Impatience in mobile networks and its application to data pricing

We consider in this paper an import Quality of Experience (QoE) indicator in mobile networks that is reneging of users due to impatience. We specifically consider a cell under heavy load conditions and compute the reneging probability by using a fluid limit analysis. By solving the fixed point equation, we obtain a new QoE perturbation metric quantifying the impact of reneging on the performance of the system. This metric is then used to devise a new pricing scheme accounting of reneging. We specifically propose several flavors of this pricing around the idea of having a flat rate for accessing the network and an elastic price related to the level of QoE perturbation induced by communications.

cs.NI↗

arXiv2013

Stationary analysis of the Shortest Queue First service policy

We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two parallel queues and assuming Poisson arrivals and general service time distributions, we first establish the functional equations satisfied by the Laplace transforms of the workloads in each queue. We further specialize these equations to the so-called "symmetric case", with same arrival rates and identical exponential service time distributions at each queue; we then obtain a functional equation $$ M(z) = q(z) \cdot M \circ h(z) + L(z) $$ for unknown function $M$, where given functions $q$, $L$ and $h$ are related to one branch of a cubic polynomial equation. We study the analyticity domain of function $M$ and express it by a series expansion involving all iterates of function $h$. This allows us to determine empty queue probabilities along with the tail of the workload distribution in each queue. This tail appears to be identical to that of the Head-of-Line preemptive priority system, which is the key feature desired for the SQF discipline.

cs.PF↗

arXiv2013

Stationary analysis of the "Shortest Queue First" service policy: the asymmetric case

As a follow-up to a recent paper considering two symmetric queues, the \textit{Shortest Queue First} service discipline is presently analysed for two general asymmetric queues. Using the results previously established and assuming exponentially distributed service times, the bivariate Laplace transform of workloads in each queue is shown to depend on the solution $\mathbf{M}$ to a two-dimensional functional equation $$ \mathbf{M} = Q_1 \cdot \mathbf{M}\circ h_1 + Q_2 \cdot \mathbf{M}\circ h_2 + \mathbf{L} $$ with given matrices $Q_1$, $Q_2$ and vector $\mathbf{L}$ and where functions $h_1$ and $h_2$ are defined each on some rational curve; solution $\mathbf{M}$ can then represented by a series expansion involving the semi-group $< h_1, h_2 >$ generated by these two functions. The empty queue probabilities along with the tail behaviour of the workload distribution at each queue are characterised.

cs.PF↗

arXiv2013

Analysis of a non-work conserving Generalized Processor Sharing queue

We consider in this paper a non work-conserving Generalized Processor Sharing (GPS) system composed of two queues with Poisson arrivals and exponential service times. Using general results due to Fayolle \emph{et al}, we first establish the stability condition for this system. We then determine the functional equation satisfied by the generating function of the numbers of jobs in both queues and the associated Riemann-Hilbert problem. We prove the existence and the uniqueness of the solution. This allows us to completely characterize the system, in particular to compute the empty queue probability. We finally derive the tail asymptotics of the number of jobs in one queue.

cs.PF↗

arXiv2009

On the Statistical Characterization of Flows in Internet Traffic with Application to Sampling

A new method of estimating some statistical characteristics of TCP flows in the Internet is developed in this paper. For this purpose, a new set of random variables (referred to as observables) is defined. When dealing with sampled traffic, these observables can easily be computed from sampled data. By adopting a convenient mouse/elephant dichotomy also dependent on traffic, it is shown how these variables give a reliable statistical representation of the number of packets transmitted by large flows during successive time intervals with an appropriate duration. A mathematical framework is developed to estimate the accuracy of the method. As an application, it is shown how one can estimate the number of large TCP flows when only sampled traffic is available. The algorithm proposed is tested against experimental data collected from different types of IP networks.

cs.NI↗

arXiv2009

An identification problem in an urn and ball model with heavy tailed distributions

We consider in this paper an urn and ball problem with replacement, where balls are with different colors and are drawn uniformly from a unique urn. The numbers of balls with a given color are i.i.d. random variables with a heavy tailed probability distribution, for instance a Pareto or a Weibull distribution. We draw a small fraction $p\ll 1$ of the total number of balls. The basic problem addressed in this paper is to know to which extent we can infer the total number of colors and the distribution of the number of balls with a given color. By means of Le Cam's inequality and Chen-Stein method, bounds for the total variation norm between the distribution of the number of balls drawn with a given color and the Poisson distribution with the same mean are obtained. We then show that the distribution of the number of balls drawn with a given color has the same tail as that of the original number of balls. We finally establish explicit bounds between the two distributions when each ball is drawn with fixed probability $p$.

cs.NI↗

arXiv2009

Adaptive algorithms for identifying large flows in IP traffic

We propose in this paper an on-line algorithm based on Bloom filters for identifying large flows in IP traffic (a.k.a. elephants). Because of the large number of small flows, hash tables of these algorithms have to be regularly refreshed. Recognizing that the periodic erasure scheme usually used in the technical literature turns out to be quite inefficient when using real traffic traces over a long period of time, we introduce a simple adaptive scheme that closely follows the variations of traffic. When tested against real traffic traces, the proposed on-line algorithm performs well in the sense that the detection ratio of long flows by the algorithm over a long time period is quite high. Beyond the identification of elephants, this same class of algorithms is applied to the closely related problem of detection of anomalies in IP traffic, e.g., SYN flood due for instance to attacks. An algorithm for detecting SYN and volume flood anomalies in Internet traffic is designed. Experiments show that an anomaly is detected in less than one minute and the targeted destinations are identified at the same time.

cs.NI↗

arXiv2008

Perturbation analysis of an M/M/1 queue in a diffusion random environment

We study in this paper an $M/M/1$ queue whose server rate depends upon the state of an independent Ornstein-Uhlenbeck diffusion process $(X(t))$ so that its value at time $t$ is $μϕ(X(t))$, where $ϕ(x)$ is some bounded function and $μ>0$. We first establish the differential system for the conditional probability density functions of the couple $(L(t),X(t))$ in the stationary regime, where $L(t)$ is the number of customers in the system at time $t$. By assuming that $ϕ(x)$ is defined by $ϕ(x) = 1-\varepsilon ((x\wedge a/\varepsilon)\vee(-b/\varepsilon))$ for some positive real numbers $a$, $b$ and $\varepsilon$, we show that the above differential system has a unique solution under some condition on $a$ and $b$. We then show that this solution is close, in some appropriate sense, to the solution to the differential system obtained when $ϕ$ is replaced with $Φ(x)=1-\varepsilon x$ for sufficiently small $\varepsilon$. We finally perform a perturbation analysis of this latter solution for small $\varepsilon$. This allows us to check at the first order the validity of the so-called reduced service rate approximation, stating that everything happens as if the server rate were constant and equal to $μ(1-\eps\E(X(t)))$.

cs.NI↗

arXiv2008

Inference of Flow Statistics via Packet Sampling in the Internet

We show in this note that by deterministic packet sampling, the tail of the distribution of the original flow size can be obtained by rescaling that of the sampled flow size. To recover information on the flow size distribution lost through packet sampling, we propose some heuristics based on measurements from different backbone IP networks. These heuristic arguments allow us to recover the complete flow size distribution.

cs.NI↗