Hind Castel-Taleb

• Professor
• Institut Mines-Télécom

Network slicing allows multiplexing virtualized networks, called slices, over a single physical network infrastructure. Research has extensively focused on the placement of virtual functions and the links that compose each network slice. On the other hand, performance greatly depends on how many resources are allocated to virtual nodes and links, a...

We propose a model for the virtual function placement problem and several novel algorithms using ideas based on multi-armed bandits. We prove that these algorithms learn the optimal placement policy rapidly, and their regret grows at a rate at most $O( N M \sqrt{T\ln T} )$ while respecting the feasibility constraints with high probability. We show...

https://hal.science/hal-04769024

High dimensionality of model-based Reinforcement Learning and Markov Decision Processes can be reduced using abstractions of the state and action spaces. Although hierarchical learning and state abstraction methods have been explored over the past decades, explicit methods to build useful abstractions of models are rarely provided. In this work, we...

Energy consumption represents a major part of the operating expenses of mobile network operators. With the densification foreseen with 5G and beyond, energy optimization has become a problem of crucial importance. While energy optimization is widely studied in the literature, there are limited insights and algorithms for energy-saving techniques fo...

The paper addresses the problem of performance-energy trade-off in DVFS (Dynamic Voltage Frequency Scaling) systems. We propose a stochastic hybrid model between hysteresis models and server block models. We provide a closed form for the steady-state distribution probability and we establish a "st" type order to compare the performance measures. Th...

We consider a horizontal and dynamic auto-scaling technique in a cloud system where virtual machines hosted on a physical node are turned on and off in order to minimise energy consumption while meeting performance requirements. Finding cloud management policies that adapt the system to the load is not straightforward and we consider here that virt...

In this article, we consider the Virtual Network Embedding (VNE) problem for 5G networks slicing. This problem requires to allocate multiple Virtual Networks (VN) on a substrate virtualized physical network while maximizing among others, resource utilization, maximum number of placed VNs and network operator’s benefit. We solve the online version o...

Within network slicing, Virtual Network Embedding has been vastly studied, i.e., deciding in which physical nodes and links to place virtual functions and links. However, the performance of slices does not only depend on where virtual functions and links are placed, but also on how much resources they can use, which has been mostly neglected in the...

We address the problem of a Network Operator (NO) owning limited resources at the network edge. The NO wishes to enable advanced services, by virtualizing and allocating such resources among multiple tenants, i.e., third-party Service Providers, co-existing at the edge, with different Quality of Service (QoS) constraints. The NO applies a resource...

Network slicing in the upcoming Telecom generation is a fundamental feature which is deployed to satisfy the various demands in term of data rate and latency. On the other hand, it is seen as a topic that imposes other questions such as the coexistence of physical and virtual functions. In this context, we consider the resource management problem f...

Dynamic Voltage and Frequency Scaling (DVFS) involves adjusting the speed to match power consumption and performance requirements of the system. This technology has been shown to provide major power and energy savings in many system components (processor cores, memory system ...). In this work, we study the DVFS mechanism for a processor that imple...

We consider three-tier network architecture modeled with two physical nodes in tandem where an autonomous agent controls the number of active resources on each node. We analyse the learning of auto-scaling strategies in order to optimise both performance and energy consumption of the whole system. We compare several model-based reinforcement learni...

In this paper, we consider the Virtual Network Embedding (VNE) problem for 5G networks slicing. This consists in optimally allocating multiple Virtual Networks (VN) on a substrate virtualized physical network while maximizing among others, resource utilization, maximum number of placed VNs and network operator's benefit. We solve the online version...

We consider an auto-scaling technique in a cloud system where virtual machines hosted on a physical node are turned on and off depending on the queue's occupation (or thresholds), in order to minimise a global cost integrating both energy consumption and performance. We propose several efficient optimisation methods to find threshold values minimis...

This book constitutes the refereed proceedings of the 17th European Workshop on Computer Performance Engineering, EPEW 2021, and the 26th International Conference, on Analytical and Stochastic Modelling Techniques and Applications, ASMTA 2021, held in December 2021. The conference was held virtually due to COVID 19 pandemic. The 29 papers presented...

We consider an Energy Packet Network (EPN) model where the service times of the packets follow a Coxian distribution. EPNs are a recent type of models proposed by Gelenbe and his colleagues to study the interactions between energy consumption and the processing or the transmission of data. We prove that such a network has a product form solution fo...

Reducing the energy consumption of a data center is a major goal in today’s digital world. We consider a cloud system represented by a set of physical servers hosting several Virtual Machines, and each one running tasks. We define a resource management policy that implements task migrations between overused servers to unused servers. The advantage...

We study the performance of the optical network architecture NGreen which is based on an optical slotted ring. The random part of the end to end delay comes from the times needed to build an optical container from arriving Data Units and the insertion of the optical container on the ring. Here, to study the first problem, we build a Discrete Time M...

We model the end to end delay and energy efficiency in the optical network architecture NGREEN . As the architecture is based on an optical ring, the random part of the delay comes from the random times needed to build an optical container from arriving Data Units and the insertion of the optical container on the ring. We first build a DTMC (Discre...

Current architecture of many computer systems relies on dynamic allocation of a pool of resources according to workload conditions to meet specific performance objectives while minimizing cost (e.g., energy or billing). In such systems, different levels of operation may be defined, and switching between operating levels occurs at certain thresholds...

We analyze here a cloud system represented by hysteresis multi server queueing system. It is characterized by forward and backward thresholds for activation and deactivation of block of servers representing a set of VMs (Virtual Machines). The system is represented by a complex Markov Chain which is difficult to analyse when the size of the system...

The IEEE 802.15.4 standard has been introduced for low latency and low energy consumption in wireless sensor networks. To better support the requirements of industrial applications, where the use of this standard is limited, the low latency deterministic network (LLDN) mechanism of the IEEE 802.15.4e amendment has been proposed. In this paper, we d...

We generalise to non stationary traffics an approach that we have previously proposed to derive performance bounds of a queue under histogram-based input traffics. We use strong stochastic ordering to derive stochastic bounds on the queue length and the output traffic. These bounds are valid for transient distributions of these measures and also fo...

We present an extension of a methodology based on monotonicity of various networking elements and measurements performed on real networks. Assuming the stationarity of flows, we obtain histograms (distributions) for the arrivals. Unfortunately, these distributions have a large number of values and the numerical analysis is extremely time-consuming....

We present an approach to derive performance bounds of a queue under histogram-based input traffics. The results are obtained through strong stochastic bounds on the queue length and on the output traffic. The bounds provide probability inequalities on transient behaviors and on steady-state when it exists. We consider both stationary and non-stati...

We state some stochastic comparison results for the loss probabilities and the time to live in a tandem network with two queues. We consider such a network under batch arrivals and constant service time. We show that making the service capacity of the first queue finite will improve the performance. More precisely, we derive stochastic bounds for t...

We propose to evaluate the performance of a cloud node (data center) using hysteresis queueing systems and stochastic bound methods. We represent the dynamic behavior of the cloud node by a hysteresis queueing system with forward and backward threshold vectors. The client requests (or jobs) are represented by bulk arrivals entering the buffer, and...

In this paper, we propose to model a node cloud by a threshold based queueing system with hysteresis. The client requests (or jobs) arrive into the buffer, and are executed by service centers or Virtual Machines (VMs). We suppose that virtual machines are activated and deactivated according to the occupation of the queue, in order to model the dyna...

Cloud providers need to size their systems to determine the right amount of resources to allocate as a function of customer’s needs so as to meet their SLAs (Service Level Agreement), while at the same time minimizing their costs and energy use. Queueing theory based tools are a natural choice when dealing with performance aspects of the QoS (Quali...

We study queueing networks similar to Jackson networks, modelled by a multidimensional Markov chain. The performance analysis may be very difficult or intractable, if there is no specific solution form. We explain how stochastic comparisons of Markov chains can be used to overcome this problem. We build new queueing which are easier to analyse and...

L'algorithme de calcul des bornes sur les distributions empiriques est accessible sur http://www.prism.uvsq.fr/~safa/Publications_files/wodes12.pdf et il a été présenté à WODES 2012.

We analyze the performance of a network under general traffics derived from traces. We apply stochastic comparisons in order to derive bounding histograms with a reduced size and complexity. We prove some stochastic monotonicity properties for the network elements, in order to derive bounds on the performance measures such as delays and losses. We...

Exact analysis of queueing networks under real traffic histograms becomes quickly intractable due to the state explosion. In this paper, we propose to apply the stochastic comparison method to derive performance measure bounds under histogram-based traffics. We apply an algorithm based on dynamic programming to derive bounding traffic histograms on...

We analyze transient and stationary behaviors of multidimensional Markov chains defined on large state spaces. In this paper, we apply stochastic comparisons on partially ordered state which could be very interesting for performance evaluation of computer networks. We propose an algorithm for bounding aggregations in order to derive upper and lower...

We point out the impact of buffer management and packet scheduling policy on QoS parameter values. We propose a new buffering/scheduling algorithm adopted in optical metro/core network to manage the performance of packet loss ratio (PLR) taking into account different classes of service. As a result, we compare PLR of the new buffering/scheduling al...

In mobile networks, call admission control (CAC) is widely used in reaching of the quality of service (QoS) requirements. However, as the CACs schemes give priority to the handoff calls, the blocking probability is degraded. In this paper we propose a new scheme which is based on the combinaison of CAC scheme and load sharing policy between a clust...

We consider large queueing networks for which transient and stationary probability distributions are very difficult or impossible to obtain due to the state space explosion problem. In performance analysis, we need in general to study only a part of the network (a node or a path). Thus, we propose to define bounding systems that lead to compute bou...

We present an algorithmic technique based on stochastic ordering to obtain upper and lower bounding distributions for the results of some optimisation problems on discrete random variables which are hard to solve exactly due to the multiplicative increasing size of the distribution at each step. We illustrate the approach with the distribution of t...

End to end QoS (Quality of Service) is crucial in computer networks, but very hard to study as the systems are in general very complex. We suppose that systems can be modeled by multidimensional Markov processes, which could be very hard to analyse if there is no specific solution form. We propose to apply stochastic comparisons of Markov processes...

The ⪯φ stochastic comparison (⪯φ ε {⪯st, ⪯wk, ⪯wk*}) of multidimensional Continuous Time Markov Chains (CTMC)s is an efficient but a complex method for the performability evaluation of computer systems. Different techniques can be applied for the stochastic comparison of Markov chains. The coupling is an intuitive method, and may be applied by comp...

We apply stochastic comparisons in order to bound the transient behavior of G-networks with catastrophes. These networks belong to Gelenbe's networks, with both positive and negative customers (or signals). We consider catastrophes where the signal deletes all customers in a queue. G-networks have a known product form steady-state distribution, but...

The study focuses on packet aggregation mechanisms on the edge router of an optical network. The device works as an interface between the electronic and optical domains : it takes IP packets coming from client layers and converts them into optical packets to be sent into the optical network. An efficient aggregation mechanism supporting QoS (Qualit...

We propose to study end to end delays in slotted optical MAN (Metropolitan Area Networks) ring networks. Edge nodes interconnect the fibre of the MAN and the client layer. We propose a mechanism based on IP traffic aggregations with QoS requirements in order to build optical packets. IP packet aggregation is performed in a loop manner by always beg...

We study the transient distribution of some G-networks of queues with customers and signals. After its service completion a customer moves to another queue and may become a signal. We consider catastrophes where the signal deletes all customers in a queue. Both networks with negative customers and with catastrophes belong to well- known Gelenbe’s n...

In this paper, we study the performability of telecommunication systems. Performability verification may be very complex as it is the joint evaluation of performance and dependability. We consider the composite Erlang loss model representing a telecommunication switching system. In this model we suppose that each channel can be free/busy for the pe...

Quality of performance measure bounds is crucial for an accurate dimensioning of computer network resources. We study stochastic comparisons of multidimensional Markov processes for which quantitative analysis could be intractable if there is no specific solution form. On partially ordered state space, different stochastic orderings can be defined...

Stochastic monotonicity is one of the sufficient conditions for stochastic comparisons of Markov chains. On a partially ordered state space, several stochastic orderings can be defined by means of increasing sets. The most known is the strong stochastic (sample-path) ordering, but weaker orderings (weak and weak*) could be defined by restricting th...

The probabilistic model checking provides a precise formalism for the performance and reliability verification of telecommunication systems modeled by Markov chains. We study a queueing system similar to a Jackson network except that queues have a finite capacity. We propose to study in this paper (state and path) formulas from the Continuous Stoch...

We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indices bounds. The main objective is to find Markovian bounding models with reduced state spaces, which are easier to solve. We apply the methodology to performance evaluation of complex telecommunication systems modelled by larg...

The IEEE 802.11 wireless standard uses the carrier sense multiple access with collision avoidance (CSMA/CA) as its MAC protocol (during the distributed coordination function period). This protocol is an adaptation of the CSMA/CD of the wired networks. CSMA/CA mechanism cannot guarantee quality of service (QoS) required by the application because of...

This paper presents an algorithm based on stochastic comparisons in order to check formulas with rewards on multidimensional continuous time Markov chains (CTMC). These formulas are expressed in continuous stochastic logic (CSL) which includes means to express transient, steady-state and path performance measures. However, using simulations or anal...

End to end QoS of communication systems is essential for users but their performance evaluation is a complex issue. The abstraction of such systems are usually given by multidimensional Markov processes whose analysis is very difficult and even intractable, if there is no specific solution form. In this study, we propose an algorithm in order to au...

We use a mathematical method based on stochastic comparison of multidimensional Markov chains in order to compute packet loss rates in IP routers for MPLS networks. The key idea of this methodology is that given a complex system represented by a Markov chain which is too large to be solved, we propose to build smaller Markov chains providing perfor...

In this paper, a novel approach for efficiently supporting IP packets directly into a slotted optical wavelength-division-multiplexing (WDM) layer with several quality of service (QoS) requirements is presented and analyzed. The approach is based on two main features. First, an aggregation cycle is performed at fixed time intervals by assembling se...

Spacial wavelength reuse, or destination stripping, increases the capacity of packet-switched unidirectional and bidirectional ring networks, and promotes them to support multicast traffic. In this paper, an analytical model is developed to evaluate the maximum achievable transmitter throughput (i.e., the capacity) of such networks, in the presence...

Performance evaluation of telecommunication and computer systems is essential but a complex issue in general. Quantitative analysis of systems represented by multidimensional Markov processes models is very difficult and may be intractable if there is no specific solution form. In this study, we propose an algorithm in order to derive aggregated Ma...

Scheutzow et al. have presented an analytical model to evaluate the capacity of the unidirectional and bidirectional TT-FR packet-switched ring network under multicast traffic (i.e., a ring where each node is equipped with one tuned transmitter, TT, and one fixed receiver, FR). In this paper, we investigate the impact of multicast on the access del...

A simple analytical model is presented to evaluate the effective multicast capacity of unidirectional multi-channel slotted ring networks where each node is equipped with one fixed or tuned transmitter and an array of fixed receivers (i.e., FT-FR w and TT-FR w systems). Furthermore, an approximate approach is developed to compare the mean access de...

In this contribution, we consider a novel approach for efficiently supporting IP packets directly into a slotted optical wavelength-division-multiplexing (WDM) layer with several quality of service (QoS) requirements. The approach is based on performing IP packet aggregation at fixed time intervals before the optical conversion phase. We introduce...

The paper proposes two IP packet aggregation techniques, called DAT (Deterministic Aggregation Technique) and WATT (Work-conserving Aggregation Technique with Timer), to adapt IP traffic to a multi-service optical slotted network. To perform aggregation, IP packets belonging to different classes of service (CoS) are polled according to the strict p...

The modeling of mobile networks is difficult because of the number of users and their mobilities. In this study, we present a new methodology based upon stochastic ordering of Markov chains in order to evaluate the performance measures in wireless networks. These kind of networks are based on cellular systems. The cellular systems use different fre...

We propose in this paper to evaluate the performance of an IP switch in MPLS networks. We focus our study on an important QoS parameters for users which is the packet loss rates. We use a mathematical method based on stochastic comparisons of Markov chains in order to compute loss rate bounds. The system understudy can be represented by a multi-dim...

We present in this paper a mathematical method based on stochastic comparisons of Markov chains in order to compute in a mobile network performance measures that are important Q parameters for users: the dropping handover of voice and the blocking probability of a new voice call. The key idea of this methodology is that given a complex system repre...

We apply stochastic bounding methods with a partial order on the state space to the analysis of memory overflow in a router. Usually, stochastic bounds are associated to a total order implying useless constraints and decreasing the tightness of bounds. Here we present the basic methodology of sample path comparison with a partial order and some num...

In this paper we present an analytical model for the evaluation of access delays and bandwidth efficiency in wavelength-division multiplexing slotted-ring networks where nodes are equipped with one fixed transmitter and several fixed receivers. The system has been analyzed under uniform and non-uniform traffic patterns, for both source and destinat...

Based on discrete time Markov Chains, we develop an exact mathematical model for the performance evaluation of packet aggregation on the edge router of an optical network. This device works as an interface between the electronic and optical domains: it receives IP packets from the client layer and converts them into optical packets to be sent insid...

Summary form only given. Due to random access in wireless networks using CSMA/CA like in Wifi networks, the integration of services with a lot of quality of service needs is impossible. In this paper, we propose to study and to evaluate a new MAC protocol that takes into account different types of traffic (e.g.. voice and data) and for each traffic...

We propose to compute mean packet delays in an optical MAN ring for different optical packet formats: FLP, SVLP and VLP. Several stations are connected to the ring. Each of them generates electronic packets (IP, Ethernet) which are transformed into optical packets. The MAC protocol is based on the empty slot procedure. The upstream station connecte...

We propose to study the performance of an unslotted optical MAN ring operating with asynchronous variable length optical packets. Source stations are connected to the optical ring. They take electronic packets coming from client layers and convert them into optical packets. The MAC protocol is based on the synchronous “empty slot” procedure. The pe...

This study focuses on the edge router of an optical network. This device works as an interface between the electronic and optical domains : it takes packets coming from client layers and converts them into optical packets to be sent into the optical network. Arriving variable length client packets fill the optical packet until the latter is full or...

We describe a specialized modeling tool based on a new model of synchronized activities, which is a superset of Queuing Networks. The tool includes a graphical user interface, a simulator and a range of analytical solvers. INTRODUCTION The study of quantitative models for workloadarchitecture (in)adequacy is of central importance in the context of...

In this paper, we compute the stochastic bounds on the cell loss rates in an ATM switch. The spatial priority in the buffer is controlled by the Push-Out mechanism, while the time priority is managed in the FIFO manner. We consider an i.i.d arrival process of cells and a constant switching time of a cell. Therefore, the system can be modelled by a...

This paper presents an algorithm based on stochas-tic comparisons in order to check formulas with rewards on multidimensional Continuous Time Markov Chains (CTMC). These formulas are expressed in Continuous Stochastic Logic (CSL) which includes means to express transient, steady-state and path performance measures. However, computation of transient...

In this contribution, we consider a novel approach for e-ciently supporting IP packets directly into a slotted optical wavelength-division-multiplexing (WDM) layer with several QoS requirements. The approach is based on two main features. First, an aggregation cycle is performed at flxed time intervals by assembling several IP packets in a single m...

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