Risk-hedging using options for an upgrading investment in a data network

In this paper, we illustrate how a mobile data network operator can plan an upgrading investment to anticipate explosions of the demand, taking into account the expected generated profit and the customers satisfaction. The former parameter grows with the demand, whereas the latter sinks if the demand is too high as throughput may collapse. As the equipment price decreases with time, it may be interesting to wait rather than to invest at once. We then propose a real option strategy to hedge against the risk that the investment has to take place earlier than expected. At last, we price this option with a backward dynamic programming approach, using recent improvements based on least-squares estimations.

Optimizing the date of an upgrading investment in a data network

Due to the introduction of new services, the volume of data transferred in mobile networks is rapidly growing and operators periodically face the necessity to upgrade their network. Such upgrades allow them to increase the capacity and provide adequate Quality of Service (QoS). In this paper we propose a general framework for deriving the optimal date for a network upgrade. We show that this date is the result of a compromise between the decrease of upgrade investment cost with time and the loss of profit generated by insufficient capacity. The upgrade should hence be performed when the loss of profit, derived using analytical capacity expressions, exceeds the expected discount. The model presented herein accounts for the randomness of the demand and upgrading cost functions, and results are given for a HSDPA network.data flows, brownian motion, quality of service, customer satisfaction

A population model based on a Poisson line tessellation

International audienceIn this paper, we introduce a new population model. Taking the geometry of cities into account by adding roads, we build a Cox process driven by a Poisson line tessellation. We perform several shot-noise computations according to various generalizations of our original process. This allows us to derive analytical formulas for the uplink coverage probability in each case

An Interaction-Based Mobility Model for Dynamic Hot Spot Analysis

International audienceIn this paper, we analyze phenomena related to user clumps and hot spots occuring in mobile networks at the occasion of large urban mass gatherings in large cities. Our analysis is based on observations made on mobility traces of GSM users in several large cities. Classical mobility models, such as the random waypoint, do not allow one to represent the observed dynamics of clumps in a proper manner. This motivates the introduction and the mathematical analysis of a new interaction-based mobility model, which is the main contribution of the present paper. This model is shown to allow one to describe the dynamics of clumps and in particular to predict key phenomena such as the building of hot spots and the scattering between hot spots, which play a key role in the engineering of wireless networks during such events. We show how to obtain the main parameters of this model from simple communication activity measurements and we illustrate this calibration process on real cases

An Interaction-Based Mobility Model for Dynamic Hot Spot Analysis

In this paper, we analyze phenomena related to user clumps and hot spots occurring in mobile networks at the occasion of large urban mass gatherings in large cities. Our analysis is based on observations made on mobility traces of GSM users in several large cities. Classical mobility models, such as the random waypoint, do not allow one to represent the observed dynamics of clumps in a proper manner. This motivates the introduction and the mathematical analysis of a new interaction based mobility model, which is the main contribution of the present paper. This model is shown to allow one to describe the dynamics of clumps and in particular to predict key phenomena such as the building of hot spots and the scattering between hot spots, which play a key role in the engineering of wireless networks during such events. We show how to obtain the main parameters of this model from simple communication activity measurements and we illustrate this calibration process on real cases

Space-time processes in stochastic geometry and application to modelling of telecommunication networks

L'objectif de cette thèse est de réunir les deux approches suivantes qui existent actuellement pour étudier une foule: ou bien à temps fixé on s'intéresse à la distribution spatiale des individus, ou bien on suit un seul individu à la fois au cours du temps. On se propose de construire des processus spatio-temporels, qui, comme leur nom l'indique, permettraient de rendre compte du caractère aléatoire des usages d'une foule dans un réseau de télécommunication, à la fois du point de vue spatial (modèles de route) et du point de vue temporel (déplacements sur ces routes, usages qui varient au cours de ces déplacements…). Une fois ces processus construits de manière rigoureuse, on étudie leur comportement d'une manière fine. Nous développons trois modèles différents qui chacun mènent à des formules analytiques fermées, ce qui permet de les utiliser d'une manière très confortable à des fins de dimensionnement.This thesis consists in joining two approaches that currently exist when one wants to study crowds phenomena: either taking a snapshot by freezing time to study the spatial repartition of the individuals, or following one given individual over time.We build space-time processes that let us model random phenomena in a crowd, being on a spatial level (roads models) or a time level (movings on these roads, space-dependent behaviors…). Once we have built them in a rigorous manner, we study their properties, which let us obtain analytical closed formulas that can be widely used for dimensioning purposes

Space-time processes in stochastic geometry and application to modelling of telecommunication networks

L'objectif de cette thèse est de réunir les deux approches suivantes qui existent actuellement pour étudier une foule: ou bien à temps fixé on s'intéresse à la distribution spatiale des individus, ou bien on suit un seul individu à la fois au cours du temps. On se propose de construire des processus spatio-temporels, qui, comme leur nom l'indique, permettraient de rendre compte du caractère aléatoire des usages d'une foule dans un réseau de télécommunication, à la fois du point de vue spatial (modèles de route) et du point de vue temporel (déplacements sur ces routes, usages qui varient au cours de ces déplacements…). Une fois ces processus construits de manière rigoureuse, on étudie leur comportement d'une manière fine. Nous développons trois modèles différents qui chacun mènent à des formules analytiques fermées, ce qui permet de les utiliser d'une manière très confortable à des fins de dimensionnement.This thesis consists in joining two approaches that currently exist when one wants to study crowds phenomena: either taking a snapshot by freezing time to study the spatial repartition of the individuals, or following one given individual over time.We build space-time processes that let us model random phenomena in a crowd, being on a spatial level (roads models) or a time level (movings on these roads, space-dependent behaviors…). Once we have built them in a rigorous manner, we study their properties, which let us obtain analytical closed formulas that can be widely used for dimensioning purposes

Processus spatio-temporels en géométrie stochastique et application à la modélisation de réseaux de télécommunication

This thesis consists in joining two approaches that currently exist when one wants to study crowds phenomena: either taking a snapshot by freezing time to study the spatial repartition of the individuals, or following one given individual over time.We build space-time processes that let us model random phenomena in a crowd, being on a spatial level (roads models) or a time level (movings on these roads, space-dependent behaviors…). Once we have built them in a rigorous manner, we study their properties, which let us obtain analytical closed formulas that can be widely used for dimensioning purposes.L'objectif de cette thèse est de réunir les deux approches suivantes qui existent actuellement pour étudier une foule: ou bien à temps fixé on s'intéresse à la distribution spatiale des individus, ou bien on suit un seul individu à la fois au cours du temps. On se propose de construire des processus spatio-temporels, qui, comme leur nom l'indique, permettraient de rendre compte du caractère aléatoire des usages d'une foule dans un réseau de télécommunication, à la fois du point de vue spatial (modèles de route) et du point de vue temporel (déplacements sur ces routes, usages qui varient au cours de ces déplacements…). Une fois ces processus construits de manière rigoureuse, on étudie leur comportement d'une manière fine. Nous développons trois modèles différents qui chacun mènent à des formules analytiques fermées, ce qui permet de les utiliser d'une manière très confortable à des fins de dimensionnement