Yezekael Hayel

A mathematical analysis of the cumulus pricing scheme

One important task in current and future communication networks is to define a suitable pricing scheme. It is then preferable to formulate a mathematical model, so that parameters will be optimized and important properties such as fairness or truthful anticipated load revelation (or incentive compatibility) will be verified. In this paper we study a simple and promising scheme called the cumulus pricing scheme, which can address service differentiation and scalability among other issues. Based on a mathematical model, we determine values for optimizing the providers revenue, which happens under the constraint that each user has an incentive to reveal its anticipated load. This has led to a small variation of the initial model from the literature as in the modelling, cumulus points are translated into financial terms, and measurements induce a cost as well.

Pricing for heterogeneous services at a discriminatory processor sharing queue

In order to deal with applications with different quality of service requirements, service differentiation has to be implemented, especially in case of congestion. Different scheduling policies can be applied at a queue, such as strict priorities, generalized processor sharing, or discriminatory processor sharing. While prices optimizing the network revenue have been determined in the first two above cases, and the optimal revenue compared, nothing had been done yet on discriminatory processor sharing (DPS). Though, at the session level, processor sharing is known to properly model TCP flows behavior. DPS then models multiple TCP flows at a router providing differentiated services. We study here what pricing induces on a DPS router when two types of application compete for service, what is the resulting equilibrium, and explain how optimal prices can be found.

An Anonymous Sequential Game Approach for Battery State Dependent Power Control

The sensitivity of mobile terminals to energy and power limitations keeps posing challenges to wireless technology. The ratio between the useful signals power and that of noise and interferences has a crucial impact on the achievable throughputs and on outage aspects, little has been done concerning another central challenge that limited energy poses: that of limitation on battery life. In this paper we study power control in a way that combines the two aforementioned aspects. We propose a modeling approach which extends the Anonymous Sequential Game framework introduced in 1988 by Jovanovic and Rosenthal. The approach is designed for systems that have a very large number of interacting decision makers, so large that they can be modeled as a continuum of players. We introduce an appropriate equilibrium concept for this game (which extends the Wardrop equilibrium by including random individual states with controlled transitions), characterize the structure of the equilibrium policies and provide two efficient equilibrium computation procedures.

Optimal Static Pricing of Reverse-Link DS-CDMA Multiclass Traffic

Nowadays, third generation (3G) wireless systems are becoming very popular. Direct-sequence code-division multiple-access (DS-CDMA) is implemented in these systems but, due to a limited radio spectrum and the growing number of demanding applications, it seems likely that congestion would still remain an issue. Pricing appears as a simple way to tackle this problem. This paper studies the impact of a per-packet static pricing scheme on the use of the reverse-link in a cell, where demand (defined through the so-called utility functions) decreases when prices increase or quality of service decreases. Since DS-CDMA supports integrated services, we also deal with pricing of multiple classes. In a first step, we determine as a Nash equilibrium the number of customers that actually apply for service, depending on demand. In a second step, assuming perfect power control, we find the prices and received powers optimizing the service providers revenue. We find that in the case where potential demand always exceeds capacity, the base stations best interest is to favor only one class, but that is not the case in a realistic situation when considering potential demand as a random variable over time

State policy couple dynamics in evolutionary games

Standard Evolutionary Game framework is a useful tool to study large interacting systems and to understand the strategic behavior of individuals in such complex systems. Adding an individual state to model local feature of each player in this context, allows one to study a wider range of problems in various application areas as networking, biology, etc. In this paper, we introduce such an extension of evolutionary game framework and particularly, we focus on the dynamical aspects of this system. Precisely, we study the coupled dynamics of the strategies and the individual states inside a population of interacting individuals. We consider here a two strategies evolutionary game. We first obtain a system of combined dynamics and we show that the rest-points of this system are equilibria of our evolutionary game with individual state. Second, by assuming two different time scales between states and strategy dynamics, we can compute explicitly the equilibria. Then, by transforming our evolutionary game with individual states into a standard evolutionary game, we obtain an equilibrium which is equivalent, in terms of occupation measure, to the previous one. All our results are illustrated with numerical results.

Analysis of a Yield Management Model for on Demand Computing Centers

The concept of yield management for IT infrastructures, and in particular for on demand IT utilities was recently introduced in [17]. The present paper provides a detailed analysis of that model, both in simplified cases where an analytical analysis is possible, and numerically on larger problem instances, and confirms the significant revenue benefit that can accrue through use of yield management in an IT on demand operating environment.