Greedy walk on the real line

We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space-time half plane. The server adopts a greedy routing mechanism, traveling toward the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.Comment: Published at http://dx.doi.org/10.1214/13-AOP898 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Evolution of a Spatial Stochastic Network

The asymptotic behavior of a stochastic network represented by a birth and death processes of particles on a compact state space is analyzed. Births: Particles are created at rate $\lambda_+$ and their location is independent of the current configuration. Deaths are due to negative particles arriving at rate $\lambda_-$. The death of a particle occurs when a negative particle arrives in its neighborhood and kills it. Several killing schemes are considered. The arriving locations of positive and negative particles are assumed to have the same distribution. By using a combination of monotonicity properties and invariance relations it is shown that the configurations of particles converge in distribution for several models. The problems of uniqueness of invariant measures and of the existence of accumulation points for the limiting configurations are also investigated. It is shown for several natural models that if $\lambda_+<\lambda_-$ then the asymptotic configuration has a finite number of points with probability 1. Examples with $\lambda_+<\lambda_-$ and an infinite number of particles in the limit are also presented

Scheduling algorithms for throughput maximization in time-varying networks with reconfiguration delays

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 247-258).We consider the control of possibly time-varying wireless networks under reconfiguration delays. Reconfiguration delay is the time it takes to switch network resources from one subset of nodes to another and it is a widespread phenomenon observed in many practical systems. Optimal control of networks has been studied to a great extent in the literature, however, the significant effects of reconfiguration delays received limited attention. Moreover, simultaneous presence of time-varying channels and reconfiguration delays has never been considered and we show that it impacts the system fundamentally. We first consider a Delay Tolerant Network model where data messages arriving randomly in time and space are collected by mobile collectors. In this setting reconfiguration delays correspond to travel times of collectors. We utilize a combination of wireless transmission and controlled mobility to improve the system delay scaling with load [rho] from [theta](1/(1-[rho])²) to [theta](1/1-[rho]), where the former is the delay for the corresponding system without wireless transmission. We propose control algorithms that stabilize the system whenever possible and have optimal delay scaling. Next, we consider a general queuing network model under reconfiguration delays and interference constraints which includes wireless, satellite and optical networks as special cases. We characterize the impacts of reconfiguration delays on system stability and delay, and propose scheduling algorithms that persist with service schedules for durations of time based on queue lengths to minimize negative impacts of reconfiguration delays. These algorithms provide throughput-optimality without requiring knowledge of arrival rates since they dynamically adapt inter-switching durations to stochastic arrivals. Finally, we present optimal scheduling under time-varying channels and reconfiguration delays, which is the main contribution of this thesis. We show that under the simultaneous presence of these two phenomenon network stability region shrinks, previously suggested policies are unstable, and new algorithmic approaches are necessary. We propose techniques based on state-action frequencies of Markov Decision Process theory to characterize the network stability region and propose throughput-optimal algorithms. The state-action frequency technique is applicable to a broad class of systems with or without reconfiguration delays, and provides a new framework for characterizing network stability region and developing throughput-optimal scheduling policies.by Güner Dinc̦er C̦elik.Ph.D

Towards Thompson Sampling for Complex Bayesian Reasoning

Paper III, IV, and VI are not available as a part of the dissertation due to the copyright.Thompson Sampling (TS) is a state-of-art algorithm for bandit problems set in a Bayesian framework. Both the theoretical foundation and the empirical efficiency of TS is wellexplored for plain bandit problems. However, the Bayesian underpinning of TS means that TS could potentially be applied to other, more complex, problems as well, beyond the bandit problem, if suitable Bayesian structures can be found. The objective of this thesis is the development and analysis of TS-based schemes for more complex optimization problems, founded on Bayesian reasoning. We address several complex optimization problems where the previous state-of-art relies on a relatively myopic perspective on the problem. These includes stochastic searching on the line, the Goore game, the knapsack problem, travel time estimation, and equipartitioning. Instead of employing Bayesian reasoning to obtain a solution, they rely on carefully engineered rules. In all brevity, we recast each of these optimization problems in a Bayesian framework, introducing dedicated TS based solution schemes. For all of the addressed problems, the results show that besides being more effective, the TS based approaches we introduce are also capable of solving more adverse versions of the problems, such as dealing with stochastic liars.publishedVersio

Prediction-based techniques for the optimization of mobile networks

Mención Internacional en el título de doctorMobile cellular networks are complex system whose behavior is characterized by the superposition of several random phenomena, most of which, related to human activities, such as mobility, communications and network usage. However, when observed in their totality, the many individual components merge into more deterministic patterns and trends start to be identifiable and predictable. In this thesis we analyze a recent branch of network optimization that is commonly referred to as anticipatory networking and that entails the combination of prediction solutions and network optimization schemes. The main intuition behind anticipatory networking is that knowing in advance what is going on in the network can help understanding potentially severe problems and mitigate their impact by applying solution when they are still in their initial states. Conversely, network forecast might also indicate a future improvement in the overall network condition (i.e. load reduction or better signal quality reported from users). In such a case, resources can be assigned more sparingly requiring users to rely on buffered information while waiting for the better condition when it will be more convenient to grant more resources. In the beginning of this thesis we will survey the current anticipatory networking panorama and the many prediction and optimization solutions proposed so far. In the main body of the work, we will propose our novel solutions to the problem, the tools and methodologies we designed to evaluate them and to perform a real world evaluation of our schemes. By the end of this work it will be clear that not only is anticipatory networking a very promising theoretical framework, but also that it is feasible and it can deliver substantial benefit to current and next generation mobile networks. In fact, with both our theoretical and practical results we show evidences that more than one third of the resources can be saved and even larger gain can be achieved for data rate enhancements.Programa Oficial de Doctorado en Ingeniería TelemáticaPresidente: Albert Banchs Roca.- Presidente: Pablo Serrano Yañez-Mingot.- Secretario: Jorge Ortín Gracia.- Vocal: Guevara Noubi