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While cognitive radio enables spectrum-efficient wireless communication, radio frequency (RF) energy harvesting from ambient interference is an enabler for energy-efficient wireless communication. In this paper, we model and analyze cognitive and energy harvesting-based D2D communication in cellular networks. The cognitive D2D transmitters harvest energy from ambient interference and use one of the channels allocated to cellular users (in uplink or downlink), which is referred to as the D2D channel, to communicate with the corresponding receivers. We investigate two spectrum access policies for cellular communication in the uplink or downlink, namely, random spectrum access (RSA) policy and prioritized spectrum access (PSA) policy. In RSA, any of the available channels including the channel used by the D2D transmitters can be selected randomly for cellular communication, while in PSA the D2D channel is used only when all of the other channels are occupied. A D2D transmitter can communicate successfully with its receiver only when it harvests enough energy to perform channel inversion toward the receiver, the D2D channel is free, and the $\mathsf{SINR}$ at the receiver is above the required threshold; otherwise, an outage occurs for the D2D communication. We use tools from stochastic geometry to evaluate the performance of the proposed communication system model with general path-loss exponent in terms of outage probability for D2D and cellular users. We show that energy harvesting can be a reliable alternative to power cognitive D2D transmitters while achieving acceptable performance. Under the same $\mathsf{SINR}$ outage requirements as for the non-cognitive case, cognitive channel access improves the outage probability for D2D users for both the spectrum access policies.

This research lays down a mathematical framework within which a system of interacting entities, such as a swarm robotic system, operating in a dynamic and uncertain environment can be analyzed for its properties such as stability, robustness, and emergent behavior. The framework, based upon stochastic differential equations and the Fokker-Planck formalism, allows the calculation of transient and steady state probability densities of the states of these systems. The framework has been applied to two scenarios related to swarm systems. The first scenario relates to a robotic swarm, the dynamics of which is inspired by ant foraging. The article develops a continuous time reaction-diffusion model based on Keller-Segel model of bactetrial chemotaxis and establishes a connection with the Fokker-Planck formalism. In addition, the authors also present a distributed control law in continuous time that combines gradient following for pheromone concentration as well as food scent with random motion seen in ants. The second scenario relates to a system of robots interacting via non-linear potentials and experiencing random excitations. The proposed framework allows calculation of probability density functions of states of the robots, such as positions and velocities, that helps analyze the stability of system and study its response to random excitations.

Supply and demand in the World oil market are balanced through responses to price movement with considerable complexity in the evolution of underlying supply-demand expectation process. In order to be able to understand the price balancing process, it is important to know the economic forces and the behavior of energy commodity spot price processes. The relationship between the different energy sources and its utility together with uncertainty also play a role in many important energy issues. The qualitative and quantitative behavior of energy commodities in which the trend in price of one commodity coincides with the trend in price of other commodities, have always raised the questions regarding their interactions. Moreover, if there is any interaction, then one would like to know the extent of influence on each other. In this work, we undertake the study to shed a light on the above highlighted processes and issues. The presented study systematically deals with the development of stochastic dynamic models and mathematical, statistical and computational analysis of energy commodity spot price and interaction processes.

In this report, we include the dissertation thesis the grant has funded together with a list of publications, and invitations the funded research has generated. Concepts in classification and recognition problems. 1. We have explored the potential of combining geometrical as well as topological information in capturing the essence of an object for classification and recognition purposes. The geometrical information within a topologically homogeneous part of an object is captured through a set of level curves, while the topology is extracted from the singular points. 2. Defining probability models on manifolds as would be required by the surface of an object remains a challenging topic. The approach here exploits a triangulated approximation on which a geodesic is defined to capture the nonlinear intrinsic structure of an object surface. 3. Obtaining distribution for objects in turn allows us to compare them by IT measures.

In this report, we include the dissertation thesis the grant has funded together with a list of publications, and invitations the funded research has generated. Concepts in classification and recognition problems. 1. We have explored the potential of combining geometrical as well as topological information in capturing the essence of an object for classification and recognition purposes. The geometrical information within a topologically homogeneous part of an object is captured through a set of level curves, while the topology is extracted from the singular points. 2. Defining probability models on manifolds as would be required by the surface of an object remains a challenging topic. The approach here exploits a triangulated approximation on which a geodesic is defined to capture the nonlinear intrinsic structure of an object surface. 3. Obtaining distribution for objects in turn allows us to compare them by IT measures.

This paper presents a tutorial on stochastic geometry (SG) based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. The paper starts by modeling and analyzing the baseband interference in a basic cellular network model. Then, it characterizes signal-to-interference-plus-noise-ratio (SINR) and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and rate analysis is presented. Although the main focus of the paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. The paper then extends the baseline unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. Finally, we point out future research directions.

We present a new stochastic service model with capacity sharing and interruptions, appropriate for the evaluation of the quality of real-time streaming (RTS), like e.g. mobile TV, in wireless cellular networks. The general model takes into account multi-class Markovian process of call arrivals, (to capture different radio channel conditions, requested streaming bit-rates and durations) and allows for a general resource allocation policy saying which users are temporarily denied the requested fixed streaming bit-rates (put in outage) due to resource constraints. We give expressions for several important performance characteristics of the model, including mean time spent in outage and mean number of outage incidents for a typical user of a given class. These expressions involve only stationary probabilities of the (free) traffic demand process, which is a vector of independent Poisson random variables describing the number of users of different classes. In order to analyze RTS in 3GPP Long Term Evolution (LTE) cellular networks, we specify our general model assuming orthogonal user channels with the peak bit-rates close to the theoretical Shannon's bound in the additive white Gaussian noise (AWGN) channel, which leads to the resource constraints in a multi-rate linear form. In this setting we consider a natural class of least-effort-served-first resource allocation policies, for which the characteristics of the model can be further evaluated using Fourier analysis of Poisson variables. Within this class we identify and evaluate an optimal and a fair policy, the latter being suggested by LTE implementations. We also propose some intermediate policies, which allow to solve the optimality/fairness tradeoff caused by unequal user radio-channel conditions. Our results can be used for the evaluation of the quality of RTS in LTE networks and dimensioning of these networks.

The Internet of Things (IoT) is large-scale by nature, which is manifested by the massive number of connected devices as well as their vast spatial existence. Cellular networks, which provide ubiquitous, reliable, and efficient wireless access, are natural candidates to provide the first-mile access for the data tsunami to be generated by the IoT. However, cellular networks may have scalability problems to provide uplink connectivity to massive numbers of connected things. To characterize the scalability of cellular uplink in the context of IoT networks, this paper develops a traffic-aware spatiotemporal mathematical model for IoT devices supported by cellular uplink connectivity. The developed model is based on stochastic geometry and queueing theory to account for the traffic requirement per IoT device, the different transmission strategies, and the mutual interference between the IoT devices. To this end, the developed model is utilized to characterize the extent to which cellular networks can accommodate IoT traffic as well as to assess and compare three different transmission strategies that incorporate a combination of transmission persistency, backoff, and power-ramping. The analysis and the results clearly illustrate the scalability problem imposed by IoT on cellular network and offer insights into effective scenarios for each transmission strategy.

Device-to-device (D2D) communication has huge potential for capacity and coverage enhancements for next generation cellular networks. The number of potential nodes for D2D communication is an important parameter that directly impacts the system capacity. In this paper, we derive analytic expression for average coverage probability of cellular user and corresponding number of potential D2D users. In this context, mature framework of stochastic geometry and Poisson point process has been used. The retention probability has been incorporated in Laplace functional to capture reduced path-loss and shortest distance criterion based D2D pairing. The numerical results show a close match between analytic expression and simulation setup.

This correspondence studies the secrecy communication of the single-input single-output multi-eavesdropper (SISOME) channel with multiple single-antenna jammers, where the jammers and eavesdroppers are distributed according to the independent two-dimensional homogeneous Poisson point process (PPP). For enhancing the physical layer security, we propose an opportunistic multiple jammer selection scheme, where the jammers whose channel gains to the legitimate receiver less than a threshold, are selected to transmit independent and identically distributed (\emph{i.i.d.}) Gaussian jamming signals to confound the eavesdroppers. We characterize the secrecy throughput achieved by our proposed jammer selection scheme, and show that the secrecy throughput is a quasi-concave function of the selection threshold.

In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying on a noise-limited approximation for typical millimeter wave network deployments, simple and exact integral as well as approximated and closed-form formulas for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. The proposed mathematical framework is applicable to cell association criteria based on the smallest path-loss and on the highest received power. It accounts for beamforming alignment errors and for multi-tier cellular network deployments. Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, both in terms of coverage probability and average rate.

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The advent of high speed computing on the PC provides new possibilities for data based modeling. One key is simulation. Simulation gives us a venue for dealing with parameter estimation in stochastic models not previously tractable. We consider examples from oncology, economics, statistical process control and epidemiology. We essentially consider two realities, the first consisting of random nonparametric interpolations of the data and the second random implementations based on a mathematical model. We use simulation to change the model parameters to bring the reality of the model to consistency with that of the data. Also, high speed computing enables us to carry out nonparametric data analysis in higher dimensions. The key here is to build algebraic rather than geometrical algorithms. We show how nonparametric data analysis in high dimensions (say greater than three) should generally not be treated as one of nonparametric density estimation but rather should start with finding centers of relatively high density and then use parametric approximations in the neighborhoods of these modes.

In a variety of neutron lifetime experiments, in addition to $\beta-$decay, neutrons can be lost by other mechanisms including wall losses. Failure to account for these other loss mechanisms produces systematic measurement error and associated systematic uncertainties in neutron lifetime measurements. In this work, we develop a physical model for neutron wall losses and construct a competing risks survival analysis model to account for losses due to the joint effect of $\beta-$decay losses, wall losses of marginally trapped neutrons, and an additional absorption mechanism. We determine the survival probability function associated with the wall loss mechanism by a Monte Carlo method. Based on a fit of the competing risks model to a subset of the NIST experimental data, we determine the mean lifetime of trapped neutrons to be approximately 700 s -- considerably less than the current best estimate of (880.1 $\pm$ 1.1) s promulgated by the Particle Data Group [1]. Currently, experimental studies are underway to determine if this discrepancy can be explained by neutron capture by ${}^3$He impurities in the trapping volume. Analysis of the full NIST data will be presented in a later publication.

This article is from PLoS ONE , volume 9 . Abstract Decision makers in epidemiology and other disciplines are faced with the daunting challenge of designing interventions that will be successful with high probability and robust against a multitude of uncertainties. To facilitate the decision making process in the context of a goal-oriented objective (e.g., eradicate polio by ), stochastic models can be used to map the probability of achieving the goal as a function of parameters. Each run of a stochastic model can be viewed as a Bernoulli trial in which “success” is returned if and only if the goal is achieved in simulation. However, each run can take a significant amount of time to complete, and many replicates are required to characterize each point in parameter space, so specialized algorithms are required to locate desirable interventions. To address this need, we present the Separatrix Algorithm, which strategically locates parameter combinations that are expected to achieve the goal with a user-specified probability of success (e.g. 95%). Technically, the algorithm iteratively combines density-corrected binary kernel regression with a novel information-gathering experiment design to produce results that are asymptotically correct and work well in practice. The Separatrix Algorithm is demonstrated on several test problems, and on a detailed individual-based simulation of malaria.

This paper aims at familiarizing the reader with Stochastic Hybrid Systems (SHSs) and enabling her to use these systems to model and analyze Networked Control Systems (NCSs). Towards this goal, we introduce two different models of SHSs and a set of theoretical tools for their analysis. In parallel with the presentation of the mathematical models and results, we provide a few simple examples that illustrate the use of SHSs to models NCSs.

Solid state drives (SSDs) have seen wide deployment in mobiles, desktops, and data centers due to their high I/O performance and low energy consumption. As SSDs write data out-of-place, garbage collection (GC) is required to erase and reclaim space with invalid data. However, GC poses additional writes that hinder the I/O performance, while SSD blocks can only endure a finite number of erasures. Thus, there is a performance-durability tradeoff on the design space of GC. To characterize the optimal tradeoff, this paper formulates an analytical model that explores the full optimal design space of any GC algorithm. We first present a stochastic Markov chain model that captures the I/O dynamics of large-scale SSDs, and adapt the mean-field approach to derive the asymptotic steady-state performance. We further prove the model convergence and generalize the model for all types of workload. Inspired by this model, we propose a randomized greedy algorithm (RGA) that can operate along the optimal tradeoff curve with a tunable parameter. Using trace-driven simulation on DiskSim with SSD add-ons, we demonstrate how RGA can be parameterized to realize the performance-durability tradeoff.

Due to the increasing heterogeneity and deployment density of emerging cellular networks, new flexible and scalable approaches for their modeling, simulation, analysis and optimization are needed. Recently, a new approach has been proposed: it is based on the theory of point processes and it leverages tools from stochastic geometry for tractable system-level modeling, performance evaluation and optimization. In this paper, we investigate the accuracy of this emerging abstraction for modeling cellular networks, by explicitly taking realistic base station locations, building footprints, spatial blockages and antenna radiation patterns into account. More specifically, the base station locations and the building footprints are taken from two publicly available databases from the United Kingdom. Our study confirms that the abstraction model based on stochastic geometry is capable of accurately modeling the communication performance of cellular networks in dense urban environments.

A barrage relay network (BRN) is a broadcast oriented ad hoc network involving autonomous cooperative communication, a slotted time-division frame format, and a coarse slot-level synchronization. While inherently a broadcast protocol, BRNs can support unicast transmission by superimposing a plurality of controlled barrage regions (CBRs) onto the network. Within each CBRs, a new packet is injected by the unicast source during the first time slot of each new radio frame. When a CBRs is sufficiently long that a packet might not be able to reach the other end within a radio frame, multiple packets can be active at the same time via spatial pipelining, resulting in interference within the CBRs. In this paper, the dynamics of packet transmission within a CBRs is described as a Markov process, and the outage probability of each link within the CBRs is evaluated in closed form, thereby accounting for fading and co-channel interference. In order to account for the linkage between simultaneous active packets and their temporal correlation, a Viterbi-like algorithm is used. Using this accurate analytical framework, a line network is optimized, which identifies the code rate, the number of relays, and the length of a radio frame that maximizes the transport capacity.

Our investigation consists of three inter-related thrusts: traffic modeling and analysis, network control, and information assurance in wireline and wireless networks. We model multi-scale behavior in network systems, where traffic and system behavior can be highly correlated over multiple time scales (e.g., LRD). We investigate the causes of LRD traffic in network systems, which may result from traffic correlation, protocol behavior (e.g., retransmissions), and network congestion; and statistically analyzed the properties of LRD traffic from empirical data sets. We develop a unifying theory for network control that exploits the interactions across network functionalities, operates at appropriate time-scales, and is effective in the presence of LRD. We formulate optimization and distributed control problems for providing network services, and study the impact of LRD traffic on network control, performance, and security. We also develop an integrative approach that combines the LRD modeling and network control to obtain non-parametric or semi-parametric techniques for the distributed detection of information flow and flow changes needed for preventing security attacks. We characterize flow detectability as a function of flow rate, delay and memory constraints, and developed distributed detection schemes that guarantee vanishingly low detection error probabilities.

Modeling and Analysis of Stochastic Systems

Modeling and Analysis of Stochastic Systems

Modeling and Analysis of Stochastic Systems