Neighbor selection and hitting probability in small-world graphs

Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very little knowledge of the graph itself. In an attempt to understand how such graphs arise we introduce a different criterion for graphs to be navigable in this sense, relating the neighbor selection of a vertex to the hitting probability of routed walks. In several models starting from both discrete and continuous settings, this can be shown to lead to graphs with the desired properties. It also leads directly to an evolutionary model for the creation of similar graphs by the stepwise rewiring of the edges, and we conjecture, supported by simulations, that these too are navigable.Comment: Published in at http://dx.doi.org/10.1214/07-AAP499 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

PERFORMANCE ANALYSIS AND OPTIMIZATION OF QUERY-BASED WIRELESS SENSOR NETWORKS

This dissertation is concerned with the modeling, analysis, and optimization of large-scale, query-based wireless sensor networks (WSNs). It addresses issues related to the time sensitivity of information retrieval and dissemination, network lifetime maximization, and optimal clustering of sensor nodes in mobile WSNs. First, a queueing-theoretic framework is proposed to evaluate the performance of such networks whose nodes detect and advertise significant events that are useful for only a limited time; queries generated by sensor nodes are also time-limited. The main performance parameter is the steady state proportion of generated queries that fail to be answered on time. A scalable approximation for this parameter is first derived assuming the transmission range of sensors is unlimited. Subsequently, the proportion of failed queries is approximated using a finite transmission range. The latter approximation is remarkably accurate, even when key model assumptions related to event and query lifetime distributions and network topology are violated. Second, optimization models are proposed to maximize the lifetime of a query-based WSN by selecting the transmission range for all of the sensor nodes, the resource replication level (or time-to-live counter) and the active/sleep schedule of nodes, subject to connectivity and quality-of-service constraints. An improved lower bound is provided for the minimum transmission range needed to ensure no network nodes are isolated with high probability. The optimization models select the optimal operating parameters in each period of a finite planning horizon, and computational results indicate that the maximum lifetime can be significantly extended by adjusting the key operating parameters as sensors fail over time due to energy depletion. Finally, optimization models are proposed to maximize the demand coverage and minimize the costs of locating, and relocating, cluster heads in mobile WSNs. In these models, the locations of mobile sensor nodes evolve randomly so that each sensor must be optimally assigned to a cluster head during each period of a finite planning horizon. Additionally, these models prescribe the optimal times at which to update the sensor locations to improve coverage. Computational experiments illustrate the usefulness of dynamically updating cluster head locations and sensor location information over time

Ambulance Emergency Response Optimization in Developing Countries

The lack of emergency medical transportation is viewed as the main barrier to the access of emergency medical care in low and middle-income countries (LMICs). In this paper, we present a robust optimization approach to optimize both the location and routing of emergency response vehicles, accounting for uncertainty in travel times and spatial demand characteristic of LMICs. We traveled to Dhaka, Bangladesh, the sixth largest and third most densely populated city in the world, to conduct field research resulting in the collection of two unique datasets that inform our approach. This data is leveraged to develop machine learning methodologies to estimate demand for emergency medical services in a LMIC setting and to predict the travel time between any two locations in the road network for different times of day and days of the week. We combine our robust optimization and machine learning frameworks with real data to provide an in-depth investigation into three policy-related questions. First, we demonstrate that outpost locations optimized for weekday rush hour lead to good performance for all times of day and days of the week. Second, we find that significant improvements in emergency response times can be achieved by re-locating a small number of outposts and that the performance of the current system could be replicated using only 30% of the resources. Lastly, we show that a fleet of small motorcycle-based ambulances has the potential to significantly outperform traditional ambulance vans. In particular, they are able to capture three times more demand while reducing the median response time by 42% due to increased routing flexibility offered by nimble vehicles on a larger road network. Our results provide practical insights for emergency response optimization that can be leveraged by hospital-based and private ambulance providers in Dhaka and other urban centers in LMICs

Delay, memory, and messaging tradeoffs in distributed service systems

We consider the following distributed service model: jobs with unit mean, exponentially distributed, and independent processing times arrive as a Poisson process of rate $\lambda n$, with $0<\lambda<1$, and are immediately dispatched by a centralized dispatcher to one of $n$ First-In-First-Out queues associated with $n$ identical servers. The dispatcher is endowed with a finite memory, and with the ability to exchange messages with the servers. We propose and study a resource-constrained "pull-based" dispatching policy that involves two parameters: (i) the number of memory bits available at the dispatcher, and (ii) the average rate at which servers communicate with the dispatcher. We establish (using a fluid limit approach) that the asymptotic, as $n\to\infty$, expected queueing delay is zero when either (i) the number of memory bits grows logarithmically with $n$ and the message rate grows superlinearly with $n$, or (ii) the number of memory bits grows superlogarithmically with $n$ and the message rate is at least $\lambda n$. Furthermore, when the number of memory bits grows only logarithmically with $n$ and the message rate is proportional to $n$, we obtain a closed-form expression for the (now positive) asymptotic delay. Finally, we demonstrate an interesting phase transition in the resource-constrained regime where the asymptotic delay is non-zero. In particular, we show that for any given $\alpha>0$ (no matter how small), if our policy only uses a linear message rate $\alpha n$, the resulting asymptotic delay is upper bounded, uniformly over all $\lambda<1$; this is in sharp contrast to the delay obtained when no messages are used ($\alpha = 0$), which grows as $1/(1-\lambda)$ when $\lambda\uparrow 1$, or when the popular power-of-$d$-choices is used, in which the delay grows as $\log(1/(1-\lambda))$

Modeling the Emergency Care Delivery System Using a Queueing Approach

This thesis considers a regional emergency care delivery system that has a common emergency medical service (EMS) provider and two hospitals, each with a single emergency department (ED) and an inpatient department (ID). Patients arrive at one of the hospital EDs either by ambulance or self-transportation, and we assume that an ambulance patient has preemptive priority over a walk-in patient. Both types of patients can potentially be admitted into the ID or discharged directly from the ED. An admitted patient who cannot access the ID due to the lack of available inpatient beds becomes a boarding patient and blocks an ED server. An ED goes on diversion, e.g., requests the EMS provider to divert incoming ambulances to the neighboring facility, if the total number of its ambulance patients and boarding patients exceeds its capacity (the total number of its servers). The EMS provider will accept the diversion request if the neighboring ED is not on diversion. Both EDs choose its capacity as its diversion threshold and never change the threshold value strategically, and hence they never game. Although the network could be an idealized model of an actual operation, it can be thought of as the simplest network model that is rich enough to reproduce the variety of interactions among different system components. In particular, we aim to highlight the bottleneck effect of inpatient units on ED overcrowding and the network effects resulting from ED diversions. A continuous time Markov chain is introduced for the network model. We show that the chain is irreversible and hence its stationary distribution is difficult to characterize analytically. We identify an alternative solution that builds on queueing decomposition and matrix-analytic methods. We demonstrate through discrete-event simulations the effectiveness of this solution on deriving various performance measures of the original network model. Moreover, by conducting extensive numerical experiments, we provide potential explanations for the overcrowding and delays in a network of hospitals. We suggest remedies from a queueing perspective for the operational challenges facing emergency care delivery systems

PEV Charging Infrastructure Integration into Smart Grid

Plug-in electric vehicles (PEVs) represent a huge step forward in a green transportation system, contribute to the reduction of greenhouse gas emission, and reduce the dependence on fossil fuel. With the increasing popularity of PEVs, public electric-vehicle charging infrastructure (EVCI) becomes indispensable to meet the PEV user requirements. EVCI can consist of various types of charging technologies, offering multiple charging services for PEV users. Proper integration of the charging infrastructure into smart grid is key to promote widespread adoption of PEVs. Planning and operation of EVCI are technically challenging, since PEVs are characterized by their limited driving range, long charging duration, and high charging power, in addition to the randomness in driving patterns and charging decisions of PEV users. EVCI planning involves both the siting and capacity planning of charging facilities. Charging facility siting must ensure not only a satisfactory charging service for PEV users but also a high utilization and profitability for the chosen facility locations. Thus, the various types of charging facilities should be located based on an accurate location estimation of the potential PEV charging demand. Capacity planning of charging facilities must ensure a satisfactory charging service for PEV users in addition to a reliable operation of the power grid. During the operation of EVCI, price-based coordination mechanisms can be leveraged to dynamically preserve the quality-of-service (QoS) requirements of charging facilities and ensure the profitability of the charging service. This research is to investigate and develop solutions for integrating the EVCI into the smart grid. It consists of three research topics: First, we investigate PEV charging infrastructure siting. We propose a spatial-temporal flow capturing location model. This model determines the locations of various types of charging facilities based on the spatial-temporal distribution of traffic flows. In the proposed model, we consider transportation network dynamics and congestion, in addition to different characteristics and usage patterns of each charging facility type. Second, we propose a QoS aware capacity planning of EVCI. The proposed framework accounts for the link between the charging QoS and the power distribution network (PDN) capability. Towards this end, we firstly optimize charging facility sizes to achieve a targeted QoS level. Then, we minimize the integration cost for the PDN by attaining the most cost-effective allocation of the energy storage systems and/or upgrading the PDN substation and feeders. Additionally, we capture the correlation between the occupation levels of neighboring charging facilities and the blocked PEV user behaviors. Lastly, we investigate the coordination of PEV charging demands. We develop a differentiated pricing mechanism for a multiservice EVCI using deep reinforcement learning (RL). The proposed framework enhances the performance of charging facilities by motivating PEV users to avoid over-usage of particular service classes. Since customer-side information is stochastic, non-stationary, and expensive to collect at scale, the proposed pricing mechanism utilizes the model-free deep RL approach. In the proposed RL approach, deep neural networks are trained to determine a pricing policy while interacting with the dynamically changing environment. The neural networks take the current EVCI state as input and generate pricing signals that coordinate the anticipated PEV charging demand

Dynamic power allocation and routing for satellite and wireless networks with time varying channels

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2004.Includes bibliographical references (p. 283-295).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Satellite and wireless networks operate over time varying channels that depend on attenuation conditions, power allocation decisions, and inter-channel interference. In order to reliably integrate these systems into a high speed data network and meet the increasing demand for high throughput and low delay, it is necessary to develop efficient network layer strategies that fully utilize the physical layer capabilities of each network element. In this thesis, we develop the notion of network layer capacity and describe capacity achieving power allocation and routing algorithms for general networks with wireless links and adaptive transmission rates. Fundamental issues of delay, throughput optimality, fairness, implementation complexity, and robustness to time varying channel conditions and changing user demands are discussed. Analysis is performed at the packet level and fully considers the queueing dynamics in systems with arbitrary, potentially bursty, arrival processes. Applications of this research are examined for the specific cases of satellite networks and ad-hoc wireless networks. Indeed, in Chapter 3 we consider a multi-beam satellite downlink and develop a dynamic power allocation algorithm that allocates power to each link in reaction to queue backlog and current channel conditions. The algorithm operates without knowledge of the arriving traffic or channel statistics, and is shown to achieve maximum throughput while maintaining average delay guarantees. At the end of Chapter 4, a crosslinked collection of such satellites is considered and a satellite separation principle is developed, demonstrating that joint optimal control can be implemented with separate algorithms for the downlinks and crosslinks.(cont.) Ad-hoc wireless networks are given special attention in Chapter 6. A simple cell- partitioned model for a mobile ad-hoc network with N users is constructed, and exact expressions for capacity and delay are derived. End-to-end delay is shown to be O(N), and hence grows large as the size of the network is increased. To reduce delay, a transmission protocol which sends redundant packet information over multiple paths is developed and shown to provide O(vN) delay at the cost of reducing throughput. A fundamental rate- delay tradeoff curve is established, and the given protocols for achieving O(N) and O(vN) delay are shown to operate on distinct boundary points of this curve. In Chapters 4 and 5 we consider optimal control for a general time-varying network. A cross-layer strategy is developed that stabilizes the network whenever possible, and makes fair decisions about which data to serve when inputs exceed capacity. The strategy is decoupled into separate algorithms for dynamic flow control, power allocation, and routing, and allows for each user to make greedy decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimally fair operating point that is achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an end-to-end delay increase for data that is served by the network.by Michael J. Neely.Ph.D

Solving Multi-objective Integer Programs using Convex Preference Cones

Esta encuesta tiene dos objetivos: en primer lugar, identificar a los individuos que fueron víctimas de algún tipo de delito y la manera en que ocurrió el mismo. En segundo lugar, medir la eficacia de las distintas autoridades competentes una vez que los individuos denunciaron el delito que sufrieron. Adicionalmente la ENVEI busca indagar las percepciones que los ciudadanos tienen sobre las instituciones de justicia y el estado de derecho en Méxic