Queues and risk models with simultaneous arrivals

We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue) we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline how the two-dimensional risk model with a general two-dimensional claim size distribution (hence without ordering of claim sizes) is related to a known Riemann boundary value problem

A new algorithm for finding the k shortest transport paths in dynamic stochastic networks

The static K shortest paths (KSP) problem has been resolved. In reality, however, most of the networks are actually dynamic stochastic networks. The state of the arcs and nodes are not only uncertain in dynamic stochastic networks but also interrelated. Furthermore, the cost of the arcs and nodes are subject to a certain probability distribution. The KSP problem is generally regarded as a dynamic stochastic optimization problem. The dynamic stochastic characteristics of the network and the relationships between the arcs and nodes of the network are analyzed in this paper, and the probabilistic shortest path concept is defined. The mathematical optimization model of the dynamic stochastic KSP and a genetic algorithm for solving the dynamic stochastic KSP problem are proposed. A heuristic population initialization algorithm is designed to avoid loops and dead points due to the topological characteristics of the network. The reasonable crossover and mutation operators are designed to avoid the illegal individuals according to the sparsity characteristic of the network. Results show that the proposed model and algorithm can effectively solve the dynamic stochastic KSP problem. The proposed model can also solve the network flow stochastic optimization problems in transportation, communication networks, and other networks

Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author

Intelligent Traffic Management: From Practical Stochastic Path Planning to Reinforcement Learning Based City-Wide Traffic Optimization

This research focuses on intelligent traffic management including stochastic path planning and city scale traffic optimization. Stochastic path planning focuses on finding paths when edge weights are not fixed and change depending on the time of day/week. Then we focus on minimizing the running time of the overall procedure at query time utilizing precomputation and approximation. The city graph is partitioned into smaller groups of nodes and represented by its exemplar. In query time, source and destination pairs are connected to their respective exemplars and the path between those exemplars is found. After this, we move toward minimizing the city wide traffic congestion by making structural changes include changing the number of lanes, using ramp metering, varying speed limit, and modifying signal timing is possible. We propose a multi agent reinforcement learning (RL) framework for improving traffic flow in city networks. Our framework utilizes two level learning: a) each single agent learns the initial policy and b) multiple agents (changing the environment at the same time) update their policy based on the interaction with the dynamic environment and in agreement with other agents. The goal of RL agents is to interact with the environment to learn the optimal modification for each road segment through maximizing the cumulative reward over the set of possible actions in state space

Engineering Algorithms for Route Planning in Multimodal Transportation Networks

Practical algorithms for route planning in transportation networks are a showpiece of successful Algorithm Engineering. This has produced many speedup techniques, varying in preprocessing time, space, query performance, simplicity, and ease of implementation. This thesis explores solutions to more realistic scenarios, taking into account, e.g., traffic, user preferences, public transit schedules, and the options offered by the many modalities of modern transportation networks

System optimum vs. user equilibrium in static and dynamic traffic routing

This thesis treats traffic as flow in static and dynamic networks. This may be any kind of traffic; cars, information etc. Two flows are of particular interest: The system optimum, which minimizes total travel time for all traffic, and the user equilibrium, in which all traffic with common origin and destination experiences the same cost. The system optimality problem is given globally as a minimization problem, whereas the user equilibrium is given locally on the flow of each origin-destination pair. A network consists of a directed graph G = (V, A) where each arc has a transition time, or latency function, dependent on the amount of flow along it. In addition arcs may have flow capacities. Some of the vertices also have supplies or demands, and a flow needs to satisfy all constraints in the network. The static networks are allowed to have convex non-decreasing latency functions, which makes finding the system optimum or the user equilibrium for a given network a convex optimization problem in general. The thesis also treats some special cases. The main results in this area are : (1) A system optimality criterion given locally on the flow of each origin-destination pair, similar to the criterion for a user equilibrium. This makes checking for optimality simple, and can in some cases simplify finding the system optimum. (2) An algorithm for determining taxes on the arcs of a static network such that the system optimum when considering only latency costs and the user equilibrium when considering latencies and taxes coincide. This can for instance be used to determine taxes that will make vehicle traffic in cities distribute itself in a system optimum, minimizing the total amount of time spent in traffic by all vehicles. The dynamic networks are restricted to having only constant latency functions on the arcs. This allows discretizing the the network along the time axis, which again allows for a linear optimization formulation of the dynamic system optimality problem. The main result in this area is an algorithm for finding the dynamic system optimum without discretizing the network, and thus reducing the required computational time by a large amount. This algorithm is based on the Successive Shortest Path algorithm for finding minimum cost static flows, and has the same running time as this algorithm. The resulting dynamic flow is one that consists of different extreme static flows at different time intervals. Combining this result with (2) from the static flow work ultimately results in a method for computing a dynamic system optimal flow and turning this into a user equilibrium by adding time dependent taxes along the arcs of the network

Algebraic and Geometric Models for Space Networking

In this paper we introduce some new algebraic and geometric perspectives on networked space communications. Our main contribution is a novel definition of a time-varying graph (TVG), defined in terms of a matrix with values in subsets of the real line P(R). We leverage semi-ring properties of P(R) to model multi-hop communication in a TVG using matrix multiplication and a truncated Kleene star. This leads to novel statistics on the communication capacity of TVGs called lifetime curves, which we generate for large samples of randomly chosen STARLINK satellites, whose connectivity is modeled over day-long simulations. Determining when a large subsample of STARLINK is temporally strongly connected is further analyzed using novel metrics introduced here that are inspired by topological data analysis (TDA). To better model networking scenarios between the Earth and Mars, we introduce various semi-rings capable of modeling propagation delay as well as protocols common to Delay Tolerant Networking (DTN), such as store-and-forward. Finally, we illustrate the applicability of zigzag persistence for featurizing different space networks and demonstrate the efficacy of K-Nearest Neighbors (KNN) classification for distinguishing Earth-Mars and Earth-Moon satellite systems using time-varying topology alone.Comment: 43 pages, 18 figures, comments welcom

Data organization for routing on the multi-modal public transportation system: a GIS-T prototype of Hong Kong Island.

Yu Hongbo.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 130-138).Abstracts in English and Chinese.ABSTRACT IN ENGLISH --- p.i-iiABSTRACT IN CHINESE --- p.iiiACKNOWLEDGEMENTS --- p.iv-vTABLE OF CONTENTS --- p.vi-viiiLIST OF TABLES --- p.ixLIST OF FIGURES --- p.x-xiChapter CHAPTER I --- INTRODUCTIONChapter 1.1 --- Problem Statement --- p.1Chapter 1.2 --- Research Purpose --- p.5Chapter 1.3 --- Significance --- p.7Chapter 1.4 --- Methodology --- p.8Chapter 1.5 --- Outline of the Thesis --- p.9Chapter CHAPTER II --- LITERATURE REVIEWChapter 2.1 --- Introduction --- p.12Chapter 2.2 --- Origin of GIS --- p.12Chapter 2.3 --- Development of GIS-T --- p.15Chapter 2.4 --- Capabilities of GIS-T --- p.18Chapter 2.5 --- Structure of a GIS-T --- p.19Chapter 2.5.1 --- Data Models for GIS-T --- p.19Chapter 2.5.2 --- Relational DBMS and Dueker-Butler's Data Model for Transportation --- p.22Chapter 2.5.3 --- Objected-oriented Approach --- p.25Chapter 2.6 --- Main Techniques of GIS-T --- p.26Chapter 2.6.1 --- Linear Location Reference System --- p.26Chapter 2.6.2 --- Dynamic Segmentation --- p.27Chapter 2.6.3 --- Planar and Non-planar Networks --- p.28Chapter 2.6.4 --- Turn-table --- p.28Chapter 2.7 --- Algorithms for Finding Shortest Paths on a Network --- p.29Chapter 2.7.1 --- Overview of Routing Algorithms --- p.29Chapter 2.7.2 --- Dijkstra's Algorithm --- p.31Chapter 2.7.3 --- Routing Models for the Multi-modal Network --- p.32Chapter 2.8 --- Recent Researches on GIS Data Models for the Multi-modal Transportation System --- p.33Chapter 2.9 --- Main Software Packages for GIS-T --- p.36Chapter 2.10 --- Summary --- p.37Chapter CHAPTER III --- MODELING THE MULTI-MODAL PUBLIC TRANSPORTATION SYSTEMChapter 3.1 --- Introduction --- p.40Chapter 3.2 --- Elaborated Stages and Methods for GIS Modeling --- p.40Chapter 3.3 --- Application Domain: The Multi-modal Public Transportation System --- p.43Chapter 3.3.1 --- Definition of a Multi-modal Public Transportation System --- p.43Chapter 3.3.2 --- Descriptions of the Multi-modal Public transportation System --- p.44Chapter 3.3.3 --- Objective of the Modeling Work --- p.46Chapter 3.4 --- A Layer-cake Based Application Domain Model for the Multi- modal Public Transportation System --- p.46Chapter 3.5 --- A Conceptual Model for the Multi-modal Public Transportation System --- p.49Chapter 3.6 --- Logical and Physical Implementation of the Data Model for the Multi-modal Public Transportation System --- p.54Chapter 3.7 --- Criteria for Routing on the Multi-modal Public Transportation System --- p.57Chapter 3.7.1 --- Least-time Routing --- p.58Chapter 3.7.2 --- Least-fare Routing --- p.60Chapter 3.7.3 --- Least-transfer Routing --- p.60Chapter 3.8 --- Summary --- p.61Chapter CHAPTER IV --- DATA PREPARATION FOR THE STUDY AREAChapter 4.1 --- Introduction --- p.53Chapter 4.2 --- The Study Area: Hong Kong Island --- p.63Chapter 4.2.1 --- General Information of the Transportation System on Hong Kong Island --- p.63Chapter 4.2.2 --- Reasons for Choosing Hong Kong Island as the Study Area --- p.66Chapter 4.2.3 --- Mass Transit Routes Selected for the Prototype --- p.67Chapter 4.3 --- Data Source and Data Collection --- p.67Chapter 4.4 --- Geographical Data Preparation --- p.71Chapter 4.4.1 --- Data Conversion --- p.73Chapter 4.4.2 --- Geographical Data Input --- p.79Chapter 4.5 --- Attribute Data Input --- p.86Chapter 4.6 --- Summary --- p.88Chapter CHAPTER V --- IMPLEMENTATION OF THE PROTOTYPEChapter 5.1 --- Introduction --- p.89Chapter 5.2 --- Construction of the Route Service Network --- p.89Chapter 5.2.1 --- Generation of the Geographical Network --- p.90Chapter 5.2.2 --- Setting Attribute Data for the Route Service Network --- p.95Chapter 5.3 --- A GIS-T Prototype for the Study Area --- p.102Chapter 5.4 --- General GIS Functions of the Prototype --- p.104Chapter 5.4.1 --- Information Retrieve --- p.104Chapter 5.4.2 --- Display --- p.105Chapter 5.4.3 --- Data Query --- p.105Chapter 5.5 --- Routing in the Prototype --- p.105Chapter 5.5.1 --- Routing Procedure --- p.108Chapter 5.5.2 --- Examples and Results --- p.110Chapter 5.5.3 --- Comparison and Analysis --- p.113Chapter 5.6 --- Summary --- p.118Chapter CHAPTER VI --- CONCLUSIONChapter 6.1 --- Research Findings --- p.123Chapter 6.2 --- Research Limitations --- p.126Chapter 6.3 --- Direction of Further Studies --- p.128BIBLIOGRAPHY --- p.13