On the accuracy of phase-type approximations of heavy-tailed risk models

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.Comment: 24 pages, 13 figures, 8 tables, 38 reference

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

A Unified Mobility Management Architecture for Interworked Heterogeneous Mobile Networks

The buzzword of this decade has been convergence: the convergence of telecommunications, Internet, entertainment, and information technologies for the seamless provisioning of multimedia services across different network types. Thus the future Next Generation Mobile Network (NGMN) can be envisioned as a group of co-existing heterogeneous mobile data networking technologies sharing a common Internet Protocol (IP) based backbone. In such all-IP based heterogeneous networking environments, ongoing sessions from roaming users are subjected to frequent vertical handoffs across network boundaries. Therefore, ensuring uninterrupted service continuity during session handoffs requires successful mobility and session management mechanisms to be implemented in these participating access networks. Therefore, it is essential for a common interworking framework to be in place for ensuring seamless service continuity over dissimilar networks to enable a potential user to freely roam from one network to another. For the best of our knowledge, the need for a suitable unified mobility and session management framework for the NGMN has not been successfully addressed as yet. This can be seen as the primary motivation of this research. Therefore, the key objectives of this thesis can be stated as: To propose a mobility-aware novel architecture for interworking between heterogeneous mobile data networks To propose a framework for facilitating unified real-time session management (inclusive of session establishment and seamless session handoff) across these different networks. In order to achieve the above goals, an interworking architecture is designed by incorporating the IP Multimedia Subsystem (IMS) as the coupling mediator between dissipate mobile data networking technologies. Subsequently, two different mobility management frameworks are proposed and implemented over the initial interworking architectural design. The first mobility management framework is fully handled by the IMS at the Application Layer. This framework is primarily dependant on the IMS’s default session management protocol, which is the Session Initiation Protocol (SIP). The second framework is a combined method based on SIP and the Mobile IP (MIP) protocols, which is essentially operated at the Network Layer. An analytical model is derived for evaluating the proposed scheme for analyzing the network Quality of Service (QoS) metrics and measures involved in session mobility management for the proposed mobility management frameworks. More precisely, these analyzed QoS metrics include vertical handoff delay, transient packet loss, jitter, and signaling overhead/cost. The results of the QoS analysis indicates that a MIP-SIP based mobility management framework performs better than its predecessor, the Pure-SIP based mobility management method. Also, the analysis results indicate that the QoS performances for the investigated parameters are within acceptable levels for real-time VoIP conversations. An OPNET based simulation platform is also used for modeling the proposed mobility management frameworks. All simulated scenarios prove to be capable of performing successful VoIP session handoffs between dissimilar networks whilst maintaining acceptable QoS levels. Lastly, based on the findings, the contributions made by this thesis can be summarized as: The development of a novel framework for interworked heterogeneous mobile data networks in a NGMN environment. The final design conveniently enables 3G cellular technologies (such as the Universal Mobile Telecommunications Systems (UMTS) or Code Division Multiple Access 2000 (CDMA2000) type systems), Wireless Local Area Networking (WLAN) technologies, and Wireless Metropolitan Area Networking (WMAN) technologies (e.g., Broadband Wireless Access (BWA) systems such as WiMAX) to interwork under a common signaling platform. The introduction of a novel unified/centralized mobility and session management platform by exploiting the IMS as a universal coupling mediator for real-time session negotiation and management. This enables a roaming user to seamlessly handoff sessions between different heterogeneous networks. As secondary outcomes of this thesis, an analytical framework and an OPNET simulation framework are developed for analyzing vertical handoff performance. This OPNET simulation platform is suitable for commercial use