Ljiljana Trajkovic

Artificial parameter homotopy methods for the DC operating point problem

Efficient and robust computation of one or more of the operating points of a nonlinear circuit is a necessary first step in a circuit simulator. The application of globally convergent probability-one homotopy methods to various systems of nonlinear equations that arise in circuit simulation is discussed. The coercivity conditions required for such methods are established using concepts from circuit theory. The theoretical claims of global convergence for such methods are substantiated by experiments with a collection of examples that have proved difficult for commercial simulation packages that do not use homotopy methods. Moreover, by careful design of the homotopy equations, the performance of the homotopy methods can be made quite reasonable. An extension to the steady-state problem in the time domain is also discussed. >

Congestion control for multimedia services

The problem of congestion control in high-speed networks for multimedia traffic, such as voice and video, is considered. It is shown that the performance requirements of high-speed networks involve delay, delay-jitter, and packet loss. A framing congestion control strategy based on a packet admission policy at the edges of the network and on a service discipline called stop-and-go queuing at the switching nodes is described. This strategy provides bounded end-to-end delay and a small and controllable delay-jitter. The strategy is applicable to packet switching networks in general, including fixed cell length asynchronous transfer mode (ATM), as well as networks with variable-size packets.<<ETX>>

Impact of self-similarity on wireless data network performance

In this paper we investigate the impact of traffic patterns on wireless data networks. Modeling and simulation of the cellular digital packet data (CDPD) network of Telus Mobility (a commercial service provider) were performed using the OPNET tool. We use trace-driven simulations with genuine traffic trace collected from the CDPD network to evaluate the performance of the CDPD protocol. This trace tends to exhibit long-range dependent behavior. Our simulation results indicate that genuine traffic traces, compared to traditional traffic models such as the Poisson model, produce longer queues and, thus, require larger buffers in the deployed networks elements.

KASER: knowledge amplification by structured expert randomization

In this paper and attached video, we present a third-generation expert system named Knowledge Amplification by Structured Expert Randomization (KASER) for which a patent has been filed by the U.S. Navys SPAWAR Systems Center, San Diego, CA (SSC SD). KASER is a creative expert system. It is capable of deductive, inductive, and mixed derivations. Its qualitative creativity is realized by using a tree-search mechanism. The system achieves creative reasoning by using a declarative representation of knowledge consisting of object trees and inheritance. KASER computes with words and phrases. It possesses a capability for metaphor-based explanations. This capability is useful in explaining its creative suggestions and serves to augment the capabilities provided by the explanation subsystems of conventional expert systems. KASER also exhibits an accelerated capability to learn. However, this capability depends on the particulars of the selected application domain. For example, application domains such as the game of chess exhibit a high degree of geometric symmetry. Conversely, application domains such as the game of craps played with two dice exhibit no predictable pattern, unless the dice are loaded. More generally, we say that domains whose informative content can be compressed to a significant degree without loss (or with relatively little loss) are symmetric. Incompressible domains are said to be asymmetric or random. The measure of symmetry plus the measure of randomness must always sum to unity.

Passivity and no-gain properties establish global convergence of a homotopy method for DC operating points

Finding the DC operating points of transistor circuits is an important task in circuit simulation. The problem is equivalent to solving sets of nonlinear algebraic equations describing transistor circuits. Existing circuit simulators use Newtons method, or its variants, to achieve this task. Newtons method is local and requires a good initial guess for convergence, while its variants globally converge under restrictive conditions. Recent mathematical results guarantee the existence of constructive, globally convergent homotopy methods for finding zeros of nonlinear maps with probability one. These results are applied to the DC operating point problem by constructing various homotopies to create a simple problem that is solved before proceeding with the continuation process that will transform it into the initially stated difficult problem. It is shown that for a certain class of circuits used in the design of integrated circuits, nodal equations satisfy the conditions required by the globally convergent homotopy methods.<<ETX>>

Analysis of public safety traffic on trunked land mobile radio systems

Mobile radio systems for public safety and agencies engaged in emergency response and disaster recovery operations must support multicast voice traffic. In this paper, we analyze the distribution of call interarrival and call holding times for multicast voice (talk group) traffic on a transmission trunked mobile radio system. In such systems, the channel is held only while a user is making a call (while the push-to-talk key is pressed and the radio is transmitting). We find that the call interarrival time distributions are exponential and exhibit tendency toward long-range dependence. The call holding times best fit lognormal distributions and are not correlated. A potentially important implication of these findings is that performance estimation methods that assume memoryless Markov arrival and departure processes may not be viable approaches.

Finding DC operating points of transistor circuits using homotopy methods

Finding the DC operating points of transistor circuits is one of the most important tasks in electrical circuit simulation. To resolve DC convergence difficulties that often arise when simulating bipolar and MOS transistor circuits, the authors use homotopy methods to solve nonlinear circuit equations. The authors exploit the properties of the equations and construct various homotopies that prove useful in finding their solutions. Criteria are provided for choosing homotopy parameters and a good starting point for homotopy paths. Homotopy methods are robust, accurate, and capable of finding multiple operating points. The authors present a circuit that could not be simulated using techniques available in current circuit simulators, while the solutions were successfully obtained using homotopy methods.<<ETX>>

A generalization of Brayton-Moser's mixed potential function

In this paper we give algorithms for constructing the Brayton-Mosers mixed potential function for a class of nonlinear reciprocal RLC networks, and we state necessary conditions for their existence. We have attempted to find the largest possible class of networks for which such a scalar function of state variables consisting of capacitor voltages and inductor currents can be constructed explicitly. Our results are applicable to a certain subclass of complete networks. From a mathematical point of view, we show that the corresponding network equations belong to the class of index I systems.

Simulation and Analysis of Packet Loss in User Datagram Protocol Transfers

Understanding packet loss patterns in Internet Protocol (IP) networks is important for achieving the desired quality of service in multimedia transfers. In this paper, we study the loss patterns in video transfers using User Datagram Protocol (UDP) in a congested packet network. We use trace-driven ns-2 simulations to collect packet loss traces in networks, and we apply wavelet analysis to investigate the behavior of packet loss on various time-scales. We show that time-scales are essential for understanding loss behavior and that packet loss exhibits long-range dependence over the coarser time-scales.

An overview and comparison of analytical TCP models

Modeling TCP performance is an important issue that attracted research attention over the past decade. In this paper, we present an overview of models used to capture the TCP behavior. We compare several existing analytical methods with respect to modeled attributes, modeling assumptions, and validation techniques. We also identify features that new TCP models should possess. Finally, we address the importance of devising common validation techniques and performance evaluation metrics for TCP models.