Parallel algorithms for simulating continuous time Markov chains

We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors

Fast simulation of packet loss rates in a shared buffer communications switch

This paper describes an efficient technique for estimating, via simulation, the probability of buffer overflows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has a buffer of finite capacity. Each stream is designated as either being of high or low priority. When the queue length reaches a certain threshold, only high priority packets are admitted to the switch's buffer. The problem is to estimate the loss rate of high priority packets. An asymptotically optimal importance sampling approach is developed for this rare event simulation problem. In this approach, the importance sampling is done in two distinct phases. In the first phase, an importance sampling change of measure is used to bring the queue length up to the threshold at which low priority packets get rejected. In the second phase, a different importance sampling change of measure is used to move the queue length from the threshold to the buffer capacity

Parallel Execution for Serial Simulators

This paper describes an approach to discrete event simulation modeling that appears to be effective for developing portable and efficient parallel execution of models of large distributed systems and communication networks. In this approach, the modeler develops sub-models with an existing sequential simulation modeling tool, using the full expressive power of the tool. A set of modeling language extensions permit automatically synchronized communication between sub-models; however, the automation requires that any such communication must take a non-zero amount of simulation time. Within this modeling paradigm, a variety of conservative synchronization protocols can transparently support conservative execution of sub-models on potentially different processors. A specific implementation of this approach, U.P.S. (Utilitarian Parallel Simulator), is described, along with performance results on the Intel Paragon and on the IBM SP2. Portions of this paper are reproduced with permission fr..

On Extending Parallelism to Serial Simulators

This paper describes an approach to discrete event simulation modeling that appears to be e�ective for developing portable and e�cient parallel execution of models of large distributed systems and communication networks. In this approach, the modeler develops sub-models using an existing sequential simulation modeling tool, using the full expressive power of the tool. A set of modeling language extensions permit automatically synchronized communication between sub-models; however, the automation requires that any such communication must take a non-zero amount of simulation time. Within this modeling paradigm, a variety of conservative synchronization protocols can transparently support conservative execution of sub-models on potentially di�erent processors. A speci�c implementation of this approach, U.P.S. �Utilitarian Parallel Simulator�, is described, along with performance results on th

Importance Sampling and Stratification for Value-at-Risk

This paper proposes and evaluates variance reduction techniques for efficient estimation of portfolio loss probabilities using Monte Carlo simulation. Precise estimation of loss probabilities is essential to calculating value-at-risk, which is simply a percentile of the loss distribution. The methods we develop build on delta-gamma approximations to changes in portfolio value. The simplest way to use such approximations for variance reduction employs them as control variates; we show, however, that far greater variance reduction is possible if the approximations are used as a basis for importance sampling, stratified sampling, or combinations of the two. This is especially true in estimating very small loss probabilities. 1 Introduction Value-at-Risk (VAR) has become an important measure for estimating and managing portfolio risk [11, 13]. VAR is defined as a certain quantile of the change in a portfolio's value during a specified holding period. To be more specific, suppose the curre..

Asymptotically Optimal Importance Sampling and Stratification for Pricing Path-Dependent Options

This paper develops a variance reduction technique for Monte Carlo simulations of pathdependent options driven by high-dimensional Gaussian vectors. The method combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions. The change of drift is selected through a large deviations analysis and is shown to be optimal in an asymptotic sense. The drift selected has an interpretation as the path of the underlying state variables that maximizes the product of probability and payoff --- the most important path. The directions used for stratified sampling are optimal for a quadratic approximation to the integrand or payoff function. Indeed, under differentiability assumptions our importance sampling method eliminates variability due to the linear part of the payoff function and stratification eliminates much of the variability due to the quadratic part of the payoff. The two parts of the method are linked because the asymptotically op..