Importance Sampling for a Markov Modulated Queuing Network with Customer Impatience until the End of Service

For more than two decades, there has been a growing of interest in fast simulation techniques for estimating probabilities of rare events in queuing networks. Importance sampling is a variance reduction method for simulating rare events. The present paper carries out strict deadlines to the paper by Dupuis et al for a two node tandem network with feedback whose arrival and service rates are modulated by an exogenous finite state Markov process. We derive a closed form solution for the probability of missing deadlines. Then we have employed the results to an importance sampling technique to estimate the probability of total population overflow which is a rare event. We have also shown that the probability of this rare event may be affected by various deadline values.Importance Sampling, Queuing Network, Rare Event, Markov Process, Deadline

Techniques for the Fast Simulation of Models of Highly dependable Systems

With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system

Variance Reduction Techniques in Monte Carlo Methods

Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the introduction of computers. This increased computer power has stimulated simulation analysts to develop ever more realistic models, so that the net result has not been faster execution of simulation experiments; e.g., some modern simulation models need hours or days for a single ’run’ (one replication of one scenario or combination of simulation input values). Moreover there are some simulation models that represent rare events which have extremely small probabilities of occurrence), so even modern computer would take ’for ever’ (centuries) to execute a single run - were it not that special VRT can reduce theses excessively long runtimes to practical magnitudes.common random numbers;antithetic random numbers;importance sampling;control variates;conditioning;stratied sampling;splitting;quasi Monte Carlo

Control Variates for Reversible MCMC Samplers

A general methodology is introduced for the construction and effective application of control variates to estimation problems involving data from reversible MCMC samplers. We propose the use of a specific class of functions as control variates, and we introduce a new, consistent estimator for the values of the coefficients of the optimal linear combination of these functions. The form and proposed construction of the control variates is derived from our solution of the Poisson equation associated with a specific MCMC scenario. The new estimator, which can be applied to the same MCMC sample, is derived from a novel, finite-dimensional, explicit representation for the optimal coefficients. The resulting variance-reduction methodology is primarily applicable when the simulated data are generated by a conjugate random-scan Gibbs sampler. MCMC examples of Bayesian inference problems demonstrate that the corresponding reduction in the estimation variance is significant, and that in some cases it can be quite dramatic. Extensions of this methodology in several directions are given, including certain families of Metropolis-Hastings samplers and hybrid Metropolis-within-Gibbs algorithms. Corresponding simulation examples are presented illustrating the utility of the proposed methods. All methodological and asymptotic arguments are rigorously justified under easily verifiable and essentially minimal conditions.Comment: 44 pages; 6 figures; 5 table

Uniformisation techniques for stochastic simulation of chemical reaction networks

This work considers the method of uniformisation for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformisation can be beneficial in the context of time-inhomogeneous models, such as chemical reaction networks incorporating extrinsic noise. This paper lays focus on the understanding of uniformisation from the viewpoint of sample paths of chemical reaction networks. In particular, an efficient pathwise stochastic simulation algorithm for time-homogeneous models is presented which is complexity-wise equal to Gillespie's direct method. This new approach therefore enlarges the class of problems for which the uniformisation approach forms a computationally attractive choice. Furthermore, as a new application of the uniformisation method, we provide a novel variance reduction method for (raw) moment estimators of chemical reaction networks based upon the combination of stratification and uniformisation

The Kentucky Noisy Monte Carlo Algorithm for Wilson Dynamical Fermions

We develop an implementation for a recently proposed Noisy Monte Carlo approach to the simulation of lattice QCD with dynamical fermions by incorporating the full fermion determinant directly. Our algorithm uses a quenched gauge field update with a shifted gauge coupling to minimize fluctuations in the trace log of the Wilson Dirac matrix. The details of tuning the gauge coupling shift as well as results for the distribution of noisy estimators in our implementation are given. We present data for some basic observables from the noisy method, as well as acceptance rate information and discuss potential autocorrelation and sign violation effects. Both the results and the efficiency of the algorithm are compared against those of Hybrid Monte Carlo. PACS Numbers: 12.38.Gc, 11.15.Ha, 02.70.Uu Keywords: Noisy Monte Carlo, Lattice QCD, Determinant, Finite Density, QCDSPComment: 30 pages, 6 figure