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

Integrated performance evaluation of extended queueing network models with line

Despite the large literature on queueing theory and its applications, tool support to analyze these models ismostly focused on discrete-event simulation and mean-value analysis (MVA). This circumstance diminishesthe applicability of other types of advanced queueing analysis methods to practical engineering problems,for example analytical methods to extract probability measures useful in learning and inference. In this toolpaper, we present LINE 2.0, an integrated software package to specify and analyze extended queueingnetwork models. This new version of the tool is underpinned by an object-oriented language to declarea fairly broad class of extended queueing networks. These abstractions have been used to integrate in acoherent setting over 40 different simulation-based and analytical solution methods, facilitating their use inapplications

A Bayesian Approach to Parameter Inference in Queueing Networks

The application of queueing network models to real-world applications often involves the task of estimating the service demand placed by requests at queueing nodes. In this article, we propose a methodology to estimate service demands in closed multiclass queueing networks based on Gibbs sampling. Our methodology requires measurements of the number of jobs at resources and can accept prior probabilities on the demands. Gibbs sampling is challenging to apply to estimation problems for queueing networks since it requires one to efficiently evaluate a likelihood function on the measured data. This likelihood function depends on the equilibrium solution of the network, which is difficult to compute in closed models due to the presence of the normalizing constant of the equilibrium state probabilities. To tackle this obstacle, we define a novel iterative approximation of the normalizing constant and show the improved accuracy of this approach, compared to existing methods, for use in conjunction with Gibbs sampling. We also demonstrate that, as a demand estimation tool, Gibbs sampling outperforms other popular Markov Chain Monte Carlo approximations. Experimental validation based on traces from a cloud application demonstrates the effectiveness of Gibbs sampling for service demand estimation in real-world studies

Comparison of Queueing Data-Structures for Kinetic Monte Carlo Simulations of Heterogeneous Catalysts

On-lattice Kinetic Monte Carlo (KMC) is a computational method used to simulate (among others) physico-chemical processes on catalytic surfaces. The KMC algorithm propagates the system through discrete configurations by selecting (with the use of random numbers) the next elementary process to be simulated, e.g. adsorption, desorption, diffusion or reaction. An implementation of such a selection procedure is the first-reaction method in which all realizable elementary processes are identified and assigned a random occurrence time based on their rate constant. The next event to be executed will then be the one with the minimum inter-arrival time. Thus, a fast and efficient algorithm for selecting the most imminent process and performing all the necessary updates on the list of realizable processes post-execution, is of great importance. In the current work, we implement five data-structures to handle the elementary process queue during a KMC run: an unsorted list, a binary heap, a pairing heap, a 1-way skip list, and finally, a novel 2-way skip list with a mapping array specialized for KMC simulations. We also investigate the effect of compiler optimizations on the performance of these data-structures on three benchmark models, capturing CO-oxidation, a simplified water-gas shift mechanism, and a temperature programmed desorption run. Excluding the least efficient and impractical for large problems unsorted list, we observe a 3× speedup of the binary or pairing heaps (most efficient) compared to the 1-way skip list (least efficient). Compiler optimizations deliver a speedup of up to 1.8×. These benchmarks provide valuable insight on the importance of, often-overlooked, implementation-related aspects of KMC simulations, such as the queueing data-structures. Our results could be particularly useful in guiding the choice of data-structures and algorithms that would minimize the computational cost of large-scale simulations

Maximum likelihood estimation by monte carlo simulation:Toward data-driven stochastic modeling

We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo-based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results