Estimating Network Characteristics in Stochastic Activity Networks

Article Abstract:

This paper describes a Monte Carlo method based on the theory of quasirandom points for estimating the distribution functions and means of network completion time and shortest path time in a stochastic activity network. In particular, the method leads to estimators whose absolute errors converge as (log K) to the power of N divided by K, where K denotes the number of replications collected in the experiment and N is the number of dimensions for sampling. This rate compares favorably with the standard error of estimate 0 (1 divided by K to the power of 1-2) which obtains for experiments that use random sampling. Moreover, since quasirandom points are nonrandom, the upper bound (log K) to the power of N divided by K is deterministic in contrast to the random sampling rate 0 (1 divided by K to the power of 1-2) which is probabilistic. The paper demonstrates how the use of a cutset of the network reduces N in the bound when estimating the distribution functions. Two examples illustrate the benefits and costs of using quasirandom points. (Reprinted by Permission of Publisher.)

Management science, Network analyzers, LAN Monitor, Networks, Estimation, Stochastic Model, Operations Research, Sampling, Monte Carlo Methods, Variance Reduction

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Estimating network characteristics in stochastic activity networks

Article Abstract:

A Monte Carlo method based on the theory of quasi-random points for estimating the distribution functions and means of network completion time and shortest path time in a stochastic activity network is described. The stochastic network problem is presented in detail, characterized through numerical integration, and tackled using crude Monte Carlo methods. The benefits of conditional sampling are then described, the concepts of quasi-random points as they relate to multivariable numerical integration are discussed, and the extent to which known results apply to the problem at hand are shown. Algorithms essential for Monte Carlo network analyses are presented, and a comprehensive sampling plan is described, listing all essential steps in using the cutset approach together with quasi-random points to estimate network quantities of interest.

Methods, Analysis, Network analysis (Planning), Usage, Stochastic processes

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Improving Monte Carlo efficiency by increasing variance

Article Abstract:

The standard Monte Carlo approach and the Markov chain Monte Carlo procedure are compared in terms of their efficiency in estimating an unknown quality while the problem size increases. The first method yields K i.i.d data points while the second draws its data from a Markov chain-produced single K-step sample path. The conditions under which the Markov chain estimation approach can prove more efficient than the standard Monte Carlo approach are identified. Likewise, the particular cases in which the improved efficiency of the Markov chain approach will increase along with problem size are specified. A number of examples are provided showing how improved efficiency is achieved.

Research, Markov processes, Samples (Merchandising), Samples (Products)

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