Smooth flexible models of nonhomogeneous poisson processes using one or more process realizations

Kuhl,; Deo,; Wilson, F. F.

doi:10.1109/wsc.2008.4736088

Cited by 7 publications

(4 citation statements)

References 6 publications

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“…Several procedures have been developed for modeling and estimating the mean-value function (rate function) of an NHPP; see Kuhl et al (2008) and Kuhl et al (2010) and the references therein. In this tutorial, we consider the case where λ (t) exhibits trends and cyclic effects and present the following parametric rate function proposed by Kuhl et al (1997a) for capturing trends and cyclic effects.…”

Section: Input Processes Changing Over Timementioning

confidence: 99%

Introduction to simulation input modeling

Biller

Gunes

2010

Proceedings of the 2010 Winter Simulation Conference

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In this tutorial we first review introductory techniques for simulation input modeling. We then identify situations in which the standard input models fail to adequately represent the available input data. In particular, we consider the cases where the input process may (i) have marginal characteristics that are not captured by standard distributions; (ii) exhibit dependence; and (iii) change over time. For case (i), we review flexible distribution systems, while we review two widely used multivariate input models for case (ii). Finally, we review nonhomogeneous Poisson processes for the last case. We focus our discussion around continuous random variables; however, when appropriate references are provided for discrete random variables. Detailed examples will be illustrated in the tutorial presentation.

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Section: Input Processes Changing Over Timementioning

confidence: 99%

Introduction to simulation input modeling

Biller

Gunes

2010

Proceedings of the 2010 Winter Simulation Conference

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“…A general model frequently used to represent non-stationary processes, specially arrival times, is Nonhomogeneous Poisson Processes (NHPP) which has successfully been performed to model complex time-dependent arrival processes in many simulation studies (Kuhl et al, 2008). Some examples in this category include (a) Repairable systems such as fan motors and turbines (Kuhl et al (2008)), (b) Calls for online analysis at a hospital in Houston (Kao and Chang (1998)), and (c) Respiratory cancer deaths in Scotland (Lawson (1970)). In a NHPP, it is assumed that the arrival rate λ depends on time.…”

Section: Introductionmentioning

confidence: 99%

“…Lee et al (1991), Kuhl et al (1997), and Kuhl and Wilson (2000) addressed the estimation of meanvalue function using parametric methods. Lewis and Shedler (1976), Pritsker et al (1995), Leemis (1991;2000;, Kuhl and Wilson (2001), Kuhl et al (2006), Alexopoulos et al (2008), and Kuhl et al (2008) proposed different nonparametric or semiparametric methods to estimate the mean-value of a NHPP as a function of t. More recently, did a comprehensive review on various methods for modeling and simulating NHPPs in simulation applications.…”

Section: Introductionmentioning

confidence: 99%

Modeling clustered non-stationary Poisson processes for stochastic simulation inputs

Shams¹,

Ajorlou²,

Yang³

2013

Computers & Industrial Engineering

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A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the random inputs vary over time in such a way that the functional forms of the distributions and/or their parameters depend on time. This paper answers the question whether a sequence of observations from a process follow the same statistical distribution, and if not, where the exact change points are, so that observations within two consecutive change points follow the same distribution. We propose two different methods based on likelihood ratio test and cluster analysis to detect multiple change points when observations follow non-stationary Poisson process with diverse occurrence rates over time. Results from a comprehensive Monte Carlo study indicate satisfactory performance for the proposed methods. A well-known example is also considered to show the application of our findings in real world cases.

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“…In this situation, the question of how to estimate λ(t) from a set of input variables on an arrival process, has been of interest to many researchers. For example, different parametric methods are developed in (Lee, et al, 1991) and (Johnson, et al, 1994a) whilst (Kuhl, Deo, and Wilson, 2008) proposed a nonparametric approach to estimate λ(t). These methods generally involve calculating the mean value of λ(t) over time and are suitable, especially, when the arrival rate shows a heavy dependence or a specific pattern i.e.…”

Section: Introductionmentioning

confidence: 99%

Analysis of nonhomogeneous input data using likelihood ratio test

Shams

Shahanaghi

2009

2009 IEEE International Conference on Industrial Engineering and Engineering Management

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Performing an accurate input analysis in simulation experimentation basically involves selecting the exact probability distributions of random input variables. Frequently in practice these inputs are not constant over time i.e., the underlying distribution may be affected by their time-dependent parameters. In this paper, we propose an approach that can identify whether or not a set of observations follow an identical distribution in a specific period. The model is formulated in a base of likelihood ratio test in the case that input observations come from nonhomogeneous exponentially random variable. Finally, performance comparisons are explored through simulation studies. Keywords -Simulation input data analysis, change point detection, likelihood ratio test, nonhomogeneous Poisson process978-1-4244-4870-8/09/$26.00 ©2009 IEEE

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Smooth flexible models of nonhomogeneous poisson processes using one or more process realizations

Cited by 7 publications

References 6 publications

Introduction to simulation input modeling

Introduction to simulation input modeling

Modeling clustered non-stationary Poisson processes for stochastic simulation inputs

Analysis of nonhomogeneous input data using likelihood ratio test

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