Cited By
View all- Kuhl M(2017)History of random variate generationProceedings of the 2017 Winter Simulation Conference10.5555/3242181.3242196(1-12)Online publication date: 3-Dec-2017
Combined inversion and thinning methods for simulating nonstationary non-poisson arrival processes
Abstract
We develop and evaluate SCIATA, a simplified combined inversion-and-thinning algorithm for simulating a nonstationary non-Poisson process (NNPP) over a finite time horizon, with the target arrival process having a given "rate" function and associated mean-value function together with a given variance-to-mean (dispersion) ratio. Designed for routine use when the dispersion ratio is at most two, SCIATA encompasses the following steps: (i) computing a piecewise-constant majorizing rate function that closely approximates the given rate function; (ii) computing the associated piecewise-linear majorizing mean-value function; (iii) generating an equilibrium renewal process (ERP) whose noninitial interrenewal times are Weibull distributed with mean one and variance equal to the given dispersion ratio; (iv) inverting the majorizing mean-value function at the ERP's renewal epochs to generate the associated majorizing NNPP; and (v) thinning the resulting arrival epochs to obtain an NNPP with the given rate function and dispersion ratio. Numerical examples illustrate the effectiveness of SCIATA in practice.
References
[1]
Çinlar, E. 1975. Introduction to Stochastic Processes. Englewood Cliffs, New Jersey: Prentice-Hall.
[2]
Gerhardt, I., and B. L. Nelson. 2009. "Transforming Renewal Processes for Simulation of Nonstationary Arrival Processes". INFORMS Journal on Computing 21 (4): 630--640.
[3]
Harper, A. M., S. E. Taranto, E. B. Edwards, and O. P. Daily. 2000. "Organ Transplantation Policies: An Update on a Successful Simulation Project: The Unos Liver Allocation Model". In Proceedings of the 2000 Winter Simulation Conference, edited by J. A. Joines, R. R. Barton, K. Kang, and P. A. Fishwick, 1955--1962. Piscataway, New Jersey: Institute of Electrical and Electronics Engineers.
[4]
Kim, S.-H., P. Vel, W. Whitt, and W. C. Cha. 2015. "Poisson and non-Poisson Properties in Appointment-Generated Arrival Processes: The Case of an Endocrinology Clinic". Operations Research Letters 43:247--253.
[5]
Kuhl, M. E., S. C. Deo, and J. R. Wilson. 2008. "Smooth Flexible Models of Nonhomogeneous Poisson Processes Using One or More Process Realizations". In Proceedings of the 2008 Winter Simulation Conference, edited by S. J. Mason, R. R. Hill, L. Mönch, O. Rose, T. Jefferson, and J. W. Fowler, 353--361. Piscataway, New Jersey: Institute of Electrical and Electronics Engineers.
[6]
Kuhl, M. E., and J. R. Wilson. 2001. "Modeling and Simulating Poisson Processes Having Trends or Nontrigonometric Cyclic Effects". European Journal of Operational Research 133 (3): 566--582.
[7]
Kuhl, M. E., J. R. Wilson, and M. A. Johnson. 1997. "Estimating and Simulating Poisson Processes Having Trends or Multiple Periodicities". IIE Transactions 29 (3): 201--211.
[8]
Lee, S., J. R. Wilson, and M. M. Crawford. 1991. "Modeling and Simulation of a Nonhomogeneous Poisson Process Having Cyclic Behavior". Communications in Statistics---Simulation and Computation 20 (2-3): 777--809.
[9]
Leemis, L. 2004. "Nonparametric Estimation and Variate Generation for a Nonhomogeneous Poisson Process from Event Count Data". IIE Transactions 36 (12): 1155--1160.
[10]
Lewis, P. A. W., and G. S. Shedler. 1976. "Statistical Analysis of Non-stationary Series of Events in a Data Base System". IBM Journal of Research and Development 20 (5): 465--482.
[11]
Liu, R., M. E. Kuhl, Y. Liu, and J. R. Wilson. 2015. "Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes". INFORMS Journal on Computing in revision.
[12]
Whitt, W., and X. Zhang. 2015. "A Data-Generated Model of an Emergency Department". Technical report, Department of Industrial Enginering and Operations Research, Columbia University, New York, NY.
Recommendations
Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes
We develop CIATA, a combined inversion-and-thinning approach for modeling a nonstationary non-Poisson process (NNPP), where the target arrival process is described by a given rate function and its associated mean-value function together with a given ...
On Poisson Approximations for Superposition Arrival Processes in Queues
We report on simulations of ΣiGIi/M/1 queues; the arrival process is the superposition sum of up to 1024 i.i.d. renewal processes and there is a single exponential server. As one might anticipate, the simulation estimate of the expected number of ...
Simulation methods for Poisson processes in nonstationary systems
WSC '78: Proceedings of the 10th conference on Winter simulation - Volume 1The nonhomogeneous Poisson process is a widely used model for a series of events (stochastic point process) in which the “rate” or “intensity” of occurrence of points varies, usually with time. The process has the characteristic properties that the ...
Comments
Information & Contributors
Information
Published In
December 2015
4051 pages
ISBN:9781467397414
Sponsors
Publisher
IEEE Press
Publication History
Published: 06 December 2015
Check for updates
Qualifiers
- Research-article
Conference
WSC '15
Sponsor:
Acceptance Rates
WSC '15 Paper Acceptance Rate 202 of 296 submissions, 68%;
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 21Total Downloads
- Downloads (Last 12 months)1
- Downloads (Last 6 weeks)0
Reflects downloads up to 10 Aug 2024
Other Metrics
Citations
Cited By
View all- Kuhl M(2017)History of random variate generationProceedings of the 2017 Winter Simulation Conference10.5555/3242181.3242196(1-12)Online publication date: 3-Dec-2017
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in