IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20030057.html
   My bibliography  Save this paper

Gradient Estimation for a Class of Systems with Bulk Services: A Problem in Public Transportation

Author

Listed:
  • Felisa J. Vazquez-Abad

    (Université de Montreal)

  • Bernd Heidergott

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

Abstract

This discussion paper led to a publication in 'ACM Transactions on Modeling and Computer Simulation' , 2009, 19(3), article 13. This paper deals with a system where batch arrivals wait in a station until a server (a train) is available, at which moment it services all customers in waiting. This is an example of a bulk server, which has many applications in public transportation, telecommunications, computer resource allocation, and multiple access telecommuncation networks, among others. We consider a subway model and focus on a metro line serving a particular metro station. Denote the planned inter-departure time of this line by theta. The metro station is served by several other lines and passengers change trainsat the station. Traveling times of trains are assumed to be given by fixed times and an additional stochastic noise. We perform a sensitivity analysis of the total delay ofpassengers waiting for the "" line with respect to theta. We establish a smoothed perturbation analysis (SPA), a measure--valued differentiation (MVD), and a score function (SF) estimator. Numerical experiments are performed to compare the ensuing estimators. It turns out that the SPA and MVD estimators are intrinsically different and the model presented in this paper may serve as a counter--example to the widespread belief that SPA and MVD yield similar estimators.

Suggested Citation

  • Felisa J. Vazquez-Abad & Bernd Heidergott, 2003. "Gradient Estimation for a Class of Systems with Bulk Services: A Problem in Public Transportation," Tinbergen Institute Discussion Papers 03-057/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20030057
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/03057.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Martin I. Reiman & Alan Weiss, 1989. "Sensitivity Analysis for Simulations via Likelihood Ratios," Operations Research, INFORMS, vol. 37(5), pages 830-844, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kleijnen, Jack P. C. & Rubinstein, Reuven Y., 1996. "Optimization and sensitivity analysis of computer simulation models by the score function method," European Journal of Operational Research, Elsevier, vol. 88(3), pages 413-427, February.
    2. Calvin, James M. & Nakayama, Marvin K., 2004. "Permuted derivative and importance-sampling estimators for regenerative simulations," European Journal of Operational Research, Elsevier, vol. 156(2), pages 390-414, July.
    3. Abbas, K. & Heidergott, B.F. & Aissani, D., 2011. "A Taylor series expansion approach to the functional approximation of finite queues," Serie Research Memoranda 0049, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. Laub, Patrick J. & Salomone, Robert & Botev, Zdravko I., 2019. "Monte Carlo estimation of the density of the sum of dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 23-31.
    5. Gilles Pages & Olivier Pironneau & Guillaume Sall, 2015. "Vibrato and Automatic Differentiation for High Order Derivatives and Sensitivities of Financial Options," Working Papers hal-01234637, HAL.
    6. Michael C. Fu, 2008. "What you should know about simulation and derivatives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 723-736, December.
    7. Sarazin, Gabriel & Morio, Jérôme & Lagnoux, Agnès & Balesdent, Mathieu & Brevault, Loïc, 2021. "Reliability-oriented sensitivity analysis in presence of data-driven epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    8. Akiyama, Naho & Yamada, Toshihiro, 2024. "A weak approximation for Bismut’s formula: An algorithmic differentiation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 386-396.
    9. Xin Yun & L. Jeff Hong & Guangxin Jiang & Shouyang Wang, 2019. "On gamma estimation via matrix kriging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 393-410, August.
    10. Soumyadip Ghosh & Henry Lam, 2019. "Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees," Operations Research, INFORMS, vol. 67(1), pages 232-249, January.
    11. Yongqiang Wang & Michael C. Fu & Steven I. Marcus, 2012. "A New Stochastic Derivative Estimator for Discontinuous Payoff Functions with Application to Financial Derivatives," Operations Research, INFORMS, vol. 60(2), pages 447-460, April.
    12. Mark J. Cathcart & Steven Morrison & Alexander J. McNeil, 2011. "Calculating Variable Annuity Liability 'Greeks' Using Monte Carlo Simulation," Papers 1110.4516, arXiv.org.
    13. Li, Jinghui & Mosleh, Ali & Kang, Rui, 2011. "Likelihood ratio gradient estimation for dynamic reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1667-1679.
    14. Kleijnen, J.P.C. & Rubinstein, R.Y., 1996. "Optimization and Sensitivity Analysis of Computer Simulation Models by the Score Function Method," Other publications TiSEM 958c9b9a-544f-48f3-a3d1-c, Tilburg University, School of Economics and Management.
    15. Jingxu Xu & Zeyu Zheng, 2023. "Gradient-Based Simulation Optimization Algorithms via Multi-Resolution System Approximations," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 633-651, May.
    16. Gilles Pag`es & Olivier Pironneau & Guillaume Sall, 2016. "Vibrato and automatic differentiation for high order derivatives and sensitivities of financial options," Papers 1606.06143, arXiv.org.
    17. Detemple, Jerome & Rindisbacher, Marcel, 2007. "Monte Carlo methods for derivatives of options with discontinuous payoffs," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3393-3417, April.
    18. Sridhar Bashyam & Michael C. Fu, 1994. "Application of perturbation analysis to a class of periodic review (s, S) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 47-80, February.
    19. Marvin K. Nakayama & Perwez Shahabuddin, 1998. "Likelihood Ratio Derivative Estimation for Finite-Time Performance Measures in Generalized Semi-Markov Processes," Management Science, INFORMS, vol. 44(10), pages 1426-1441, October.
    20. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.

    More about this item

    Keywords

    sensitivity analysis; smoothed perturbation analysis; score function; measure-valued differentiation; bulk servers.;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20030057. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.