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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
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    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.
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    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

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