The use of simulation techniques has been increasing in recent years in the transportation and related fields to accommodate flexible and behaviorally realistic structures for analysis of decision processes. This paper proposes a randomized and scrambled version of the Halton sequence for use in simulation estimation of discrete choice models. The scrambling of the Halton sequence is motivated by the rapid deterioration of the standard Halton sequence’s coverage of the integration domain in high dimensions of integration. The randomization of the sequence is motivated from a need to statistically compute the simulation variance of model parameters. The resulting hybrid sequence combines the good coverage property of quasi-Monte Carlo sequences with the ease of estimating simulation error using traditional Monte Carlo methods. The paper develops an evaluation framework for assessing the performance of the traditional pseudo-random sequence, the standard Halton sequence, and the scrambled Halton sequence. The results of computational experiments indicate that the scrambled Halton sequence performs better than the standard Halton sequence and the traditional pseudo-random sequence for simulation estimation of models with high dimensionality of integration.

https://www.caee.utexas.edu/prof/bhat/ABSTRACTS/Scrambled_Halton_Sequences.pdf

Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences

The Monte Carlo method.- Sampling from known distributions.- Pseudorandom number generators.- Variance reduction techniques.- Quasi-Monte Carlo constructions.- Using quasi-Monte Carlo constructions.- Using quasi-Monte Carlo in practice.- Financial applications.- Beyond numerical integration.- Review of algebra.- Error and variance analysis for Halton sequences.- References.- Index.

Monte Carlo and Quasi-Monte Carlo Sampling

This paper provides a comprehensive overview of the literature on transportation infrastructure system performance in disasters Specifically, it reviews those articles appearing in refereed journals, conference proceedings, and technical reports since the late 1990s that provide insights and tools for the assessment of anticipated transportation system performance, along with its management, given the possibility of physical damage resulting from a future hazard event In the considered literature, performance may be gauged under characteristics of risk, vulnerability, reliability, robustness, flexibility, survivability, and resilience, the most common concepts or measures in the literature In addition to providing an archive and synthesis of recent literature on this topic, the approximately 200 articles are classified based on a host of criteria, including applied measure (qualitative or quantitative), conceptual approach, and methodology

Measuring the performance of transportation infrastructure systems in disasters: a comprehensive review

We survey some of the recent developments on quasi-Monte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a high-dimensional integral. We review several QMC constructions and different randomizations that have been proposed to provide unbiased estimators and for error estimation. Randomizing QMC methods allows us to view them as variance reduction techniques. New and old results on this topic are used to explain how these methods can improve over the MC method in practice. We also discuss how this methodology can be coupled with clever transformations of the integrand in order to reduce the variance further. Additional topics included in this survey are the description of figures of merit used to measure the quality of the constructions underlying these methods, and other related techniques for multidimensional integration.

Recent Advances in Randomized Quasi-Monte Carlo Methods

Randomized Halton sequences

There have been few studies on practical error estimation methods of quasi-Monte Carlo integrations. Recently, some theoretical works were developed by Owen to analyze the quasi-Monte Carlo integration error. However his method given by those works is complicated to be implemented and needs huge computational efforts, so it would be of some interest to investigate into a simple error estimation method. In this paper, we will use a simple method, and give some theoretical considerations on the errors given by these two methods. Numerical experiments are also reported.

A Practical Approach to the Error Estimation of Quasi-Monte Carlo Integrations

Applying the shortest‐path‐counting problem to evaluate the importance of city road segments and the connectedness of the network‐structured system

Measuring the network robustness by Monte Carlo estimation of shortest path length distribution

Aiming at improving the efficiency and reliability of ambulance service, several location models for ambulance stations have been proposed in the operations research literature. Well-known approaches to this problem are coverage model and median model. Coverage model looks for the location to maximize the (deterministic or probabilistic) covered demand of ambulance calls. Hence this model can be thought of reliability oriented model. On the other hand in median model the objective is to minimize the total traveling distance of the ambulances from the station to the scene of call. This model gives more weight to the efficiency of ambulance operation. This paper gives a comparison of those optimization models through actual patient call data from Tokyo metropolitan area to show the characteristics of each model and investigate a possibility of improvement in ambulance service. In the next section we introduce two well-known approaches to ambulance location problem, coverage model and median model. In Sec. 3 we apply these models to patient call data from Tokyo and compare the actual location and optimal solution. The result shows us the optimal solution can achieve improvement in both models, and suggests the possibility of more efficient and reliable location.

/pdf/a-case-study-of-optimal-ambulance-location-problems-4t38m1aplf.pdf

Hozumi Morohosi

Papers

A Practical Approach to the Error Estimation of Quasi-Monte Carlo Integrations

Applying the shortest‐path‐counting problem to evaluate the importance of city road segments and the connectedness of the network‐structured system

Measuring the network robustness by Monte Carlo estimation of shortest path length distribution

A case study of optimal ambulance location problems

Applying path‐counting methods for measuring the robustness of the network‐structured system