동적과정을 이용한 가변수요 통행배정모형의 알고리듬 개발 = A Solution Algorithm for Elastic Demand Traffic Assignment Model Based on Dynamic Process

국문 초록 (Abstract)

통행배정(traffic assignment)은 장래 통행수요를 예측할 뿐 아니라, 교통혼잡을 완화시키는 각종 교통정책들을 사전에 평가하는 도구로 그 활용범위가 넓어지고 있다. 현재 대표적인 통행배정방법은 Wardrop(1952)이 제시한 사용자 균형원리(user equilibrium principle)에 따라 통행자를 교통망에 배정하는 방법으로 동등 수리최소화모형(equivalent mathematical minimization model), 변동부등식(Variational inequality), 비선형상보문제(Nonlinear Complementary Problem), 고정점 모형(fixed point method) 등이 있다. 그런데, 최근 Jin(2005a)은 동적과정(dynamic process)에 기초하여 사용자 균형해를 구할 수 있는 새로운 모형을 제시하였다. 본 연구는 Jin이 제시한 모형에 대한 효과적인 알고리듬을 개발하고 이를 평가하는 데 연구의 목적이 있다. 개발된 알고리듬은 통행배정모형을 풀기 위하여 현재 널리 사용되는 Frank-Wolfe방법보다 쉽게 프로그램화 할 수 있는데, 목적함수를 평가(evaluation)하는 단계가 불필요하며 축차적인 계산과정을 통하여 해를 구하기 때문이다. 제시된 알고리듬을 예제 교통망을 대상으로 분석한 결과, 사용자 균형해(user equilibrium)를 도출함을 확인할 수 있었다.

다국어 초록 (Multilingual Abstract)

Traffic assignment has been used both for predicting travel demands and for evaluating the tools for alleviating congestion on road network in advance. Some assignment models have been proposed such as equivalent mathematical minimization method, variational inequality problem, nonlinear complementary problem and fixed point method, in following the principle of Wardrop(1952) that no driver can not improve his travel cost by unilaterally changing his route. Recently Jin(2005a) presented a traffic assignment model based on dynamic process. This paper proposes a solution algorithm for the model of Jin and assesses the performances. Compared to the Frank-Wolfe method, which has been wildly used for solving the existing assignment models, the proposed algorithm is expected to be more efficient because it does not need to evaluate the objective function. Two numerical examples are used for assessing the algorithm, and they show that the algorithm converges to user equilibrium of Wardrop.

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