대기행렬 분석과 충격파 분석의 일치성
Consistency of Queueing Analysis and Shock Wave Analysis
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대기행렬 분석과 충격파 분석은 혼잡을 분석하기 위해 널리 사용되는 대표적인 방법이다. 본 논문은 두 가지 유형의 혼잡에 대한 대기행렬 분석과 충격파 분석을 도해적인 방법으로 대응시켜 비교함으로써 두 분석의 일치성과 차별성을 검토한다. 용량의 감소로 발생하는 혼잡에 대한 분석에서 기존 연구들이 대기행렬 분석의 누적도착곡선과 누적출발곡선이 만나는 시점을 대기행렬 소멸시점으로 이해하는 것은 오류임을 보인다. 대기행렬 분석과 충격파 분석의 일치성은 충격파 분석을 통해 구성하는 차량들의 궤적이 대기행렬 분석과 동일한 누적도착곡선과 누적출발곡선을 만든다는 것에 있으며, 이로 인해 두 분석을 통해 산출하는 지체는 동일하다. 대기행렬 분석이 물리적 공간을 점유하지 않는 가상의 차량을 가정하며, 고정된 지점의 관측에 기반한다는 전제는 대기 행렬 분석과 충격파 분석이 산출하는 대기행렬 길이, 대기행렬 지속시간의 차이를 설명한다.
Abstract
Queing analysis and shock wave analysis have been used to evaluate the congestion effect and have been regarded to be consistent. The consistency and difference between two analysis are however not explained with clarity. This paper addresses the consistency by comparing the queueing analysis and the shock wave analysis with graphical illustration. In the case of congestion caused by varying capacity, it is shown that the time the cumulative arrival curve meets the cumulative departure curve in queueing diagram is different with the time the congestion regime disappears in time-space diagram. It that means the description of queueing analysis in some literatures should be corrected and the measures obtained with queueing analysis should be understood carefully. The trajectories constructed by shock wave analysis make the same cumulative arrival curve and cumulative departure curve with those constructed by queueing analysis. It ensures the consistency of two analysis and the identical delay calculation. The prerequisite that the queueing analysis measures the vertical vehicle at the fixed position explains the differences in queue length and queue duration calculations of both analyses.
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