Moderate length of time window can get the best accurate result in detecting the key incident time using extended spectral envelope. This paper presents a method to calculate the moderate length of time window. Two factors are mainly considered: (1)
The significant vertical lines consist of negative elements of eigenvectors; (2) the least amount of interruption. The elements of eigenvectors are transformed into binary variable to eliminate the interruption of positive elements. Sine transform is introduced to highlight the significant vertical lines of negative elements. A novel Quality Index (QI) is proposed to measure the effect of different lengths of time window. Empirical studies on four real traffic incidents in Beijing verify the validity of this method.
A traffic incident analysis method based on extended spectral envelope (ESE) method is presented to detect the key incident time. Sensitivity analysis of parameters (the length of time window, the length of sliding window and the study period) are di
scussed on four real traffic incidents in Beijing. The results show that: (1) Moderate length of time window got the best accurate in detection. (2) The shorter the sliding window is, the more accurate the key incident time are detected. (3) If the study period is too short, the end time of an incident cannot be detected. Empirical studies show that the proposed method can effectively discover the key incident time, which can provide a theoretic basis for traffic incident management.
Previous works have shown the universality of allometric scalings under density and total value at city level, but our understanding about the size effects of regions on them is still poor. Here, we revisit the scaling relations between gross domesti
c production (GDP) and population (POP) under total and density value. We first reveal that the superlinear scaling is a general feature under density value crossing different regions. The scaling exponent $beta$ under density value falls into the range $(1.0, 2.0]$, which unexpectedly goes beyond the range observed by Pan et al. (Nat. Commun. vol. 4, p. 1961 (2013)). To deal with the wider range, we propose a network model based on 2D lattice space with the spatial correlation factor $alpha$ as parameter. Numerical experiments prove that the generated scaling exponent $beta$ in our model is fully tunable by the spatial correlation factor $alpha$. We conjecture that our model provides a general platform for extensive urban and regional studies.
