## 4 Simulation Model of Metro Congestion Propagation Process
### Augmented Metro Network
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **Alternatives** & \multicolumn{1}{c}{**M1**} & **M2** & **M3** \\ \hline
**Parameters** & & **Value (_t-Test_)** & **Value (_t-Test_)** & **Value (_t-Test_)** \\ \hline ASC1 & & 7.790 (114.770) & 7.630 (83.200) & 7.930 (77.080) \\ AC/m & & 0.178 (13.210) & 0.167 (8.750) & 0.190 (9.870) \\ BC & & \(-0.204\) (\(-3.890\)) & \(-0.143\) (\(-1.950\)) & \(-0.273\) (\(-3.630\)) \\ RSC & Route 1 & \(-0.059\) (\(-5.460\)) & \(-0.076\) (\(-3.400\)) & \(-0.049\) (\(-3.900\)) \\ Travel cost/CNY & & \(-6.49\times 10^{-4}\) (\(-0.620\)) & \(3.69\times 10^{-3}\) (\(2.610\)) & \(-6.67\times 10^{-3}\) (\(-4.030\)) \\ Travel time/min & & \(-0.030\) (\(-33.490\)) & \(-0.032\) (\(-26.210\)) & \(-0.027\) (\(-20.940\)) \\ Transfer times & & 0.087 (5.220) & 0.089 (3.730) & 0.085 (3.580) \\ \hline ASC2 & & 5.990 (85.450) & 6.050 (64.730) & 5.910 (54.820) \\ ASC3 & & 5.640 (56.290) & 5.850 (41.650) & 5.400 (37.080) \\ ASC4 & Route 2 & 3.610 (37.940) & 3.590 (26.730) & 3.670 (26.770) \\ AC/m & Route 3 & 0.178 (13.210) & 0.167 (8.750) & 0.190 (9.870) \\ BC & Route 4 & \(-0.204\) (\(-3.890\)) & \(-0.143\) (\(-1.950\)) & \(-0.273\) (\(-3.630\)) \\ Travel cost/CNY & & \(-6.49\times 10^{-4}\) (\(-0.620\)) & \(3.69\times 10^{-3}\) (\(2.610\)) & \(-6.67\times 10^{-3}\) (\(-4.030\)) \\ Travel time/min & & \(-0.030\) (\(-33.490\)) & \(-0.032\) (\(-26.210\)) & \(-0.027\) (\(-20.940\)) \\ Transfer times & & 0.087 (5.220) & 0.089 (3.730) & 0.085 (3.580) \\ \hline ASC5 & & 2.040 (22.250) & 2.310 (18.310) & 1.730 (12.710) \\ Travel cost/CNY & Route 5 & \(-6.49\times 10^{-4}\) (\(-0.620\)) & \(3.69\times 10^{-3}\) (\(2.610\)) & \(-6.67\times 10^{-3}\) (\(-4.030\)) \\ Travel time/min & Route 6 & \(-0.030\) (\(-33.490\)) & \(-0.032\) (\(-26.210\)) & \(-0.027\) (\(-20.940\)) \\ Transfer times & & 0.087 In the augmented metro network, passengers from station \(a\) going to station \(c\) need to switch twice in transfer 1 and transfer 2, and their route contains 4 virtual stations and 2 virtual transfer links. Route from station \(b\) to station \(c\) contains 4 virtual stations but only 1 transfer in transfer station 2. Route from station \(b\) to station \(d\) contains 4 virtual stations and no transfer for station \(b\) and \(d\) are collinear stations. Travel time on each route is the summation of travel time on actual links, dwell time and transfer time. The number of virtual stations and virtual links is correlated to the number of metro lines that the transfer station connected. However, when it comes to the real metro network, which the condition is much more complicated. As mentioned above, by the end of 2018, GZM has already possessed over 250 stations. In order to construct the whole Guangzhou metro network with augmented network theory, some basic assumptions are listed below to simplify the unnecessary structures in the network and improve computing efficiency. 1. Stations at both ends of a metro line shared with other metro lines as ends are not regarded as transfer stations, for there are fewer transfer passengers in these stations, such as Guangzhou south railway station on line 2 and line 7. 2. The metro network is a directed graph, but as the distance and travel time are similar between link \(l_{ij}\) and \(l_{ji}\), it is regarded as an undirected graph in the simulation and the only difference lies in the directions of the links. Following these assumptions, we constructed a virtual metro network for GZM. Comparing with the original network, 132 virtual links, and 91 virtual stations are added into the augmented metro network. Totally, the virtual network of Guangzhou metro has 262 stations and 332 links.