# Analysis of Macroscopic Traffic Network Impacted by Structural Damage to Bridges from Earthquakes
## 3 Model Development  
Traffic simulation software packages have been widely used in modelling, planning, and analysis of traffic networks and systems [28; 29; 30; 31]. Traffic simulation models generally can be classified into microscopic, mesoscopic, and macroscopic models. Microscopic traffic simulation programs model individual vehicles of transportation systems, while macroscopic simulation programs aggregate characteristics of traffic elements with more simplified networks. In this study, large-scale performance of traffic network is investigated for various capacity loss scenarios due to bridge damage from earthquakes. Since aggregate characteristics of traffic elements such as total system travel time and average speed are compared with difference scenarios, macroscopic approach is selected for the investigation. Among many other macroscopic traffic simulation models, EMME4 was selected for the analysis [32; 33]. EMME4 is a multimodal traffic planning prediction system consisting of complementary software applications. This model is used by planners to implement a mobility model allowing virtual laboratories to test the impact and interactions of traffic policies, demographics, and urban geography on available traffic infrastructure. Among various allocation techniques in the EMME4 program, input data for EMME include origin/destination trip matrix and highway network data with detailed information about each highway link, for example, node, length, link type, number of lanes, speed limit, and volume-delay function. Output from the model include traffic volume, travel speed, and travel time for each link. Detailed information about the program can be found in [34; 35]. Among many available assignment tools provided in EMME4, second line approximation (SOLA) assignment was used in this study. SOLA is an extremely efficient implementation of linear approximation transformation, a method that is rapidly converted into a finer solution than other linear approximation. Additionally, this method provides significant performance benefits to multiprocessing systems. The definition of SOLA allocation techniques is described in [32] as follows: \"The algorithm that has been influenced in the Second Line Approximation (SOLA) traffic assignment tool is an efficient multi-threaded adjustment of the bi-conjugate line expansion method for operation of the solution\". Ref. [36]. The behavioral assumption of the problem with the equilibrium allocation method is that each user chooses the path they know best. If there is a shorter route than the one on which the driver is travelling, the driver will choose that route. This leads to a flow that satisfies the Wardrop's user-optimal principle that no user can improve travel time by changing paths. Recently, it has been demonstrated by empirical studies using GPS and GIS technologies that people's actual route choice practice has discrepancies with the Wardrop's user-optimal principle [37]. [PERSON] and [PERSON] found that about two-thirds of the subject drivers did not use the shortest travel time path during a three-week study time period. However, in most circumstances, people choose routes that were less than 5 min longer than the shortest time routes. Therefore, it can be argued that travelers are still rational following the Wardrop's user-optimal principle in minimizing their perceived travel time while limited in their capacity to get perfect information. The advantage of the Wardrop's user-optimal principle is that this behavioral assumption allows traffic simulation software programs to solve the network assignment problems with mathematical computations. For this reason, transportation simulation software programs have been using this concept for decades for network assignment problems. Under this assumption, travel times in all routes actually used are equal and less than those that would be experienced by a single vehicle on any unused route.