**2. Related Works**

Traffic control and managemen<sup>t</sup> are a primary issue in urban transport networks. In general, bottlenecks are identified and studied to find ways to overcome their negative effects on traffic. The traffic bottlenecks in urban road networks are more challenging to investigate than in freeways or simple arterial networks [8]. Traffic bottlenecks in urban road networks vary with traffic demands with spatiotemporal characteristics. Other events, such as traffic signals, traffic accidents, roadworks, and severe weather conditions, are required to consider more of their impacts on urban networks than in freeways.

When a bottleneck happens, there is a notable difference between traffic speed in the bottleneck area and its nearby downstream links. Oversaturation is usually caused by vehicle queues first occurring at some bottleneck intersections (i.e., critical intersections) and then propagating to neighboring upstream and downstream links between intersections. In [9], to identify oversaturated intersections, the authors proposed residual queue length estimation using shockwave speed. The authors also presented the detection of spill-over by identifying long detector occupancy time during the green phase. In [10], the authors proposed the identification of bottlenecks in an urban area practicing on causal congestion trees and graphs with the correlations of road segments according to the congestion propagation speed. More recently, in [11], the authors studied a traffic bottleneck identification method based on the traffic speed of loop detector data using the fusion of different collection cycles of loop detector data. To identify urban bottlenecks, in [1], the authors proposed a congestion analysis on the bottleneck core link and its neighboring links by clustering links based on the ranks of speed.

More recently, GPS-equipped vehicles were used in the field of bottleneck identification. In [12], the authors presented the processes of identifying and defining bottlenecks using GPS data obtained by trucks. In [13], the authors explored and identified bottlenecks in urban areas based on recurrent low-speed segments in the road network using GPS data. In [14,15], the authors used a spatiotemporal variation of speed to identify and classify bottlenecks using GPS data and crowdsourced traffic data. In [16], the authors tried to identify recurrent bottlenecks using spatial and temporal concepts on probe-reported speed data. In [17], the authors proposed a bottleneck identification method on urban expressways based on the traffic speed variance between the bottleneck area and its neighboring downstream links by analyzing the floating car data. In [18], the authors investigated traffic state and identified traffic bottlenecks on urban expressways using the fusion data accessible from fixed detectors and mobile navigation application data.

Future traffic condition prediction is a general concept [19]. In [20], the authors proposed the characterization of the traffic predictor to analyze vehicular traffic behavior for the different road segments using SUMO. In recent years, as deep learning techniques have advanced rapidly, researchers have started to adopt deep neural networks for high-accuracy traffic prediction. The Recurrent Neural Network (RNN) is widely known as a proper method to recognize the spatiotemporal evolution of traffic flow. In [21], the authors proposed a deep learning architecture based on the Recurrent Neural Network and Restricted Boltzmann Machine (RNN-RBM) to predict the spatiotemporal congestion evolution pattern using GPS data. In [22], the authors used an error-feedback Recurrent Convolutional Neural Network structure (eRCNN) for continuous traffic speed prediction. However, the traditional RNN fails to capture the long-term evolution. To resolve the vanishing gradient problem in RNN, a Long Short-Term Memory (LSTM) network was proposed in [23]. LSTM is well suited to classify, process, and predict time series given time lags of unknown duration. In [24], the authors proposed a novel short-term traffic volume prediction model using LSTM. More recently, in [25], the authors proposed a multiple time step short-term traffic prediction architecture using the RNN framework based on LSTM.

As mentioned above, the studies discussed identifying bottlenecks in intersections and respective upstream and downstream links in urban areas. Furthermore, LSTM has been applied in short-term traffic prediction. However, to the best of our knowledge, research on gridlock analysis has not ye<sup>t</sup> been fully studied. We hope that this research will fill this gap by discussing the bottleneck and gridlock analysis based on the bottleneck at each intersection in the urban area. Congestion from the bottleneck originates traffic jams and propagates to neighboring upstream and downstream vicinities [26]. Such a situation usually leads to gridlock, which can potentially reduce traffic efficiency to an almost halted state, especially in a complex urban road network. Gridlock is used to describe severe road traffic congestion with zero flow [27,28]. Each interrelated intersection in a road network is fully occupied by slow-speed vehicles, and vehicles on conflicting approaches cannot move forward even when receiving a green traffic light, as shown in Figure 1. In our previous work [3], we proposed gridlock detection based on recurrent and non-recurrent congestion using the measurable gridlock characteristics in terms of traffic jam length and speed for both the upstream and downstream links of corresponding intersections. In previous work, we used simulated lane area detectors to detect gridlock, but these fixed-location detectors have some spacing limitations and installation costs in practice, as mentioned above.

**Figure 1.** An example of gridlock-looped intersections.

### **3. Simulation Framework**

Simulation models that can closely represent the real-world scenario are powerful and useful. In the area of road traffic simulation, three different models [29] are used, i.e., the (1) microscopic model, (2) macroscopic model, and (3) mesoscopic model. Microscopic simulation models have been used in several transportation areas in developing ITS technologies.

In this research, the Simulation of Urban MObility (SUMO) has been used to handle large, complicated road networks at a microscopic (vehicle-level) scale. SUMO is an open-source microscopic simulator developed by the German Aerospace Centre DLR in 2001 [30]. SUMO supports the traffic simulation community with a full-featured suite of modeling utilities, including the TraCI tool [31]. This tool is a Python API allowing users during the simulation run-time to retrieve simulated objects' values, e.g., in accessing the speed of simulated GPS vehicles on each link in the simulated urban network.

For traffic police and traffic engineer deployment, an educational tool [7] has been introduced by the Chulalongkorn University's Sathorn Model project in Bangkok (Thailand), namely the Chula-Sathorn SUMO Simulator (Chula-SSS). By using this tool, traffic police can see the traffic signal phase, the queue length of vehicles in each upcoming direction at each signalized intersection, and the overall area with neighborhood road segments with user-friendly interfaces. Chula-SSS supports two calibrated datasets (morning and evening rush hours) for the Sathorn road network area. This study chose to investigate the morning case of Chula-SSS from 6 am to 9 am (corresponding to 21,600 s to 32,400 s after midnight). This time interval is the morning congestion period during weekdays [7], whereby in practice, the local traffic police have often observed the real occurrences of gridlocks in the network. The simulated Chula-SSS consists of 2375 intersection nodes, 4517 edges, and 10 signalized intersections, as shown in Figure 2.

**Figure 2.** Sathorn road network topology in SUMO.

The dataset consists of 55,000 traveling vehicles in the morning or evening rush hours. Recurrent based gridlock happens on a daily basis in both morning and evening rush hours. This gridlock phenomenon has been intentionally disabled during the calibration attempt of Chula-SSS to find the optimal mobility model parameters. To exhibit the case of gridlock during morning rush hours, the previous work [3] already included two extra routes (1 and 2) to the Sathorn critical region of Chula-SSS with traffic flows of 2125 vehicles (Route 1) and 1500 vehicles (Route 2) per hour, with their routes as shown in Figure 3. The Sathorn critical region is where about 12,000 out of 55,000 vehicles travel on 10 edges, as shown in Figure 4. The GPS data collection has different time resolutions (1 s, 5 s, 10 s, 15 s, 20 s, 25 s, 30 s, 35 s, 40 s, 45 s, 50 s, 55 s, 60 s) within the simulation time interval for three hours from 6 am to 9 am. The collected vehicle data are assumed as GPS vehicles. With the limited penetration ratio of GPS vehicles, the different number of samples of GPS vehicles (1%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%) that passed through the links in the simulated gridlock area were investigated for the development of the identification of bottlenecks and the prediction of gridlock.

**Figure 3.** Simulated additional traffic routes representing parent trips to drop off students at local schools during morning rush hour.

**Figure 4.** Links in the Sathorn critical region.
