CTM Based Calculation of Number of Stops and Waiting Times

The Cell Transmission Model (CTM) is a numerical approximation of the shockwave theory. The CTM divides the links into discrete segments, known as cells, and updates the density of each cell (number of vehicles) after every second. Due to its simple formulations and highspeed execution, the CTM is considered advantageous for model-based Adaptive Traffic Control Systems (ATCSs). A CTM implementation was developed within Sitraffic Motion, the “Motion-CTM” [9]. The “Extended Motion-CTM” [11] calculates two performance indices for the online signal plan optimization in Sitraffic Motion: the number of stops and the waiting time. The Extended Motion-CTM introduces a new variable for every cell in the network, the Congestion Indicator ????????????????. The ???????? not only facilitates the calculation of the number of stops and the waiting time, but also assigns the calculated values to the appropriate signal. The significance of this novel idea is that it enables the calculation of signal related performance indices for the whole network in each second. The development of the ???????? algorithm in the form of a finite-state machine diagram is the core of this work. For the calculation of the number of stops, the ???????? is utilized to identify the cells at the end of the queue. Based on the outflow (vehicles per second) of these cells, the number of stops is derived. For the calculation of the waiting time, the ???????? is utilized to identify the cells that are in the queue. The waiting time is derived from the density of these cells and their outflow. The evaluation of the proposed algorithms shows that both the derived number of stops and waiting time are very close to the theoretical values obtained from the shockwave theory. Regarding the number of stops, the evaluation shows that the proposed algorithms perform much better than the approximation by Lin [10]. Regarding the waiting time, the evaluation shows that the delay calculation based on Almasri [6] and the waiting time in the Extended Motion-CTM give very similar results.     «

The Cell Transmission Model (CTM) is a numerical approximation of the shockwave theory. The CTM divides the links into discrete segments, known as cells, and updates the density of each cell (number of vehicles) after every second. Due to its simple formulations and highspeed execution, the CTM is considered advantageous for model-based Adaptive Traffic Control Systems (ATCSs). A CTM implementation was developed within Sitraffic Motion, the “Motion-CTM” [9]. The “Extended Motion-CTM” [11] c...     »