Abstract
This research aims to model traffic flow queuing system of three crossroads, namely the Monjali, Kentungan, and Gejayan crossroads in Yogyakarta with one underpass at the Kentungan crossroad using max-plus algebra. This research is based on data of traffic flow density, especially cars and traffic light duration data on the three crossroads. Then, a crossing condition scheme is created and represents the direction of car movement especially in the direction from Monjali to Gejayan. Then the model is compiled which includes the waiting time of cars when the red traffic light is on, the time cars leave the crossroad during the green traffic light is on, and the travel time of cars between crossroad with max-plus algebra, so that the total vehicle time can be determined from Monjali to the Gejayan crossroad . The results show that the queueing system can be modelled using max-plus algebra. Furthermore, it can be determined the waiting time, the time to leave crossroad, and the total time needed to cross from the Monjali crossroad to exit the Gejayan crossroad. The resulting model can reduce congestion on the lines of the intersection of Monjali, Kentungan and Gejayan.
Highlights
The model is compiled which includes the waiting time of cars when the red traffic light is on, the time cars leave the crossroad during the green traffic light is on, and the travel time of cars between crossroad with max-plus algebra, so that the total vehicle time can be determined from Monjali to the Gejayan crossroad
This research is located at the Kentungan, Monjali and Gejayan intersections in Yogyakarta
From the Max-plus algebra model and the data obtained from direct observation, it can be determined that the eigenvectors and eigenvalues are used to determine the travel time of the vehicle every 1 round
Summary
Transportation movement issues, especially congestion problems in urban areas, often occur at crossroads. Kentungan-Gejayan underpass is one of the alternative traffic systems to facilitate the density that occurs in the area. Maxplus algebra (the set of all real numbers R equipped with max and plus operations) can be wellused to model and analyze algebraically network problems, such as problems: scheduling (project) and queuing systems, more details can be seen in [2]. Max-Plus algebra is a set R ∪ {−∞} and R is a set of all real numbers equipped with maximum operation, denoted by ⨁ and addition operation denoted by ⨂. Graphs in max-plus algebra are discussed [3]
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