Discrete-event modelling of the capacity of the toll collection exit point and the formation of congestion

Application of Simulation Modeling to Assess the Operation of Urban Toll Plazas

“…Since perturbations in the form of user behavior effects are added to the model, the gamma law of the service time distribution seems to be quite expected, as being more general with respect to the Erlang distribution (see more details in the article by Talavirya A.Yu., Laskin M.B. [33]). Figure 4 shows the distribution of service times (section traversal) for a traffic volume of 3000 vehicles/h.…”

“…Such a distribution is obtained by John Gordon Skellam [34]. Then (a detailed description is given in paper [33]):…”

“…The length of the queue V * t 0 , τ ðÞ , formed during the time interval t 0 , t 0 þ τ ½ at variable input intensity λ t ðÞwill be a discrete random variable with a distribution law (see [33] for details):…”

“…As before, X ∈ Pois λ * ðÞ is a random variable, the number of vehicles leaving the TP zone per unit time, and Y ∈ Pois λ ðÞis a random variable, the number of vehicles arriving at the start of the queue per unit time. Then, X t is the number of vehicles leaving the TP zone in time t is also a random variable and X t ∈ Pois λ * t ðÞ : It can be shown (see details in [33]) that the distribution density of the random variable T, the time in which all the vehicles arrive at the beginning of the queue per unit time (with intensity λ), with the intensity of outgoing flow λ * will leave the queue, can be written as…”

“…The Shuvalovsky interchange allows to relieve the traffic load both from the street and road network of the district and from the TP at the exit from the WHSD to Bogatyrsky Ave., which was assessed by the authors earlier in Section 3 as well as in the articles [33,39].…”