## 2 Literature Review  
[PERSON] et al. [7] introduce that the Monte Carlo simulation is a simulation process utilizing random numbers to generate simulation events. The simulation process includes data collection, random number assignment, model formulation and analysis. [PERSON] and [PERSON] [8] conclude that the specific advantages of Monte Carlo simulations can be combined, giving the modeler great flexibility in the approach to a specific problem. In addition, the Monte Carlo methods are generally easily parallelizable, with some techniques being ideal for use. The (model/methodological) novelty of its application in traffic queueing compares with its previous applications [9; 10; 11; 12; 13; 14; 15; 16] as follows. Based on the traffic flow pattern in single intersection, the authors employ the Monte Carlo method in combination with MATLAB to simulate, which is proved to be more effective than the conventional control methods [9]. [PERSON] et al. [10] argue that after selecting the queueing model, data must be collected, parameters estimated by some suitable statistical method, and performance measures computed to evaluate the system, including traffic intensity which is defined as the ratio between the arrival rate and service rate. [PERSON] et al. [11] adopt the Monte Carlo sampling method for the sake of formulating the dynamic spatial charging demand distribution map of the traffic network region. [PERSON] et al. [12] employ the Monte Carlo simulation to show how net present value decreases with stochastic prices of diesel. This result is expected as a higher fuel price incurring higher cost for Electric Jepney operations and therefore lower profits. [PERSON] et al. [13] conduct simulations for four distinct scenarios of mean vehicular flow and mean time interval between successive bus arrivals. The traffic simulator is initially designed to use a parametric approximation of the Poisson probability distribution of the considered random variables based on the Monte Carlo method. In addition, [PERSON] and [PERSON] [14] utilize the Markov Chain Monte Carlo (MCMC) sampling method to solve the Channelized Section Spillover (CSS) problem. [PERSON] et al. [15] apply the Monte Carlo simulation to develop their new traffic noise prediction approach. [PERSON] et al. [16] develop the control chart to monitor traffic intensity and further utilize the Monte Carlo simulation to verify their resulting outcomes. [PERSON] et al. [17] argue that traffic signal lights are explicitly incorporated into the network structure so that total travel time is a piecewise linear convex function of the number of units traveling on the streets. [PERSON] [18] presents a new dynamic model of peak period traffic flows on congested capacity-constrained urban road networks. The model determines the time-varying costs incurred in traversing the various routes when time-varying route inflows are specified. [PERSON] [19] uses the cell transmission model to formulate the single destination system optimum dynamic traffic assignment problem as a linear program. It addresses various related issues such as necessary and sufficient conditions of the concept of marginal travel time in a dynamic network and system optimum. [PERSON] et al. [20] introduce the dynamic multimodal supply and equilibrium model based on implicit path enumeration. It defines within-day dynamic elastic demand stochastic multimodal equilibrium as a fixed-point problem on users flows and transit line frequencies. [PERSON] [21] considers a dynamic traffic assignment model with deterministic queuing and inelastic demand for each origin-destination pair in the network. In the single bottleneck per route case, the route cost function is shown to be a monotone function of the route flow if the bottleneck capacities are all non-decreasing as functions of within-day time. [PERSON] et al. [22] describe a simulation-based, iterative dynamic equilibrium traffic assignment model. The results show that their model is applicable to medium-size networks with a reasonable computation time.