## 1 Introduction  
The traffic queueing problem in transportation network has been studied for many decades since the demand always exceeds the capacity. Furthermore, the traffic queueing problem is with the time-varying feature within a day. Usually, the analysis procedure of traffic queuing problem can be performed as a queueing system and can be solved by two concepts: the static and dynamic mode. The conventional static models can be solved in an efficient manner to derive the results based on the assumptions. However, the static models may not be able to represent the real-world situations such as the fluctuation of the demand over time and temporary over saturation of network flows. Instead, the dynamic traffic queueing models are common adopted around the world and depict the real situation. [PERSON] et al. [1] propose a Bayesian probabilistic model to estimate the traffic state with an 8.5% error rate based on synthetic test. [PERSON] et al. [2] developed a fast spatial queue model anchored to a simulation framework consisting with an agent-based travel demand. [PERSON] and [PERSON] [3] construct a mathematical framework and a predictive model of lane-based control delay to estimate lane-based incremental queue accumulations. [PERSON] et al. [4] propose their adaptive traffic signals control minimizing the congestion problem occurring at the intersection and assume the arrival rate following the Poisson distribution. They further indicate that the proposed model is efficient and minimizes the delay/congestion. As we can see, the previous studies assume the real-world situation satisfying the specific distributions to derive results. In reality, the traffic conditions may not easily be described by a distribution. In this paper, we propose a dynamic adjusting model to solve the traffic queuing problem. Our model applies the heuristic solution procedure to derive the optimal solutions. This paper further utilizes the simulation data to validate our model and adopts the Monte Carlo simulation method which is the numerical method for traffic queueing problem in our research to test the resulting outcomes. It should be noted that the reason why we apply Monte Carlo simulation is that [PERSON] and [PERSON] [5] state that the numerically simulated stochastic processes could be done well by discretizing the process into small time steps and applying pseudo-random sequences to simulate the randomness. Furthermore, based on its efficient and wide scope of applicability in [6], this research determines to utilize the Monte Carlo simulation generally applying to all simulation data that use stochastic methods to generate new configurations in Formosa Freeway of Taiwan of interest. The results show that the proposed model outperforms the previous ones. Additionally, our solution procedure can be easily applied to the real-world situation without assuming the specific distribution because of pseudo-random feature. Additionally, Radio Frequency Identification (RFID) is widely utilized to collect the data and then to identify and monitor objects. This leads to the situation where the objects can be automatically tracked and controlled. We can say that this is the Internet of Things (IoT). As a result, our solution procedure can be implemented once the RFID reaches the mature stage. The remaining parts of this paper can be organized as follows. The literature review is surveyed in Section 2. Section 3 presents our proposed model and Section 4 utilizes the illustrative example and further conducts the analysis based on the results. Finally, Section 5 concludes this study and provides the future direction of the research.