This paper proposes a model for merging sections in transportation systems and then analyzes traffic flow under this model. For this analysis, vehicles are represented by an idealized model based on a Markov chain model. Vehicles arrive at the merging section randomly in either of two inflow lines. When a vehicle arrives at the merging section, if no vehicle is present in the other line, then the vehicle must wait in order to connect with another vehicle on the other line before entering. In this merging section model, the queue length is restricted according to the travel time from the origin to destination. The mean queue length and mean queuing delay at the two inflow lines are explicitly derived here. The relation between the maximum queue length and the behavior of traffic is examined, and the obtained results clarify some characteristics of the proposed model.