It is important to discuss the behavior of traffic at merging sections for the design and realization of an automated guided vehicle system (AGVS). In this study, we deal with a merging section of the AGVS by considering a time limit for the merging of vehicles. Near the merging section, traffic flowing in one direction must form a queue to avoid collisions between vehicles. We propose an improvement in the control strategy proposed in the previous research. However, it is difficult to analyze the mathematical model of the merging section. Analysis can be performed only for the case in which the time limit is one unit. We also propose a method for analyzing the model for an arbitrary time limit using a linear recurrence relation. We quantitatively discuss the influence of the time limit on the average queue length and the detour rate.
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