In a large queuing system, the effect of the ratio of the filled data on the queue and waiting time from the head of a queue to the service gate are important factors for process efficiency because they are too large to ignore. However, many research works assumed that the factors can be considered to be negligible according to the queuing theory. Thus, the existing queuing models are not applicable to the design of large-scale systems. Such a system could be used as a product classification center for a home delivery service. In this paper, we propose a tree-queue model for large-scale systems that is more adaptive to efficient processes compared to existing models. We analyze and design a mean waiting time equation related to the ratio of the filled data in the queue. Based on simulations, the proposed model demonstrated improvement in process-efficiency, and it is more suitable to realistic system modeling than other compared models for large-scale systems.
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