This paper proposes self-similarity nature of the data; and how it plays a crucial role in queuing system in the field of congestion traffic. The proposal summarizes that arrival pattern of vehicles on Highways is self-similar in nature. Also illustrate the results in terms of Length of the Queue, delay behavior, waiting time, Traffic Intensity etc., using Queuing models. For this we provided the data from V.R Technique Consultant Pvt. Ltd, India, Using M/M/1 queuing model and an empirical with Hurst index terms mean queue length has been computed against traffic intensity. Results of the study reveal that mean queue length increases as ρ and Hincrease. This kind of research is to forecast the performance analysis and chronic improvement of toll plazas.
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