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In this paper, the priority disciplined queuing models are investigated under neutrosophic environ ment. It develops and optimizes a model with non-preemptive priorities system, denoted by NM/NM/1. It is a queuing model where the arrivals follow a Poisson process, service times are exponentially distributed and there is only one server whose arrival rate and service rate are represented in terms of single valued trapezoidal Neutrosophic number (SVTNN). Using (α, β, γ)-cut approach and Zadehs extension principle, the Neutrosophic queuing model is reduced to a crisp model and results are discussed. An illustrative example is provided to understand the analytical procedure developed in this paper.