<![CDATA[The study of queuing systems has an important role in the development of applied mathematics, especially in probability theory and stochastic processes. Classical models such as M/M/1 generally assume a Poisson arrival process so that the inter-arrival time is exponential, but in real service systems the arrival pattern is often non-Poisson with excessive variance and long tails of the distribution. This research proposes Monte Carlo simulation-based inter-arrival time distribution modeling in two scenarios: constant arrival rate (Scenario 1) and variable (Scenario 2). The interarrival data from the simulation results were analyzed using descriptive statistics and validated with the Kolmogorov–Smirnov (K–S) goodness of fit and Chi square tests for four candidate distributions: Exponential, Gamma, Weibull, and Lognormal. Descriptively, Scenario 1 has a mean of 1.9790 and a variance of 1.3238, while Scenario 2 has a mean of 2.0076 and a variance of 2.4025 and higher skewness and kurtosis. The K–S test results show that the exponential distribution is rejected in Scenario 1 (D = 0.1708; p < 0.001) and Scenario 2 (D = 0.0906; p = 0.0135). In Scenario 1, the Gamma distribution provided the best fit (K–S D = 0.0265; p=0.9808; Chi square = 19.8667; p = 0.2811). In Scenario 2, the Lognormal distribution was the most appropriate (K–S D = 0.0230; p = 0.9963; Chi square = 7.3333; p = 0.9788). These findings confirm that the exponential Poisson assumption is not always representative and that choosing a validated arrival distribution (Gamma/Lognormal) can increase the accuracy of queuing system analysis in both stable and dynamic conditions.]]>
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