COMPARATIVE ANALYSIS OF POISSON, EXPONENTIAL, AND UNIFORM DISTRIBUTIONS IN MODELING CUSTOMER ARRIVAL TIMES ON A WEB SERVER

Abstract

This study compares the Poisson, Exponential, and Uniform distributions to determine the most suitable model for customer arrival times on a web server. Server log data were processed into interarrival times and arrival counts, followed by parameter estimation using Maximum Likelihood Estimation and goodness-of-fit evaluations through Kolmogorov–Smirnov, Anderson–Darling, Chi-Square, and AIC/BIC metrics. The results show that the Exponential distribution provides the best fit for interarrival patterns, supported by a KS-statistic of 0.067 and p-value of 0.312, while the Poisson distribution demonstrates acceptable performance for arrival counts with a Chi-Square p-value of 0.224. In contrast, the Uniform distribution exhibits the weakest suitability, indicated by its highest AIC score (AIC = 9874). Queue simulation using an M/M/1 model confirms that Exponential-based arrival modeling yields the most stable system performance with an average waiting time of 0.42 seconds and server utilization of 0.73, compared to longer delays and higher utilization when using Poisson-derived rates. Overall, the findings indicate that the Exponential distribution is the most appropriate for modeling real web server arrival behavior, offering more accurate performance predictions and supporting improved capacity planning.