Random permutations generated by delay models and estimation of delay distributions

Key Points

• The main objective is to estimate the delay distribution using random permutations of arrival and departure times in systems with independent delays.
• Analyzed arrival times as independent and uniformly distributed on the unit interval.
• Examined delay times as independent with a specific distribution function.
• Utilized random permutations to connect the ranks of arrivals and departures.
• Applied empirical copulas for nonparametric analysis and pattern frequencies for parametric situations.
• Established a methodology for estimating delay distributions using random permutations.
• Identified differences in estimation approaches for nonparametric and parametric distributions.