interarrivatieregels

Interarrivalieregels, or interarrival rules, describe the rules governing the time between consecutive arrivals of events in a stochastic process. They are central in queuing theory, telecommunications, manufacturing, and service operations, where the arrival pattern of customers, data packets, or jobs influences system performance.

An interarrival time is the elapsed time between successive arrivals. If the interarrival times are independent and identically distributed according to an exponential distribution, the arrival process is a Poisson process, which is memoryless. More general models use renewal processes with arbitrary interarrival distributions, including deterministic, Erlang, hyperexponential, or heavy-tailed distributions. The chosen distribution affects the variability of arrivals and the resulting queue dynamics.

Key characteristics include the mean interarrival time, μ = E[T], and the variance var(T). The coefficient of variation, cv = sqrt(var(T))/μ, measures arrival variability. For time-homogeneous processes, the distribution is stationary; non-stationary models allow the arrival rate to change over time, as in a non-homogeneous Poisson process.

Applications span several domains. In queueing models such as M/M/1 or M/G/1, interarrival rules determine the arrival stream and influence performance metrics like waiting time and queue length. In network design and traffic engineering, they affect buffer sizing and latency. In empirical studies, interarrival times are estimated from data using methods such as maximum likelihood or method of moments, with goodness-of-fit tests to select appropriate distributions.

Overall, interarrivalieregels link the statistical properties of arrivals to system performance and operational planning, helping to predict and manage congestion, wait times, and resource utilization.