Interarrivalzeit

Interarrivalzeit refers to the time duration between successive events in a system. It is a fundamental concept in queuing theory and stochastic processes, often used to model the arrival of customers at a service point, the occurrence of network packets, or the timing of equipment failures. The interarrival time is a random variable, and its distribution provides insights into the patterns of event arrivals.

A common assumption in many queuing models is that interarrival times follow an exponential distribution. This assumption implies that the arrivals are independent of each other and occur at a constant average rate. However, in real-world scenarios, interarrival times can exhibit more complex patterns, such as deterministic, Erlang, or even hyperexponential distributions, depending on the underlying process.

Analyzing interarrival times is crucial for understanding system performance. For instance, in a call center, short interarrival times might indicate a need for more agents, while long interarrival times might suggest overstaffing. The statistical properties of interarrival times, such as their mean, variance, and distribution shape, are key parameters for designing efficient systems and predicting their behavior. Understanding interarrival times helps in capacity planning, resource allocation, and performance optimization.