Poisson arrivals
Understand irregular arrivals around a stable long-run rate and their relationship to exponential interarrival times.
Ten arrivals per hour is an average, not one arrival every six minutes. A Poisson process produces irregular gaps while the long-run count stays around the chosen rate.
Only the arrival times are random. The downstream service still handles each arrival normally.
- Poisson sourceArrivals
Arrivals happen at random times
λ = 8 / h - ActivityService
Handles each arrival when it occurs
The basic model assumes arrivals occur independently and at a constant rate. One arrival does not make another arrival more or less likely, and the rate does not drift with time.
- Good fit: independent calls or requests around a stable rate.
- Poor fit: appointments, scheduled batches, rush-hour peaks, or arrivals triggered by one another.
In a homogeneous Poisson process, the time between arrivals follows an exponential distribution. A rate of λ arrivals per hour corresponds to a mean interarrival time of 1/λ hours.
mean interarrival time = 1 / λ
If demand changes by hour, weekday, season, or event, model that changing rate explicitly. If arrivals come in groups or one event triggers others, use a process that preserves that dependence instead of forcing independent arrivals.
Compare simulated counts by time period with observed counts, inspect the distribution of interarrival times, and look for clustering or time-of-day structure. A queue can look like a capacity problem when the real error is an arrival model that smooths away bursts.