Event Registration Arrival Queue Calculator

Method and input definitions

Arrival rate λ = attendees ÷ arrival-window minutes. Service rate μ = desks ÷ minutes per attendee per desk. Service-work equivalent = attendees ÷ μ; this is total workload expressed as uninterrupted service minutes, not necessarily elapsed time from the first arrival. Under the uniform-arrival fluid model, peak backlog = max(0, (λ − μ) × window). Queue-clearance tail after the arrival window = peak backlog ÷ μ. If attendees arrive throughout a nonzero window, estimated completion from check-in start = window + tail; with zero attendees, completion is 0.

Worked example

For 300 attendees arriving uniformly across 60 minutes, 3 desks at 0.5 minutes per attendee provide 6 people/minute of capacity. The 5-person/minute arrival rate is below capacity, so peak backlog and post-window tail are zero. Total service-work equivalent is 300 ÷ 6 = 50 minutes, but estimated completion is 60 minutes from check-in start because the last arrivals occur at the end of the window.

Assumptions and limits

This is a fluid approximation: arrivals are spread uniformly through the stated window and service is continuous at a constant pooled desk capacity. For an overloaded arrival rate, the modeled queue grows during the window and drains afterward at μ. Discrete service completion, uneven arrivals, staffing breaks, group check-in, and service-time variability can change actual waits and completion time.

Inputs are bounded to finite values shown in the form. Displayed results are rounded for readability (probability percentages and proportion fractions to four, other measures to two decimal places); whole-count outputs remain exact. A changed field clears a prior result so an outdated estimate is not presented as current.

References and related tools

These are direct calculations over user-supplied values; no external empirical benchmark is assumed.

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