Queue Waiting Time and Server Capacity Calculator
Estimate steady-state waiting time and queue length for one shared queue feeding identical parallel servers.
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Calculation steps
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How to calculate
Convert arrivals to a rate per second. Use the Erlang C model for the probability that all servers are busy, then calculate mean queue wait and apply Little’s law for average queue length.
ρ=λ×mean service time/c; Wq=P(wait)/(c/mean service time−λ); Lq=λWq
Worked example
At 12 arrivals/hour, five-minute mean service and two servers, utilization is 50%, the probability of waiting is 1/3, mean queue wait is 1.6667 minutes and mean time including service is 6.6667 minutes.
Assumptions and input details
M/M/c steady-state scenario: independent Poisson arrivals, independent exponentially distributed service times, identical servers, first-come-first-served service, one shared unlimited queue, no abandonment and constant rates. Utilization must be below 100%; otherwise there is no finite steady-state mean wait. This is not a live queue forecast or a guarantee for individual customers. Zero arrivals yields zero queue wait; time including service remains the entered service mean. Threshold results concern waiting before service only.
References: IIT Guwahati NPTEL: M/M/m queues
Unit definitions
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Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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