Queue Simulation M/M/c + SLA

Inputs

λ: trucks/hour

μ: trucks/hour/server

Simulation time: hours

SLA waiting limit: minutes

Server scenarios c

Histogram bins

Random seed

Status: Ready.

Summary table

c	N	Mean wait	P95 wait	Mean system	Queue max	Util.	> SLA	≤ SLA

Time outputs are reported in minutes. Utilization is clipped to the selected simulation horizon.

Queue Simulation M/M/c + SLA

Enter the arrival rate, service rate, simulation horizon, SLA threshold, and server scenarios. Click Run Simulation to compare alternative numbers of parallel servers.

Interarrival time: T_a = −ln(U)/λ
Service time: T_s = −ln(U)/μ
System type: M/M/c, first-come first-served, unlimited waiting space

The application calculates mean waiting time, 95th percentile waiting time, mean time in system, maximum observed queue length, server utilization, and SLA compliance.

Waiting-time histograms with common bins

Mean and P95 waiting time

Percentage of SLA violations

Speed 1.00×

Run simulation first

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