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Queue simulation: fixed-time incrementing
Simulates an M/M/1 queue by the fixed-time incrementing method.
2024.Nov.25 03:30:43
α, μ Arrival rate, service rate (per minute, i.e., T−1). •
time, Δt Simulation time and increment (minutes, i.e., T). •
Lq0 Initial queue length (steady-state value if < 0).
Graph points No. of points in graph (1 per increment iff 0). •
Seed Seed for random (iff 0, no repeatability).
Show values Show graph coordinate values.

Simulates an M/M/1 queue with the parameters given, by the 'fixed-time incrementing' method, as opposed to the 'next-event incrementing' method. (The simulation run length is ajusted to one million time increments if more are given.)

If it is: (a) α < μ (recommended), the steady state may be attained, and a comparison to the analytical results is then possible; and (b) Lq0 < 0, the initial queue length will be computed as the steady-state value.

If graph points ('ngp') is not 0, Δt will be changed to 'time ⁄ ngp'.

This plate is inspired in H&L [2005, 937] (α = 3, μ = 5 / min).

References: Plate: Queuesimul

• H&L: [Hiller & Lieberman, 2005], Ch. 20, "Simulation", 20.1, "The essence of simulation", pp 937–940, Example 2, "An M/M/1 queueing system.

• 1512-03-05: Mercator Gerardus († 1594-12-02, 82 yrs.).

 
 
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Created: 2008-03-04 — Last modified: 2021-07-16