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M/M/c Queue

A classic M/M/c queue implemented as a pure discrete event simulation in Mesa.

Summary

Customers arrive according to a Poisson process (rate λ) and join a single FIFO queue. c servers each draw from the queue independently, with exponentially distributed service times (rate μ per server). This is the standard multi-server queuing model from operations research, with well-known analytical solutions for validation.

Mesa DES features demonstrated

Feature Usage
schedule_recurring Stochastic customer arrivals (exponential inter-arrival times)
schedule_event(after=...) Scheduling service completions
run_until Running a pure event-driven simulation to a target time
Dynamic agent lifecycle Customers created on arrival, remove()d after service

The model disables Mesa's default step schedule (_default_schedule.stop()) and is driven entirely by events.

Design: server-centric

Servers are active agents. When a server completes service, it checks the queue and pulls the next customer itself — a natural ABM pattern, in contrast to the system-centric routing common in traditional DES.

How to run

python model.py

Runs the simulation for 10,000 time units and prints simulated vs. analytical steady-state metrics.

Files

File Description
agents.py Customer and Server agents
model.py MMcQueue model
analytical_mmc.py Erlang C closed-form solutions for validation

Analytical validation

For a stable M/M/c system (traffic intensity $ρ = λ/(cμ) < 1$), closed-form results exist via the Erlang C formula. The model includes analytical_mmc() to compute these, so simulation output can be compared directly:

M/M/3 Queue (λ=2.0, μ=1.0, T=10000.0)
Customers served: 19992

Metric                     Simulated   Analytical
---------------------------------------------------
Server utilization              0.6672       0.6667
Avg wait time                   0.3716       0.3750
Avg system time                 1.3716       1.3750

Results converge to analytical values as simulation time increases.

Visualisation

There's no visualization yet, but an app.py implementation would be appreciated!