Poisson Process and M/M/1 Queue Simulation

This project provides a lightweight framework to:

• Simulate Poisson processes and generate event‐time histograms.
• Simulate M/M/1 queues and compute performance metrics.

Both modules support sweeping over multiple parameter values in parallel.

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Requirements

• Python 3.x
• Install dependencies via pip (e.g. numpy, matplotlib).

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Poisson Process Simulation

Run the Poisson CLI under src/poisson:

python src/poisson/main.py \
  --rates 0.5 1.0 2.0      \  # one or more λ values
  --num-events 1000 5000    \  # one or more N values
  --delta 1.0               \  # histogram bin width
  --save-plots              \  # save histogram vs theoretical PMF
  --output-dir poisson_out  \  # (optional) output folder
  [--tmax <time>]           \  # (optional) max time horizon
  [--superimpose]           \  # (optional) combine processes

• Computes counts per interval and (if requested) saves plots in poisson_out/.
• Use -h or --help for full options.

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M/M/1 Queue Simulation

Run the M/M/1 CLI under src/mm1:

python src/mm1/main.py \
  --lambda-values 0.8 1.0   \  # one or more arrival rates
  --mu-values 1.5 2.0        \  # one or more service rates
  --num-events 10000         \  # number of departure events
  [--seed 42]                \  # (optional) RNG seed

• Simulates each (λ, μ) pair in parallel.

• Prints a table with:

  • E[N]: average number in system
  • E[T_sys]: average time in system
  • E[T_q]: average waiting time
  • Util%: server utilization

• Use -h or --help for full options.

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License

This project is released under the MIT License. Feel free to use and modify.