Visual simulators of stochastic processes written in JavaScript.

• Simulation of the M/M/c queue

  • You can find that a long queue is formed due to the existence of a customer with a large service time, who occupies the server for a long time. Also, adding a server to the system makes the queue shrink drastically.

• Simulation of the Lindley equation (M/M/1)

  • This simulates the following well-known recursion for single-server queues.

    \(\qquad\quad D_n = \max(0, D_{n-1} - G_n) + H_n\)
    
    \(\quad D_n\): The sojourn time of the \(n\)th customer
    \(\quad G_n\): The inter-arrival time between \(n-1\)st and \(n\)th customers
    \(\quad H_n\): The service time of the \(n\)th customer
    Running the simulation with large samples, you can see that the process converges to the steady state.


• Simulation of an AoI process (M/M/1)

  • This simulates the dynamics of the Age of Information (AoI). Running the simulation with large samples, you can see that the process converges to the steady state.