Markovian queues with multiple-server (infinite capacity)(M/M/c)

To conduct the experiment for the M/M/c queueing model, follow these detailed steps sequentially:

  1. Set Simulation Parameters:

    • Set the Mean Arrival Rate: Input the average rate at which customers arrive at the system.
    • Set the Mean Service Rate: Input the average rate at which each server can process customers.
    • Set the Number of Servers: Define the total number of servers in the system.
  2. Ensure Steady-State Conditions:

    • Check the Relationship between Parameters: Ensure that the mean arrival rate is less than the product of the mean service rate and the number of servers. This condition is necessary for the existence of steady-state distribution, where the system can operate in equilibrium over time without the queue growing indefinitely.
  3. Set the Simulation Speed:

    • Adjust Simulation Speed: Set the simulation speed according to your requirements. Adjusting the speed can help in either speeding up the simulation process or slowing it down for more detailed observation.
  4. Start the Experiment:

    • Initiate the Simulation: Click the 'Start' button to begin the simulation. The system will start processing customers based on the parameters you have set, simulating the arrivals, services, and departures.
  5. Stop the Experiment and View Results:

    • Stop the Simulation: After allowing the simulation to run for a sufficient period to gather data, click the 'Stop' button.
    • View Results: Examine the steady-state results provided by the simulation. These results will be available both numerically and graphically, showing metrics such as the average number of customers in the system, the probability of having a certain number of customers in the system, average waiting time, and server utilization.
  6. Compare Theoretical and Experimental Results:

    • Analyze the Data: Compare the numerical and graphical results obtained from the simulation with the theoretical predictions of the M/M/c model. This comparison helps validate the theoretical model and provides insights into the system's performance under different conditions.