Infinite capacity single server queue with exponential arrivals and general distributed service (M/G/1)

Step 1: Simulation Setup

In this step, configure the simulation environment to prepare for the experiment. Open the simulation software and navigate to the configuration section. Here, set the values of the following parameters:

  • Mean Arrival Rate: This parameter represents the average rate at which entities (such as customers or tasks) arrive at the system. Choose a suitable value based on the expected arrival pattern.
  • Service Time Distribution: Select the distribution that best represents the service times in the system. Common distributions include exponential, normal, and uniform distributions.
  • Mean Service Rate: Define the average rate at which entities are served by the system. Ensure that this rate is appropriate for the workload and system capacity.
Step 2: Verify Conditions

Before proceeding with the experiment, it is crucial to verify certain conditions to ensure the validity of the results. Specifically, confirm that the mean arrival rate is less than the mean service rate. This condition is necessary for the existence of a steady-state solution in the M/G/1 queuing model. If the mean arrival rate exceeds the mean service rate, the system may experience instability or long-term queuing behaviour.

Step 3: Start Experiment

Start the experiment once the simulation environment is configured and conditions are verified. Click on the 'Start' button within the simulation software to initiate the simulation process. This action will begin the simulation, allowing entities to enter the system and be served according to the specified parameters.

Step 4: Monitor Experiment

During the experiment, closely monitor the behaviour of the simulated system. Observe how entities arrive, queue (if applicable), and are served by the system. Pay attention to any fluctuations or patterns in the system's performance. When you have gathered sufficient data or wish to analyze the system's steady-state behaviour, proceed to the next step.

Step 5: Analyze Results

After stopping the experiment, analyze the results obtained from the simulation. This analysis may include:

  • Numerical Analysis: Examine numerical metrics such as average queue length, average wait time, and system throughput.
  • Graphical Analysis: Visualize the system's behaviour through graphs or charts, depicting metrics over time or under different conditions.
  • Comparison: Compare the theoretical predictions of the M/G/1 queuing model with the experimental results obtained from the simulation. Evaluate any discrepancies and consider possible reasons for differences between theory and practice.