Infinite capacity single server queue with general distributed arrivals and exponential service (GI/M/1)
In order to perform the experiment, one needs to go through the following steps sequentially:
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:
- Arrival Time Distribution: Select the distribution that best represents the arrival times in the system. Common distributions include exponential, normal, and uniform distributions.
- Mean Service Rate: This parameter represents the average rate at which entities (such as customers or tasks) are served in the system. Choose a suitable value based on the expected service pattern.
- Mean arrival Rate: Define the average rate at which entities arrive in the system.
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 GI/M/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 GI/M/1 queuing model with the experimental results obtained from the simulation. Evaluate any discrepancies and consider possible reasons for differences between theory and practice.