Instructed by Prof. Ali Movaghar from the Department of Computer Engineering, Sharif University of Technology.

This repository contains a simulation of the M/M/1/K queue model, a classic queuing theory concept commonly used in the analysis of computer systems and network performance. These simulations are designed to analyze the performance of these queues under different scenarios.

Parameters:

• Service Rate (μ): The rate at which the service is provided.
• Arrival Rate (λ): The rate at which arrivals occur.
• Queue Capacity (K): Set to 14.

Key Aspects Covered:

• Performance Metrics: Calculation of the probability of having n customers in the system (P_n), average number of customers in the system (N_c), and probabilities of blocking (P_b) and dropping (P_d).
• Simulation Results: Results showing the impact of varying parameters on system performance.
• Formulas Used:
  • P_n(λ, μ) for the probability of n customers.
  • N_c for the average number of customers.
  • Calculation of P_b and P_d using the provided formulas.
• Analysis: Discussion on the impact of different parameters on system performance.

Key Aspects Covered:

• Round Robin Scheduling: Examination of the algorithm's performance in managing queues.
• Performance Metrics: Analysis of average wait time and throughput under different configurations.
• Theoretical Evaluation:
  • Calculation of performance metrics with given parameters (μ and θ).
  • Breakdown of theoretical results and their implications.
  • Evaluation of the impact of different time slices and system configurations.

Key Aspects Covered:

• Priority-Based Service: Analysis of how tasks or requests are processed based on assigned priority levels, enabling differentiation in service rates.
• Performance Metrics:
  • Calculation of metrics such as weighted average response time, throughput, and utilization for tasks with different priorities.
  • Probability distribution of customers in the system based on priority classes.
• Theoretical Evaluation:
  • Derivation of performance equations for systems with multiple priority levels.
  • Impact of priority differentiation on overall system performance and fairness.

• FCFS_Simulation.py: FCFS Service Order

• PS_Simulation.py: Processor Sharing Service Order

• DPS_Simulation.py: Discriminatory Processor Sharing Service Order

Evaluation Results for M/M/1/12 Queue with Exponential and Fixed Theta under different customer loads are available in the following files:

• FCFS_K12_thetaExp_10M , FCFS_K12_thetaFixed_10M, FCFS_K12_thetaExp_300M , FCFS_K12_thetaFixed_300M

• PS_K12_thetaExp_10M , PS_K12_thetaFixed_10M, PS_K12_thetaExp_100M , PS_K12_thetaFixedFixed_100M

• DPS_K12_thetaExp_1M , DPS_K12_thetaFixed_1M, DPS_K12_thetaExp_10M

• Mor. Harchol-Balter, “Performance modeling and design of computer systems: queueing theory in action", Cambridge University Press, 2013.
• Krishna. Kant, "Introduction to computer system performance evaluation" International Edition, 1992.

If you have an issue or found a bug, please raise a GitHub issue here. Pull requests are also welcome.