Queue Simulation Project

This project simulates a tandem queueing system with two queues and a single server in each queue. The simulation models the arrival and service processes using exponential distributions, allowing the evaluation of system performance under various parameter configurations.

Introduction

The tandem queueing system is a fundamental model in operations research and computer science, representing processes where tasks or customers move through a series of stages (queues) serviced by different servers. This project implements a simulation of such a system to study the behavior of queue lengths over time and understand the impact of different arrival and service rates.

The system consists of:

• Arrival Process: Customers arrive according to a Poisson process with a given rate λ.
• Service Process: Each server processes customers with exponentially distributed service times characterized by rates μ1 and μ2.

Project Structure

• main.py: Contains the main simulation logic, including the functions for generating interarrival and service times, running the simulation, and plotting the results.
• README.md: This file, describing the project, usage, and structure.

Main Logic

The core logic of the simulation involves the following steps:

1. Generate Interarrival and Service Times:

   • Interarrival times are generated using an exponential distribution with the rate parameter λ.
   • Service times for both queues are generated using exponential distributions with rates μ1 and μ2.

2. Simulation Execution:

   • The simulation runs for a specified duration (T), tracking the number of customers in each queue over time.
   • Events include arrivals, service completions at the first server, and service completions at the second server.
   • The state of the system (number of customers in each queue) is recorded at each event.

3. Plotting and Analysis:

   • The number of customers in each queue is plotted over time to visualize the queue dynamics.
   • The average number of customers in the system is calculated by integrating the area under the curve of the queue length over time.

Simulation Parameters

• λ (lambda_values): Arrival rates to the system.
• μ1 (mu1_values): Service rates for the first queue.
• μ2 (mu2_values): Service rates for the second queue.
• T_values: Simulation time for each run.
• N: Number of simulation runs.