Markov Process Source Code for Single-Server Queueing System with Implementation Analysis

This repository contains the source code implementation of a Markov process for single-server queueing systems, accompanied by detailed explanations. The implementation enables computation of critical performance metrics and system behavior analysis. Below we provide enhanced technical explanations with code implementation insights: The core algorithm utilizes discrete-event simulation to model the queueing process, where events (arrivals and departures) are processed in chronological order using a priority queue structure. The state transitions follow Markovian properties where future states depend only on the current state. - Average Queue Length: This metric represents the mean number of customers waiting in the queue within a single-server queuing system. The implementation calculates this by maintaining a running total of queue lengths observed at each event timestamp, divided by the total simulation time. This value helps assess customer waiting patterns and determine optimal server capacity requirements. The code uses time-weighted averaging to ensure statistical accuracy. - Average Waiting Time: This measures the mean duration customers spend waiting for service in single-server systems. The simulation tracks individual customer wait times by recording arrival timestamps and comparing them with service start times. This metric is crucial for evaluating service quality and determining necessary server enhancements. The algorithm accumulates waiting times across all served customers and divides by the total number of completions. - Queue Length Evolution: This describes how the number of waiting customers changes over time in the system. The implementation maintains an event log that records queue length at each state transition, allowing for temporal analysis of system congestion. This data helps understand peak load periods and optimize resource allocation. The code generates time-series data that can be analyzed for patterns and trends. - Detailed Transition Timestamps: These precise time records indicate exactly when queue length changes occur in the system. The simulation engine logs each event (arrival or departure) with high-resolution timestamps, providing granular insights into system dynamics. This information helps identify bottleneck periods and optimize server deployment schedules. The implementation uses a continuous-time Markov chain approach with exponential inter-arrival and service times. Beyond these core metrics, the implementation includes comprehensive visualization capabilities through detailed charts and graphs. These visualizations provide intuitive understanding of system behavior, including: time-series plots of queue length evolution, histograms of waiting time distributions, and state transition diagrams. The graphical outputs help identify optimization opportunities and validate system performance under various parameter configurations. This comprehensive analysis toolkit enables deeper understanding of single-server queueing systems through Markov process modeling. The code structure follows modular design principles, with separate components for event handling, statistical collection, and visualization. Key functions include event scheduling, state update procedures, and performance metric calculators. The implementation uses object-oriented programming to maintain system state and event records efficiently.