Queuing Systems Analysis (M/M/c Model)

This project explores queuing systems using the queueing and ggplot2 packages in R. The goal is to analyze how different parameters (arrival rate, service rate, number of servers) affect system performance.

Features

Models an M/M/c queue with varying number of servers.

Computes key performance metrics:

L: Average number of customers in the system

Wq: Average waiting time in queue

SU: Server utilization

ID: Idle probability

Generates plots to visualize changes in system behavior as servers increase.

Example Plots

Queue Length vs Servers

Waiting Time vs Servers

Utilization vs Servers

Idle Time vs Servers

Results

The results show how adding servers reduces queue length and waiting time, while utilization and idle time adjust accordingly.