poissonSIM- A Bank Queue Simulator

Wanna simulate a banking queue using a Poisson PMF? You're in the right place !!!

poissonSIM is a C program that simulates a bank’s customer queue over an 8-hour working day (480 minutes) using probability-based customer arrivals modeled by the Poisson distribution.
It’s written in C and demonstrates the use of linked lists, dynamic memory allocation, and basic data analysis.

The simulation tracks each customer’s arrival and service times to calculate:

• Average (mean) wait time
• Median and mode wait times
• Standard deviation
• Longest wait time observed

The program helps estimate whether an additional teller is needed based on simulated queue performance.

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Features

• Poisson arrival model using Knuth’s algorithm (references mentioned at the end)
• Queue implementation via singly linked list
• Dynamic tracking of wait times with malloc and realloc
• Statistical report generation at the end of simulation

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Concepts Used

C:

• Basic C concepts like loops, conditionals, pointers, etc.
• Structs, rand() function & dynamic memory allocation using malloc and realloc
• File modularization (.c / .h files)
• Singly linked-list implementation in C

Math:

• Probability and Poisson process
• Basic statistical analysis in C
• Random variate generation from the Poisson Distribution with given lambda

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File Structure

├── main.c # Simulation driver
├── queue.c/.h # Queue implementation
├── stats.c/.h # Statistical analysis functions
├── LICENSE
└── README.md

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How to compile and run the program?

### compile:
gcc main.c queue.c stats.c -o <your output file name> -lm
### run:
./<your output file name>
### when prompted, enter the average customer arrival rate(lambda)

Example:

gcc main.c queue.c stats.c -o bank -lm
./bank

Output:

Average Wait Time: 3.42 minutes
Median Wait Time: 2.95 minutes
Mode Wait Time: 1.60 minutes
Standard Deviation: 1.25
Longest Wait Time: 8.50 minutes

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Purpose

This project demonstrates how stochastic processes and data structures can be combined to simulate real-world queuing systems like those in banks, hospitals, or call centers.

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References

• Knuth's algorithm - Wikipedia notes
• Knuth's algorithm (other ref) - An article by John D. Cook
• Memory allocation in C - Amazing tutorial by w3schools
• Linked List Basics - Stanford edu explained linked list from the very beginning
• Linked List video tutorial - Jenny mam explained it so beautifully