Stochastic Operations Research

Python code for the book Sample Path Analysis and Simulation of Stochastic Systems by Nicky D. van Foreest. The book is available as PDF.

Dependencies

Install the following packages:

pip install random_variable latex_figures

Standard scientific Python packages (numpy, scipy, matplotlib, seaborn) are also required.

Code overview

The files are listed in the order in which they appear in the book.

Chapter 1: Introduction

• IBD_simulations.py : how uniform inter-arrival times lead to exponential inter-arrival times at the population level
• exp_convergence.py : convergence of periodic arrivals to a uniform distribution on the circle
• functions.py : helper functions (Plus, Min, normalize, grid_search)

Chapter 2: Construction of Simple Discrete-time Stochastic Processes

• psychiatrists.py : psychiatrists case with holiday schedules and queue length control
• nurse.py : nurse allocation between two wards with threshold control
• n_policy_figure.py : N-policy for switching a server on/off
• discrete_simulations.py : queue length dynamics, stability, variability, and tandem networks
• random_walk.py : random walks and their reflection
• lighthouse_case.py : model parameters for the Lighthouse Company inventory case
• ss_inventory_simulation.py : simulation of an (s,S) inventory system

Chapter 3: Construction of Simple Continuous-time Stochastic Processes

• waiting_time_distribution.py : exact and simulated waiting time distributions for the G/G/1 queue
• plot_virtual_waiting_time.py : work process and system size using heap queues
• event_stacks/ : discrete-event simulation framework and examples (see event_stacks/readme.org)

Chapter 5: Exact Models

• basestock.py : base-stock inventory policy for the Lighthouse case
• qr.py : (Q,r) inventory policy for the Lighthouse case
• inventory_base.py : base class for inventory models using hitting time analysis
• TsS.py : (T,s,S) and (T,S) inventory policies
• ss.py : (s,S) inventory policy
• sS_tss_experiments.py : numerical experiments comparing inventory policies
• batchqueues.py : M^B/M/1 queue with rejection policies

Chapter 6: Approximate Models

• setups.py : effect of batch sizes on sojourn times with setup times