In the last few decades, enormous computational speed has become accessible to many. Modern day desktop has good enough memory and processing speed that enables a data analyst to compute probabilities and perform statistical inference by writing computer programs. In such a context, this book can serve as a starting point to anyone who wishes to explore the subject of computational probability. This book has 21 puzzles that can be solved via simulation.

“Life is really simple, but we insist on making it complicated.” - Confucius

In the case of a queueing model, it is very likely that service time distributions in a real life situation, do not have an exponential tail. This means that all the analytic solutions derived in any standard textbook are no longer applicable. If the server following a generic distribution, the expression linking the distributions such as Waiting time distribution, First passage time distributions, etc. and service time distributions is in the “Laplace Transform space”.

Laplace transform is a useful mathematical tool that one must be familiar with, while doing applied work. It is widely used in Queueing models where probability distributions are characterized in terms of transforms. Inverting a Laplace transform to get to the probability distribution is an essential task in Queueing theory. For textbook examples and simple Markovian models, one might be fortunate to find convenient forms for LT inversion. However for most of the real life situations, a practitioner needs to know a way to numerically invert LT.

Via TES magazine Mary Pat Wenderoth stops herself mid-lesson and asks her class a question about the day’s work. The students turn to their notes but she stops them. “Don’t look it up. Imagine your brain is a forest and your memory is in there somewhere. The more times you make a path to that memory, the stronger that path becomes. Try to figure it out.” Wenderoth is a principal lecturer in biology at the University of Washington in Seattle, US.