Computing steady state probabilities for a queueing system is somewhat easier than computing the transient distributions. The latter typically comprises a differential-difference equation and the usual trick of recursive substitution fails as there is a derivative in the equation. The tools employed in solving a differential-difference equation are Generating functions, Laplace transforms and PDE solving tricks. Only for simple systems such as M/M/1 can one slog out and find a closed form solution.

[youtube https://www.youtube.com/watch?v=B0hMS4eUVV8?rel=0]

In a book that has about 350 pages, the first 250 odd pages are devoted to probability, ODEs and difference equations. The last part of the book covers queuing theory for specific systems, i.e, Poisson arrivals, exponential service times of one or more servers. The most painful thing about this book is that there are innumerable typos. A book that is riddled with typos on almost every other page cannot be an appealing text for an undergrad.

This puzzle has appeared in many forms but here is one variant: Five sailors were cast away on an island. To provide food, they collected all the coconuts they could find. During the night one of the sailors awoke and decided to take his share of the coconuts. He divided the nuts into five equal piles and discovered that one nut was left over, so he threw this extra one to the monkeys.

This book is a ~160 page tirade against the book “Flash Boys” that has captured everyone’s mindshare with the marketing slogan - ”U.S. stock market is rigged”. The author, Peter Kovac, has worked with a HFT firm for eight years and claims to be an industry insider. Since “Flash Boys” was basically anti-HFT book, it is natural to expect someone from the HFT to criticize the book. So, there we have Peter Kovac with a book length treatment that has similar title with Lewis book but a different tagline.