# Fundamentals of Stochastic Networks — O. Ibe

This text serves as an introductory queueing and random networks text aimed at engineers that has a bit more mathematical content than many others in its class. I wanted to be able to recommend it fully, but alas, there are several glaring issues that must be addressed. The topics covered are fairly typical, and almost always focus on the steady-state. The mathematical background required isn’t terrifically high-fairly standard for anyone with an engineering background. Should fundamentals of probability be lacking, the author provides a decent introduction. The author also breaks from the template of queueing texts to mention more interesting varieties of queueing systems such as vacation and threshold queueing and priority systems. The last bits of the book are less related to queueing in particular, focusing on graph theory and random networks on graphs (including Bayesian and Boolean). My concerns are in some egregious instances of sloppy editing and typography. An obvious error in a limit calculation should have been caught by an editor, as it was invoking the basic definition of a derivative. Moreover, while proofs are generally provided, they’re inconsistently expanded. The author will waste half a page on arithmetic simplification, yet gloss over nontrivial steps that require a bit of advanced linear algebra knowledge. Moreover, he fails to provide adequate justification when invoking limit theorems. These may seem a bit pedantic in a review of a book for engineers, but clear justification for estimations or limit theorems prevents misuse. Overall, the book should be considered a good survey of queueing and random networks, but should be supplemented with additional literature.

## Topics

• Basic Probability
• random variables, transforms, selected distributions
• Stochastic Processes Overview
• counting processes, stationarity, independent increments, relevant processes (renewal, Poisson, birth-death, Markov, Gaussian)
• Elementary Queueing
• M/M (single and multiple server, loss systems, finite capacity)
• stochastic balance
• M/G/1
• Advanced Queueing
• priority queueing
• G/M/1 and G/G/1 (including Lindley’s Integral Equation)
• vacation and threshold queueing systems
• Queueing Networks
• Burke’s Output Theorem and tandem queues
• Jackson networks
• closed networks
• BCMP networks
• algorithms for product-form networks
• negative customers
• Approximations (fluid and diffusion)
• Basic Graph Theory
• Bayesian Networks
• Boolean Networks
• Random Networks

### Attributes

 Difficulty 3 Good for teaching? 4 Proof Quality 2 Quality of Exercises 4 Self-Study 3 Readability 4