Oriented Projective Geometry: A Framework for Geometric Computations (Jorge Stolfi)

transient and steady-state analysis. A "proof" of L )W is written in a way that requires service to be in order of arrival, even though restriction can be avoided with a little explanation. The explanation of PASTA is serviceable. Chapter Three is devoted to birth-anddeath queues. A nice feature of the presentation is that the conservation of flow principle (called the rate-equality principle here) is given at the start of the chapter. It is used to get the familiar balance equations for the M/M/1 queue, Ap, + #p, Ap,_ zPn+ a more refined application would produce the rate-up equals rate-down equations, Ap, #p+, which are easier to work with. Waiting times, output processes, and busy period analysis are given for the usual models. Significant attention is paid to transient analysis, and the waiting time distribution for the finite-source FIFO model is derived. There are 22 exercises that explore variations of the basic models. The next chapter covers Markovian models that are not birth-and-death processes. This includes the method of stages for queues with Erlang arrivals or services and some bulk queues. The latter is treated extensively, and is a distinguishing feature of this book. Chapter Five is about networks of queues. Open and dosed Jackson networks are described, and a proof of Jackson’s theorem is given. The interpretation of this theorem is not stated carefully enough: "It is implied that the states n of individual nodes i, (i 1, 2,... ,k) in steady state are independent random variables." BCMP networks are defined, and the product form result is stated but not proven. The sixth chapter covers the embedded Markov chain models, M/G/I, GI/M/1, GI/M/c, and the insensitivity property of the M/G/c/c model. The penultimate chapter covers the G/G/1 models. This includes the LindIcy equations, Marshall’s characterization of the moments of the waiting time in terms of moments of the idle times, and some bounds. The final chapter contains Kingman’s heavy traffic approximation for the waiting time in the GI/G/1 queue, diffusion approximations for several non-Markovian queues, queueing systems with vacations, and design and control models. In summary, this is a good book for learning about the important formulas in queueing theory. The presentation is clean and basically correct. The exercises contain some interesting results, and the references are extensive.