At the present time simulation modeling is the most popular method for understanding the behavior of complex networks. With the availability of fairly inexpensive commercial packages for doing simulations, network designers and network performance analysts can now gain insight into the collective behavior of network devices such as servers, routers, and switches with a high degree of accuracy. This accuracy however comes at the expense of simulation time, and with the complexity of networks increasing every year, it is becoming more advantageous to use some kind of optimization procedure in simulations to cut down on the simulation time. Another approach for decreasing the simulation time is to use hybrid models that combine both analytical methods and simulation. Analytical methods by themselves frequently use assumptions that sacrifice accuracy or are not scalable to real networks. These methods do however allow tremendous insight into how network components behave, and if one is to use hybrid simulations one must understand in detail the analytical methods that are used. This book is one of the best available for the study of analytical modeling in communication networks. It covers wireless networks, and gives detailed overviews of the behavior of the TCP/IP protocol, deterministic and stochastic modeling, and the mathematical modeling of switches and routers. Only chapters 4, 5, and 7 were read by this reviewer, and so only these will be reviewed here.



Chapter 4 in particular is an overview of the `network calculus', which has been widely discussed in the literature for quite some time. The approach of network calculus is interesting and somewhat perplexing at first glance since networks are inherently stochastic in nature. Network calculus however attempts to place deterministic bounds on the network traffic, and offers worst case performance guarantees to network providers. The provisioning of a real network could not be done solely with the network calculus, since one will obtain an overestimation of the bandwidth assignments, etc, but it still provides useful insights into how to design a network for particular traffic loads. It is also interesting in that it can still obtain performance bounds for complex networks composed of many different devices. Those readers who have only limited mathematical preparation will find the presentation of the network calculus very accessible, if compared with chapter 5 which uses more advanced mathematical constructions. The authors have chosen to put the mathematical proofs of the main results in the appendices of the book, and this should also make the reading more palatable for the reader less astute mathematically. Of particular interest is the introduction of the convolution operator and its use for obtaining network `service curves' and a network process with an `envelope.' The authors illustrate the relevance of these mathematical constructions by showing how to use them to obtain the minimum link capacity required so that an arrival process has delay less than a pre-selected time. Also useful is their discussion of weighted fair queuing and how it can be understood in the framework of the network calculus. As a real example of the network calculus, they discuss voice traffic, which is a timely one considering the increasing importance of voice over IP (VOIP).



To avoid the over-provisioning of real networks by the use of the (deterministic) network calculus requires that one deal with their stochastic nature. This is done in chapter 5, wherein the authors give an exceptionally fine discussion. More mathematically sophisticated than chapter four, the discussion naturally includes that of Markov chains. The authors also give a proof of Little's theorem, which is a kind of `ergodic theorem' for network traffic and which gives an `average' performance measure. They avoid the use of measure theory in the proof, again making the presentation accessible to a wider readership. Little's theorem is used to show that the mean time that a packet spends in a multiplexer does not depend on the scheduling policy (although the higher moments do). Some queuing theory is discussed in this chapter also, with the most important discussion being that of the analysis of a multiplexer with minimal assumptions on the arrival processes. This analysis leads to the very important notion of the `effective bandwidth', the use of which leads to more optimal deployments of quality of service (QoS). The discussion of the effective bandwidth in this chapter leads to one on the Gartner-Ellis theorem and the very important topic of long-range dependence in network data. The latter topic is not discussed in detail in the book, since it must be done using the theory of large deviations, which is too mathematically advanced to be included in the book.



The dynamics of the TCP/IP protocol is extremely complicated, as anyone who has dealt with real networks will attest to. The study of TCP/IP dynamics has resulted in an enormous amount of literature, and there are indications that it is `chaotic', at least for some traffic patterns. The presentation in this book does not address the dynamics in such generality, but it does give an excellent overview of TCP/IP in the context of `adaptive bandwidth sharing.' Both the slow-start and congestion avoidance phases of TCP are discussed using elementary mathematics, including descriptions of the TCP evolution after buffer overflow, and congestion avoidance with timeout and fast recovery. The authors also include a more advanced treatment using stochastic processes and quote the famous PFTK formula for the `goodput' of the Reno version of TCP. Random early discard (RED) and explicit congestion notification (ECN) are also discussed, but interestingly, in the context of a deterministic dynamical system modeled by a differential equation. In addition, they discuss the long-range dependence of traffic under TCP via the use of the Pareto distribution. All of this analysis prepares the reader for more advanced treatments in the literature, the latter of which shows that the dynamical behavior of TCP is extremely complex, and requiring extreme caution in its analysis via real network data.