9.6. Summary

This chapter introduced powerful techniques to solve performance models of e-business sites. These techniques are based on open and queuing network models. Some of the important results in the theory of queuing networks are worth noting here. One of them is the BCMP theorem [2], developed by Baskett, Chandy, Muntz, and Palacios, that specifies the combination of service time distributions and scheduling disciplines that yield multi-class product-form queuing networks with any combination of open and closed classes. Buzen developed the Convolution Algorithm— the first computationally efficient method to solve QNs [4]. Sevcik and Mitrani [12] developed the arrival theorem and Reiser and Lavenberg [11] developed Mean Value Analysis, which is based on the arrival theorem. Several approximations to QNs for the non-product-form case were developed and reported in the literature. Some aspects of actual e-business sites such as priority at processor scheduling or at load balancing systems are not amenable to modeling with the exact queuing network models presented here. Readers interested in solution techniques for approximate models should refer to Agrawal [1], Lazowska et al [7], and Menascé et al [9].

Detailed performance models for the Web, either client-side models or server-side models, are available in Menascé and Almeida [10] as are specific issues of Web performance modeling, such as modeling of burstiness and heavy-tailed distributions. The algorithms discussed in this chapter are implemented in the MS Excel OpenQN.XLS and ClosedQN.XLS workbooks available at the site associated with this book. They solve multi-class open and closed queuing networks, respectively, and provide results, such as utilization, residence times, and queue lengths, per class and per device, as well as response times and throughputs per class.