4.10 Queueing Networks
We have now completed our review of queueing systems (which we defined in Section 4.2
as consisting of one service facility that contains a number of identical servers). In
this section we turn our attention to queueing networks (i.e., to sets of interconnected
queueing systems). Interconnected in this case implies any combination of in series
and in parallel arrangements.
It has already been indicated or implied
several times in this chapter that many urban service systems can be viewed as queueing
networks. So far, we have seen many results which are useful in analyzing individual
components of these networks. The art of queueing network analysis consists of combining
the results (and the analytical techniques) that apply to individual components and
drawing conclusions that describe the properties of the complete urban service system
The word "art" has been used
intentionally above. For one should keep in mind that queueing theory offers very few
general results that apply expressly to queueing networks. Therefore, in solving problems
that involve such networks, much depends on the ingenuity of the analyst in choosing the
"right" simplifying assumptions that preserve the essence of the problem while
making the calculation of an approximate solution possible.
In the next two sections, we shall first
present what is perhaps the single most useful general result in the analysis of queueing
networks. We shall then illustrate by example a widely applicable approach to the analysis
of an extensive family of queueing network models.