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In most complex systems of this kind, there are actually multiple classes of customers or jobs, each of which follows its own route or path through the network. In applications, we do not typically start with a model like Figure 1. Instead, we identify nodes or stations or queues and classes of customers or jobs that travel on routes or paths through the network. There is a process of aggregation to convert data by routes into the relatively simple network model in Figure 1. See Section 2.3; go trough Example 1 on p. 2791. After analyzing the simplified network in Figure 1, there also is a disaggregation step in obtaining performance descriptions for individual classes; e.g., to describe the expected time each class spends in the system before completing all required service. See Section 6.3.
We provide the following brief overview of queueing theory as a guide to reading. References are given to basic introductions as well as additional advanced topics, which might be of interest to those familiar with the basic theory. We emphasize the importance of queueing models beyond the classical birth-and-death models, without the usual independence, Markov and exponential-distribution assumptions. (The need to go beyond stationary models will be discussed later.)