Mathematics for Engineers

In the design and analysis of information processing systems, the concept of "traffic" plays a central role, especially when it comes to assessing their performance level. The mathematical methods related to these points are based upon the results of queueing theory, which this chapter will detail.
Communication networks, as well as the services they provide, make use of a large variety of mechanisms: connection set-up in a circuit-switched network, transport of IP packets in the IP world, organization of operators in a call center, task sharing in the processor of multimedia systems, etc. However, as far as performance analysis is concerned, all these phenomena come under the rule of a small number of fundamental concepts, initially established by the pioneers of teletraffic, and which are presented hereafter. The phenomena to take account of are rejection probabilities and response delays of transport protocols or control processors, examples of which are to be found in [FIC 04].
In any real-time system, the concept of traffic accounts for the volume of tasks it has to process, and of the resulting load. The traffic of a telecommunications network is the volume of information transported or processed by the network. In the computing unit of an information system, the traffic is made of all software tasks generated by customer demand. In a network control server, it is made of signaling data, routing information to be processed, administration and maintenance routines, etc.
Clearly, the more frequent and...