The telephone network is the most widespread and far-reaching among all communication networks. It is difficult to imagine a modern society without it. In fact, the telephone network is one of the largest and most complex engineering systems created by mankind. A large portion of the Internet is built upon the telephone network infrastructure. Much thought and work have gone into the design of the telephone network.

The telephone network is largely a circuit-switched network in which resource sharing is achieved at the session level. Transmission and switching facilities are dedicated to a session only when a telephone call is initiated. Using these resources, a circuit, or a connection, is formed between two end users. These facilities will be released upon the termination of the call so that other sessions may use them. While the session is ongoing, however, the resources assigned to the circuit are not shared by other circuits and can be used to carry the traffic of the circuit only. In other words, once the resources are assigned to a circuit, they are guaranteed. Of course, there is a no guarantee that a newly initiated session will get the resources that it requests. In this case, the call is said to be “blocked.” One important design issue of the circuit-switched network is how to minimize the blocking probability in a low-cost and efficient manner.

An example of this problem is the determination of the minimum number of “trunks” or transmission ...

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