Suppose users share a 1 Mbps link. Also suppose that the traffic generation process of each user alternates (independently of the other users) between periods of activity (active modes), when the user generates data at a constant rate of 100 Kbps and periods of inactivity (inactive mode) when the user generates no data. Suppose further that the user is active (independent of other users) only 10 percent of the time. (1) When circuit switching is used to allocate resources on the shared link, how many users can be supported? (2) Suppose now that users are supported by using accordance with a packet switch- ing method, so that the communications channel is shared on a statistical mul- tiplexing manner (rather than being shared by using the synchronous (fixed) multiplexing techniques employed by the circuit switching system). Assume now that the communications channel is used to support a number of users that is 4 times larger than those supported under the circuit switching oper- ation. What is now the probability that more than 10 simultaneously active users cannot be accommodated at a given point in time? Equivalently, what is the probability that 11 or more users are simultaneously in active mode at a given time?
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