Queuing delay in a concentrator. A 4:1 concentrator is fed by four terminals that each transmit 16-byte packets at a rate of 1 Gbit/s with an average rate of one packet per microsecond (an average...

Queuing delay in a concentrator. A 4:1 concentrator is fed by four terminals that each transmit 16-byte packets at a rate of 1 Gbit/s with an average rate of one packet per microsecond (an average bandwidth of 128 Mbits/s). The network channel of the concentrator has a bandwidth of 2 Gbits/s. Assuming that the inter-arrival interval is exponentially distributed, compute the following: (a) the probability that the 2 Gbits/s network channel is over-subscribed (more than two inputs transmitting packets simultaneously), and (b) the average waiting time (queuing delay) seen by a packet at the input of the concentrator.