Consider a model of a system where packets arrive to the system according to a Poisson arrival process with rate 100 packets per second. Each packet is delayed the minimum amount of time before leaving the system, subject to the following constraints: (a) the delay of each packet is at least d seconds, (b) the rate at which packets can depart is at most C bits / second, and (c) packets depart in the same order they arrived. This is equivalent to a fixed propagation delay of d seconds followed by a queuing system with a server that has a capacity of C bits/sec. In each of the cases below, find the average delay of packets through the system, as well as the average number of packets that are stored in the system.
(A) Each packet is L = 10000 bits, C = 1100000 bits/sec = 1.1 M bits/sec and d = 100 msec
(B) We model the packet lengths according to the following: With probability 0.5, a packet has L1 = 1000 bits, and with probability 0.5, a packet has L2 = 10000 bits, and it is assumed that all packet lengths are statistically independent. In this case assume C = 600 kbps and d = 100 msec.