Random Early Discard (RED) is a queueing policy implemented by IP routers to improve performance and relieve congestion on the Internet. According to this policy, a packet arriving to a queue is inserted to the queue with probability alpha_n where n represents the current number of packets in the system. Otherwise (with probability 1 - alpha_n) the packet is dropped (If the queue is full, packets are always dropped) Perform a simple analysis of RED with the following assumptions: Packets arrive to a queue of length N according to a Poisson process with rate lambda; service time of each packet is exponentially distributed with mean 1/mu; and alpha_n = 1+1 for n greaterthanorequalto 0. a) Draw a state transition rate diagram for a process representing number of packets in the system. b) Find the steady-state probability of having n packets in a system with N = 5. c) Find the mean number of packets in the system