HW3 (due Feb 29, 2008)

(1) A communication node A receives packets from two different nodes 1 and 2. The packet is then forwarded outward with a link at a rate C bits/sec. Packets from node 1 will always be processed; however, packets from node 2 will be processed only if the number of packets in queue is less than K; otherwise, the incoming packet will be thrown away. Assume the traffics from nodes 1 and 2 are Poisson with rates λ₁ and λ₂. (20 points)
(a) What is the range of values of λ₁ and λ₂ for which the expected number of packets in A will stay bounded as time increases?
(b) Draw a state transition diagram of the queue at A.
(c) For λ₁ and λ₂ in the range of part (a), find the steady-state probability of having n packets in A.
(From Dr. Reddy of TAMU)

(2) (10 points)
(a) A channel has a bit rate of 4 kbps and a propagation delay 25 ms. If we use frames of 100 bits in the forward direction and ACKs of 20 bits in the revierse direction, and the length of the header in the frame is 10 bits, what is the expected efficiency of the channel when Stop and wait protocol is used (assuming no frame error and zero processing time)?
(b) What is the expected efficiency on the same channel with a Go-back-7 protocol (assuming no frame error and zero processing time)?
(c) If the probability of frame loss is 0.5, on average how long does it takes to transmit a frame in both Stop-and-Wait and Go-Back-7 protocols?

(3) Consider data link layer communications. Let t_proc be the processing time for both transmitter and receiver, t_prop be the propagation delay, and tf and tack be the frame and acknowledgement transmission time, respectively. (10 points)
(a) If Selective-repeat protocol is used, what is the average time required to transmit a frame if there is no error? What is the average time required to transmit a frame if the frame error probability is P_f?
(b) If Stop-and-Wait protocol is used, what is the average time required to transmit a frame if there is no error? What is the average time required to transmit a frame if the frame error probability is P_f?
(c) If Go-Back-7 protocol is used, what is the average time required to transmit a frame if there is no error? What is the average time required to transmit a frame if the frame error probability is P_f?