1EE555: "Broadband Networks Architecture" HW#2: Due February 23/24(for DEN) 1. Consider a router that is managing three flows, on which packets, of fixed length, arrive at the following times: Flow A 1 3 4 5 6 7 8 Flow B 1 2 4 6 8 11 Flow C 2 4 7 10 All three flows share the same outgoing link, on which the router can transmit one packet per unit time. Assume an infinite buffer is available in router a) Suppose the router implements "Fair Queueing". Find the sequence of Packets output by the router as a function of time. I am not interested in answers only. Show me the procedure, i.e. calculate Fi for each packet. If there are "ties", resolve it in order of A, B, C b) Now suppose the router is implementing "WFQ". Flows A and B are given equal share of capacity and flow C is given twice the capacity of flow A. Find the sequence of Packets output of the router as a function of time. Show all steps of your work 2. Consider the following stream of packets (all of length 3) to be served by a router from a (very large) shared buffer. Construct a Table (like we did in class) with Departure Time; Mean Waiting Time, Mean Total Time for each group separately and also overall for the following Queueing disciplines. If departures occur at same time as arrivals, assume departures occur first. a) FCFS b) Non-Preemptive, Priority Queue (Group 2 has the higher priority) c) WFQ with group 2 getting twice the service rate as group 1 Packet Arrival Time P1.1 1 P2.1 2 P1.2 3 P1.3 4 P2.2 6 P1.4 8 P2.3 9 P2.4 102 3. Consider a router implementing RED with Maximum Probability of drop MaxP = 0.02 and with an average queue length halfway between the two thresholds. What is the probability that none of the first 50 packets are dropped? 4. The following schedule for a given flow lists for each second the number of packets sent between that time and the following second. The flow must stay within the bounds of a Token Bucket filter. What bucket depth does the flow need for the following token generating rates? a) 2 tokens/sec, b) 4 tokens/sec Time (Second) Packets sent 0 5 1 5 2 1 3 0 4 6 5 1 5. Suppose a router has accepted flows with the following Tspec, described in terms of Token Bucket filter, with token rate r tokens/sec and bucket depth b tokens. All flows are in the same directions and the router can forward one packet every 0.1 seconds. a) What is the maximum delay a packet may face? b) What is the minimum number of packets from the third flow that the router would send over 2 seconds assuming the flow sent packets at the maximum rate uniformly? r b 1 10 2 4 4 1 6. Suppose an RSVP router suddenly loses its reservation state but otherwise remain running. a) What will happen to existing reserved flows if router handles reserved and non-reserved flows in a single FIFO? b) What might happen to existing reserved flows if router used WFQ to segregate reserved and non-reserved flows?3 c) Eventually the "receivers on the these reserved flows will request that their reservation be refreshed (soft state). Is it possible that their requests are denied/ Give a scenario. 7. Consider a router handling fixed length packets using a token bucket burst control mechanism. Packets that arrive when there is no token available are marked. One token is added to the bucket at the end of each slot and the bucket depth is 5. The arrival process is defined by: Pk = Pr {k arrivals per slot}. For the case of P0 = 0.2, P1 = 0.4, P2 = 0.4. Assume that the system starts with a non-empty token bucket. a) Draw the complete Markov chain for the number of tokens available at the beginning of a slot. b) Solve the Markov chain and find the average number of marked