Written Exam in Information Networks TSIN01

Transcription

1 Written Exam in Information Networks TSIN01 10th August :00-12:00 Location: TER2 Examiner: Robert Forchheimer Teacher: Peter Johansson, 4017 or Aids: Standard mathematical/technical handbooks like Beta, TeFyMa, and electronic calculators of any kind. General language dictionaries without personal notes, e.g. English-French, English-Italian, etc. Each correctly solved problem gives the indicated number of points. There is a total of 15 points. 7 points is needed to pass the exam. Good luck!

2 1 a) We can view multiaccess communication in queueing terms: Each node has a queue of packets to be transmitted and the multiaccess channel is a common server. Ideally in a queueing system the server should view all the waiting packets as one combined queue to be served by an appropriate queueing discipline. Why is this not possible in multiaccess communication with distributed algorithm running at each node and no central control? b) What is the assumption of collision or perfect reception? What is ignored by that assumption? c) What is the desired attempt rate G for a stabilization algorithm in a slotted Aloha system and why is that chosen? 2 Suppose we are using a FCFS (first come first serve) tree splitting algorithm that at time k allocates a new interval from T(k) to T(k) Suppose this interval contains a set of packets with arrival times T(k) + 1, T(k) + 6, T(k) + 7, and T(k) + 8. a) Find the allocation intervals for each of the subsequent time slots until the CRP (collision resolution period) is completed. b) What is the feedback pattern generated? (2 p)

3 3 We are analyzing a slotted Aloha system with a fixed number m of nodes using the no buffering assumption. Packets arrive at each of the m nodes according to independent Poisson processes with the same rate. The following picture describes the behaviour for different retransmission probabilities q r a) What is on the horizontal axis? What are the curves plotted? b) Given that the retransmission probabilities used in the plot are q r = 0.1, 0.2, 0.3 how many nodes are there in the system? Which curve corresponds to which q r? c) What is the probability q a of a packet arriving at a given node during one time slot? What total arrival rate of packets into the system does that correspond to?

4 4 Walter Lancaster bought a wireless accesspoint supporting the g standard. He connects his accesspoint to his 100Mbit/s internet connection and downloads the movie trailer for Pirates of the Carribean : Dead Man s Chest. When doing so he observes a throughput of 1.9Mbyte/s. He has looked up the technical specifications for g and found that DIFS = 50µs, SIFS = 10µs, the time to send 1460 bytes of payload data (one TCP packet) over the medium in 54Mbit/s mode takes 254µs, g MAClayer ACK package takes 30µs, RTS packet (which must be sent in b mode) takes 207µs, CTS packet (also in b mode) takes 203µs, and finally the data portion of a TCP ACK packet takes 38µs. a) Explain the observed throughput by describing a plausible packet exchange between W. Lancaster s laptop and his wireless accesspoint. b) Compute the new throughput if the rate for TCP data and TCP ACK are increased to 108Mbit/s making them take 140µs and 32µs instead (there is some overhead for preamble and signal extension which does not cut the time in half). All other timings are the same. c) Compute the new throughput if instead of increasing the channel rate a technique called frame bursting is used. This means that the sender will send six consecutive data packets which are interspersed with MAC layer ACK packet replies from the receiver and between ACK and data packets there are a SIFS time slot.

5 5 Assume we have a slotted Aloha system with total packet arrival rate of 25 packets/s and a time slot of 10ms. Use the no buffering assumption with m = 3 nodes, and assume that the arrivals to the nodes are independent and Poisson distributed with same arrival rate, i.e. probability for k arrivals during a time interval of length t is (λt) k e λt. k! When modeling the system as a discrete time Markov model with the number of backlogged nodes n as state the transition probability matrix P is approximately P a) Verify that p (0.8582, , , ) is (approximately) the stationary probability distribution for the Markov chain. b) Compute the average number of backlogged nodes n and the average queueing delay T using the stationary probability distribution given in a). c) Compute the probability to get at least one arriving packet rejected during a time slot because the node it is arriving to is already backlogged.