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hw5.pdf - EE 284 F Tobagi Autumn 2017-2018 EE284 Homework...

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EE 284 F. Tobagi Autumn 2017-2018 EE284 Homework Assignment No. 5 Topics: CSMA/CD, Bridging Performance, Spanning Tree Protocol Handed out: 7 November 2017 Due: 14 November 2017 Total points: 61 Problem 1: CSMA/CD (8 points) Consider a linear bus with 3 stations transmitting packets using the Ethernet standard 1-persistent CSMA/CD with exponential back-off as described in the class. The cable is 12 units long, where one unit is the distance that the signal travels in a unit of time. The positions of A, B, C on the cable are 2, 6, 12 units respectively. Assume that the time slot used in the exponential backoff is equal to twice the length of the cable in time units. Consider that at time t = 0 the channel is sensed idle everywhere on the bus. A wants to send a packet with transmission time equal to 24 time units at time = 7, B wants to send a packet with transmission time equal to 24 time units at time = 0, C wants to send a packet with transmission time equal to 24 time units at time = 2. For each station we provide a list of random numbers between 0 and 1 to be used in the backoff algorithm. These numbers must be used in the order given, and each random number may be used only once. For A : 0 . 85 , 0 . 11 , 0 . 56 For B : 0 . 54 , 0 . 19 , 0 . 94 For C : 0 . 12 , 0 . 22 , 0 . 85 1
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Notes: 1. given a random number r , if you are to choose among N points in time at which to schedule a transmission, the point chosen is the k th point (1 k N ), where k = d rN e . 2. In Ethernet, once a transmission is aborted or finished, there is a small inter-frame gap (specified to be 9 . 6 μ seconds according to the 802.3 standard) in which no data is transmitted. In this way, all the stations on the segment are able to sense the channel idle. Stations having frames to transmit will then transmit immediately after the gap. In your solution, assume that the inter-frame gap is very small and therefore do not worry about showing it in your time diagram. Draw the packet transmissions in the space-time diagram in Figure 1. Mark on the diagram for each station the time corresponding to when each event happens at that station location. Identify explicitly the time at which each station begins and ends the successful transmission of its frame. For events falling out of the space provided in the diagram, state explicitly the events and the associated time. Problem 2: Exponential Backoff (6 points) We consider a local area network operating according to the IEEE 802.3 standard. We consider the situation whereby there are only two active stations, and these two stations have just incurred a collision. With this collision, the number of collisions incurred by Station 1’s packet is i , and the number of collisions incurred by Station 2’s packet is j . a) [1 point each] For i = 1 and j = 2, find the probability that the next packet transmission is: i) a successful transmission of Station 1’s packet.
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