If exactly two nodes transmit he uses a method to

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Unformatted text preview: ue of pa ensures that the aggregate throughput of packets received successfully by the N clients is the same as the throughput of the packets received successfully by the access point? 5. Consider the same setup as the previous problem, but only the client nodes are backlogged—the access point has no packets to send. Each client node sends with probability p (don’t assume it is 1/N ). LECTURE 10. SHARING A COMMON MEDIUM: 18 MEDIA ACCESS PROTOCOLS Ben Bitdiddle comes up with a cool improvement to the receiver at the access point. If exactly one node transmits, then the receiver works as usual and is able to correctly decode the packet. If exactly two nodes transmit, he uses a method to cancel the interference caused by each packet on the other, and is (quite remarkably) able to decode both packets correctly. (a) What is the probability, P2 , of exactly two of the N nodes transmitting in a slot? Note that we want the probability of any two nodes sending in a given slot. (b) What is the utilization of slotted Aloha with Ben’s receiver modification? Write your answer in terms of N , p, and P2 , where P2 is defined in the problem above. 6. Imagine a shared medium wireless network with N nodes. Unlike a perfect broadcast network in which all nodes can reliably hear any other node’s transmission attempt, nodes in our network hear each other probabilistically. That is, between any two nodes i and j , i can hear j ’s transmission attempt with some probability pij , where 0 ≤ pij ≤ 1. Assume that all packets are of the same size and that the time slot used in the MAC protocol is much smaller than the packet size. (a) Show a configuration of nodes where the throughput achieved when the nodes all use carrier sense is higher than if they didn’t. (b) Show a configuration of nodes where the throughput achieved when slotted ALOHA without carrier sense is higher than with carrier sense. 7. *PSet* Token-passing is a variant of a TDMA MAC protocol. Here, the N nodes sharing the medium are numbered 0, 1, . . . N − 1. The token starts at node 0. A node can send a packet if, and only if, it has the token. When node i with the token has a packet to send, it sends the packet and then passes the token to node (i + 1) mod N . If node i with the token does not have a packet to send, it passes the token to node (i + 1) mod N . To pass the token, a node broadcasts a token packet on the medium and all other nodes hear it correctly. A data packet occupies the medium for time Td . A token packet occupies the medium for time Tk . If s of the N nodes in the network have data to send when they get the token, what is the utilization of the medium? Note that the bandwidth used to send tokens is pure overhead; the throughput we want corresponds to the rate at which data packets are sent. 8. *PSet* Alyssa P. Hacker is designing a MAC protocol for a network used by people who: live on a large island, never sleep, never have guests, and are always on-line. Suppose the island’s network has N nodes, and the island dwellers always keep exactly some four of these nodes backlogged. The nodes communicate with each other by beaming their data to a satellite in the sky, which in turn broadcasts the data down. If two or more nodes transmit in the same slot, their transmissions collide (the satellite uplink doesn’t interfere with the downlink). The nodes on the ground cannot hear each other, and each node’s packet transmission probability is non-zero. Alyssa uses a slotted protocol with all packets equal to one slot in length. SECTION 10.9. SUMMARY 19 (a) For the slotted Aloha protocol with a fixed per-node transmission probability, what is the maximum utilization of this network? (Note that there are N nodes in all, of which some four are constantly backlogged.) (b) Suppose the protocol is the slotted Aloha protocol, and the each island dweller greedily doubles his node transmission probability on each packet collision (but not exceeding 1). What do you expect the network utilization to be? (c) In this network, as mentioned above, four of the N nodes are constantly backlogged, but the set of backlogged nodes is not constant. Suppose Alyssa must decide between slotted Aloha with a transmission probability of 1/5 or time division multiple access (TDMA) among the N nodes. For what N does the expected utilization of this slotted Aloha protocol exceed that of TDMA? (d) Alyssa implements a stabilization protocol to adapt the node transmission probabilities on collisions and on successful transmissions. She runs an experiment and finds that the measured utilization is 0.5. Ben Bitdiddle asserts that this utilization is too high and that she must have erred in her measurements. Explain whether or not it is possible for Alyssa’s implementation of stabilization to be consistent with her measured result....
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

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