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.
- Fall '13
- The Land