L10-11

# 71 considerably higher than the theoretical maximum

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Unformatted text preview: 4 attempts 1616 success 1368 coll 248 Node 5 attempts 1370 success 1115 coll 254 Time 10000 attempts 8668 success 7086 util 0.71 Inter-node fairness: 0.99 SECTION 10.6. GENERALIZING TO BIGGER PACKETS, AND “UNSLOTTED” ALOHA 11 The careful reader will notice something ﬁshy about the simulation output shown above (and also in the output from the simulation where we didn’t set a lower bound on p): the reported utilization is 0.71, considerably higher than the “theoretical maximum” of (1 − 1/N )N −1 = 0.4 when N = 6. What’s going on here is more apparent from Figure 10-5, which shows that there are long periods of time where any given node, though backlogged, does not get to transmit. Over time, every node in the experiment encounters times when it is starving, though over time the nodes all get the same share of the medium (fairness is 0.99). If pmax is 1 (or close to 1), then a backlogged node that has just succeeded in transmitting its packet will continue to send, while other nodes with smaller values of p end up backing off. This phenomenon is also sometimes called the capture effect, manifested by unfairness over time-scales on the order several packets. This behavior is not desirable. Setting pmax to a more reasonable value (less than 1) yields the following:4 Node 0 attempts 941 success 534 coll 407 Node 1 attempts 1153 success 637 coll 516 Node 2 attempts 1076 success 576 coll 500 Node 3 attempts 1471 success 862 coll 609 Node 4 attempts 1348 success 780 coll 568 Node 5 attempts 1166 success 683 coll 483 Time 10000 attempts 7155 success 4072 util 0.41 Inter-node fairness: 0.97 Figure 10-6 shows the corresponding plot, which has reasonable per-node fairness over both long and short time-scales. The utilization is also close to the value we calculated analytically of (1 − 1/N )N −1 . Even though the utilization is now lower, the overall result is better because all backlogged nodes get equal share of the medium even over short time scales. These experiments show the trade-off between achieving both good utilization and ensuring fairness. If our goal were only the former, the problem would be trivial: starve all but one of the backlogged nodes. Achieving a good balance between various notions of fairness and network utilization (throughput) is at the core of many network protocol designs. ￿ 10.6 Generalizing to Bigger Packets, and “Unslotted” Aloha So far, we have looked at perfectly slotted Aloha, which assumes that each packet ﬁts exactly into a slot. But what happens when packets are bigger than a single slot? In fact, one might even ask why we need slotting. What happens when nodes just transmit without regard to slot boundaries? In this section, we analyze these issues, starting with packets that span multiple slot lengths. Then, by making a slot length much smaller than a single packet size, we can calculate the utilization of the Aloha protocol where nodes can send without concern for slot boundaries—that variant is also called unslotted Aloha. Note that the pure unslotted Aloha model is one where there are no slots at all, and each node can send a packet any time it wants. However, this model may be approximated by 4 We have intentionally left the value unspeciﬁed because you will investigate how to set it in the lab. LECTURE 10. SHARING A COMMON MEDIUM: 12 MEDIA ACCESS PROTOCOLS Figure 10-6: Node transmissions and collisions when we set both lower and upper bounds on each backlogged node’s transmission probability. Notice that the capture effect is no longer present. The bottom panel is each node’s throughput. a model where a node sends a packet only at the beginning of a time slot, but each packet is many slots long. When we make the size of a packet large compared to the length of a single slot, we get the unslotted case. We will abuse terminology slightly and use the term unslotted Aloha to refer to the case when there are slots, but the packet size is large compared to the slot time. Suppose each node sends a packet of size T slots. One can then work out the probability of a successful transmission in a network with N backlogged nodes, each attempting to send its packet with probability p whenever it is not already sending a packet. The key insight here is that any packet whose transmission starts in 2T − 1 slots that have any overlap with the current packet can collide. Figure 10-7 illustrates this point, which we discuss in more detail next. Suppose that some node sends a packet in some slot. What is the probability that this transmission has no collisions? From Figure 10-7, for this packet to not collide, no other node should start its transmission in 2T − 1 slots. Because p is the probability of a backlogged node sending a packet in a slot, and there are N − 1 nodes, this probability is equal to (1 − p)(2T −1)(N −1) . (There is a bit of an inaccuracy in this e...
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## This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

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