6 generalizing to bigger packets and unslotted aloha

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Unformatted text preview: xpression, which doesn’t make a significant material difference to our conclusions below, but which is worth pointing out. This expression assumes that a node sends packet independently in each time slot with probability. Of course, in practice a node will not be able to send a packet in a time slot if it is sending a packet in the previous time slot, unless the packet being sent in the previous slot has completed. But our assumption in writing this formula is that such “self SECTION 10.6. GENERALIZING TO BIGGER PACKETS, AND “UNSLOTTED” ALOHA 13 Figure 10-7: Each packet is T slots long. Packet transmissions begin at a slot boundary. In this picture, every packet except U and W collide with V. Given packet V, any other packet sent in any one of 2T − 1 slots—the T slots of V as well as the T − 1 slots immediately preceding V’s transmission—collide with V. inteference” is permissible, which can’t occur in reality. But it doesn’t matter much for our conclusion because we are interested in the utilization when N is large, which means that p would be quite small. Moreover, this formula does represent an accurate lower bound on the throughput.) Now, the transmitting node can be chosen in N ways, and the node has a probability p of sending a packet. Hence, the utilization, U , is equal to U = Throughput/Maximum rate = N p(1 − p)(2T −1)(N −1) /(1/T ) = T N p(1 − p)(2T −1)(N −1) . (10.6) For what value of p is U maximized, and what is the maximum value? By differentiating U wrt p and crunching through some algebra, we find that the maximum value, for large N , is (2T T 1)e . − Now, we can look at what happens in the pure unslotted case, when nodes send without regard to slot boundaries. As explained above, the utilization of this scheme is identical to the case when we make the packet size T much larger than 1; i.e., if each packet is large compared to a time slot, then the fact that the model assumes that packets are sent along slot boundaries is irrelevant as far as throughput (utilization) is concerned. The maximum 1 utilization in this case when N is large is therefore equal to 2e ≈ 0.18. Note that this value is one-half of the maximum utilization of pure slotted Aloha where each packet is one slot long. (We’re making this statement for the case when N is large, but it doesn’t take N to become all that large for the statement to be roughly true, as we’ll see in the lab.) This result may be surprising at first glance, but it is intuitively quite pleasing. Slotting makes it so two packets destined to collide do so fully. Because partial collisions are just as bad as full ones in our model of the shared medium, forcing a full collision improves utilization. Unslotted Aloha has “twice the window of vulnerability” as slotted Aloha, and in the limit when the number of nodes is large, achieves only one-half the utilization. LECTURE 10. SHARING A COMMON MEDIUM: 14 ￿ MEDIA ACCESS PROTOCOLS 10.7 Carrier Sense Multiple Access (CSMA) So far, we have assumed that no two nodes using the shared medium can hear each other. This assumption is true in some networks, notably the satellite network example mentioned here. Over a wired Ethernet, it is decidedly not true, while over wireless networks, the assumption is sometimes true and sometimes not (if there are three nodes A, B, and C, such that A and C can’t usually hear each other, but B can usually hear both A and C, then A and C are said to be hidden terminals). The ability to first listen on the medium before attempting a transmission can be used to reduce the number of collisions and improve utilization. The technical term given for this capability is called carrier sense: a node, before it attempts a transmission, can listen to the medium to see if the analog voltage or signal level is higher than if the medium were unused, or even attempt to detect if a packet transmission is in progress by processing (“demodulating”, a concept we will see in later lectures) a set of samples. Then, if it determines that another packet transmission is in progress, it considers the medium to be busy, and defers its own transmission attempt until the node considers the medium to be idle. The idea is for a node to send only when it believes the medium to be idle. One can modify the stabilized version of Aloha described above to use CSMA. One advantage of CSMA is that it no longer requires each packet to be one time slot long to achieve good utilization; packets can be larger than a slot duration, and can also vary in length. Note, however, that in any practical implementation, it will takes some time for a node to detect that the medium is idle after the previous transmission ends, because it takes time to integrate the signal or sample information received and determine that the medium is indeed idle. This duration is called the detection time for the protocol. Moreover,...
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

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