When referring to storage units however one needs to

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Unformatted text preview: , “kilo” = 103 , “mega” = 106 and “giga” = 109 , when talking about network rates, speeds, or throughput. When referring to storage units, however, one needs to be more careful because “kilo”, “mega” and “giga” often (but not always) refer to 210 , 220 , and 230 , respectively. SECTION 10.3. TIME DIVISION MULTIPLE ACCESS (TDMA) 5 practice, packets will of course be of varying lengths, but this assumption simplifies our analysis and does not affect the correctness of any of the protocols we study. 4. Packets arrive for transmission according to some random process; the protocol should work correctly regardless of the process governing packet arrivals. If two or more nodes send a packet in the same time slot, they are said to collide, and none of the packets are received successfully. Note that even if only part of a packet encounters a collision, the entire packet is assumed to be lost. This “perfect collision” assumption is an accurate model for wired shared media like Ethernet, but is only a crude approximation of wireless (radio) communication. The reason is that it might be possible for multiple nodes to concurrently transmit data over radio, and depending on the positions of the receivers and the techniques used to decode packets, for the concurrent transmissions to be received successfully. 5. The sending node can discover that a packet transmission collided and may choose to retransmit such a packet. 6. Each node has a queue; any packets waiting to be sent are in the queue. A node with a non-empty queue is said to be backlogged. The next section discusses TDMA, a simple scheme that is easy to explain. Then, we will discuss a variant of the Aloha protocol, the first contention MAC protocol that was invented. ￿ 10.3 Time Division Multiple Access (TDMA) If one had a centralized resource allocator, such as a base station in a cellular network, and a way to ensure some sort of time synchronization between nodes, then a TDMA scheme is not hard to develop. The idea is for time to be divided into slots starting from 0 and incrementing by 1, and for each node to be numbered in the range [0, N − 1], where the total number of nodes sharing the medium is N . Then, node i gets to send its data in time slot t if, and only if, tmodN = i. It is easy to see how this method rotates access to the medium amongst the nodes. If the nodes send data in bursts, alternating between periods when they are backlogged and when they are not, or if the amount of data sent by each node is different, then TDMA under-utilizes the medium. The degree of under-utilization depends on how skewed the traffic pattern; the more the imbalance, the lower the utilization. Contention protocols like Aloha and CSMA don’t suffer from this problem, but unlike TDMA, they encounter packet collisions. In general, burst data and skewed workloads favor Aloha and CSMA over TDMA. The rest of this lecture describes contention protocols that are well suited to burst data patterns and skewed traffic loads from the transmitting nodes. We will start with Aloha, the first contention protocol ever invented, and which is the intellectual ancestor of many contention protocols used widely today. LECTURE 10. SHARING A COMMON MEDIUM: 6 MEDIA ACCESS PROTOCOLS Figure 10-3: The utilization of slotted Aloha as a function of p for N = 10. The maximum occurs at p = 1/N and the maximum utilization is U = (1 − 1 N −1 ) . N As N → ∞, U → 1 e ≈ 37%. N doesn’t have to be particularly large for the 1/e approximation to be close—for instance, when N = 10, the maximum utilization is 0.387. ￿ 10.4 Aloha The basic variant of the Aloha protocol that we’re going to start with is simple, and as follows: If a node is backlogged, it sends a packet from its queue with probability p. From here, until Section 10.6, we will assume that each packet is exactly one slot in length. Such a system is also called slotted Aloha. Suppose there are N backlogged nodes and each node uses the same value of p. We can then calculate the utilization of the shared medium as a function of N and p by simply counting the number of slots in which exactly one node sends a packet. By definition, a slot with 0 or greater than 1 transmissions does not correspond to a successfully delivered packet, and therefore does not contribute toward the utilization. If each node sends with probability p, then the probability that exactly one node sends in any given slot is N p(1 − p)N −1 . The reason is that the probability that a specific node sends in the time slot is p, and for its transmission to be successful, all the other nodes should not send. That combined probability is p(1 − p)N −1 . Now, we can pick the successfully transmitting node in N ways, so the probability of exactly one node sending in a slot is N p(1 − p)N −1...
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