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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 nonempty 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
underutilizes the medium. The degree of underutilization 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 103: 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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 Fall '13
 HariBalakrishnan
 The Land

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