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`Frequency Division Multiplexing` (FDM) is a static allocation scheme in which a frequency is allocated to each device attached to the shared medium. As each device uses a different transmission frequency, collisions cannot occur. In optical networks, a variant of FDM called `Wavelength Division Multiplexing` (WDM) can be used. An optical fiber can transport light at different wavelengths without interference. With WDM, a different wavelength is allocated to each of the devices that share the same optical fiber.
`Time Division Multiplexing` (TDM) is a static bandwidth allocation method that was initially defined for the telephone network. In the fixed telephone network, a voice conversation is usually transmitted as a 64 Kbps signal. Thus, a telephone conservation generates 8 KBytes per second or one byte every 125 microseconds. Telephone conversations often need to be multiplexed together on a single line. For example, in Europe, thirty 64 Kbps voice signals are multiplexed over a single 2 Mbps (E1) line. This is done by using `Time Division Multiplexing` (TDM). TDM divides the transmission opportunities into slots. In the telephone network, a slot corresponds to 125 microseconds. A position inside each slot is reserved for each voice signal. The figure below illustrates TDM on a link that is used to carry four voice conversations. The vertical lines represent the slot boundaries and the letters the different voice conversations. One byte from each voice conversation is sent during each 125 microseconds slot. The byte corresponding to a given conversation is always sent at the same position in each slot.
TDM as shown above can be completely static, i.e. the same conversations always share the link, or dynamic. In the latter case, the two endpoints of the link must exchange messages specifying which conversation uses which byte inside each slot. Thanks to these control messages, it is possible to dynamically add and remove voice conversations from a given link.
TDM and FDM are widely used in telephone networks to support fixed bandwidth conversations. Using them in Local Area Networks that support computers would probably be inefficient. Computers usually do not send information at a fixed rate. Instead, they often have an on-off behavior. During the on period, the computer tries to send at the highest possible rate, e.g. to transfer a file. During the off period, which is often much longer than the on period, the computer does not transmit any packet. Using a static allocation scheme for computers attached to a LAN would lead to huge inefficiencies, as they would only be able to transmit at :math:`\frac{1}{N}` of the total bandwidth during their on period, despite the fact that the other computers are in their off period and thus do not need to transmit any information. The dynamic MAC algorithms discussed in the remainder of this chapter aim to solve this problem.
ALOHA
In the 1960s, computers were mainly mainframes with a few dozen terminals attached to them. These terminals were usually in the same building as the mainframe and were directly connected to it. In some cases, the terminals were installed in remote locations and connected through a :term:`modem` attached to a :term:`dial-up line`. The university of Hawaii chose a different organization. Instead of using telephone lines to connect the distant terminals, they developed the first `packet radio` technology [Abramson1970]_. Until then, computer networks were built on top of either the telephone network or physical cables. ALOHANet showed that it is possible to use radio signals to interconnect computers.
The first version of ALOHANet, described in [Abramson1970]_, operated as follows. First, the terminals and the mainframe exchanged fixed-length frames composed of 704 bits. Each frame contained 80 8-bit characters, some control bits and parity information to detect transmission errors. Two channels in the 400 MHz range were reserved for the operation of ALOHANet. The first channel was used by the mainframe to send frames to all terminals. The second channel was shared among all terminals to send frames to the mainframe. As all terminals share the same transmission channel, there is a risk of collision. To deal with this problem as well as transmission errors, the mainframe verified the parity bits of the received frame and sent an acknowledgment on its channel for each correctly received frame. The terminals on the other hand had to retransmit the unacknowledged frames. As for TCP, retransmitting these frames immediately upon expiration of a fixed timeout is not a good approach as several terminals may retransmit their frames at the same time leading to a network collapse. A better approach, but still far from perfect, is for each terminal to wait a random amount of time after the expiration of its retransmission timeout. This avoids synchronization among multiple retransmitting terminals.
The pseudo-code below shows the operation of an ALOHANet terminal. We use this python syntax for all Medium Access Control algorithms described in this chapter. The algorithm is applied to each new frame that needs to be transmitted. It attempts to transmit a frame at most `max` times (`while loop`). Each transmission attempt is performed as follows. First, the frame is sent. Each frame is protected by a timeout. Then, the terminal waits for either a valid acknowledgment frame or the expiration of its timeout. If the terminal receives an acknowledgment, the frame has been delivered correctly and the algorithm terminates. Otherwise, the terminal waits for a random time and attempts to retransmit the frame.
[Abramson1970]_ analyzed the performance of ALOHANet under particular assumptions and found that ALOHANet worked well when the channel was lightly loaded. In this case, the frames are rarely retransmitted and the `channel traffic`, i.e. the total number of (correct and retransmitted) frames transmitted per unit of time is close to the `channel utilization`, i.e. the number of correctly transmitted frames per unit of time. Unfortunately, the analysis also reveals that the `channel utilization` reaches its maximum at :math:`\frac{1}{2 \times e}=0.186` times the channel bandwidth. At higher utilization, ALOHANet becomes unstable and the network collapses due to collided retransmissions.
Amateur packet radio
Packet radio technologies have evolved in various directions since the first experiments performed at the University of Hawaii. The Amateur packet radio service developed by amateur radio operators is one of the descendants ALOHANet. Many amateur radio operators are very interested in new technologies and they often spend countless hours developing new antennas or transceivers. When the first personal computers appeared, several amateur radio operators designed radio modems and their own datalink layer protocols [KPD1985]_ [BNT1997]_. This network grew and it was possible to connect to servers in several European countries by only using packet radio relays. Some amateur radio operators also developed TCP/IP protocol stacks that were used over the packet radio service. Some parts of the `amateur packet radio network <http://www.ampr.org/>`_ are connected to the global Internet and use the `44.0.0.0/8` IPv4 prefix.
Many improvements to ALOHANet have been proposed since the publication of [Abramson1970]_, and this technique, or some of its variants, are still found in wireless networks today. The slotted technique proposed in [Roberts1975]_ is important because it shows that a simple modification can significantly improve channel utilization. Instead of allowing all terminals to transmit at any time, [Roberts1975]_ proposed to divide time into slots and allow terminals to transmit only at the beginning of each slot. Each slot corresponds to the time required to transmit one fixed size frame. In practice, these slots can be imposed by a single clock that is received by all terminals. In ALOHANet, it could have been located on the central mainframe. The analysis in [Roberts1975]_ reveals that this simple modification improves the channel utilization by a factor of two.
Carrier Sense Multiple Access
ALOHA and slotted ALOHA can easily be implemented, but unfortunately, they can only be used in networks that are very lightly loaded. Designing a network for a very low utilization is possible, but it clearly increases the cost of the network. To overcome the problems of ALOHA, many Medium Access Control mechanisms have been proposed which improve channel utilization. Carrier Sense Multiple Access (CSMA) is a significant improvement compared to ALOHA. CSMA requires all nodes to listen to the transmission channel to verify that it is free before transmitting a frame [KT1975]_. When a node senses the channel to be busy, it defers its transmission until the channel becomes free again. The pseudo-code below provides a more detailed description of the operation of CSMA.
The above pseudo-code is often called `persistent CSMA` [KT1975]_ as the terminal will continuously listen to the channel and transmit its frame as soon as the channel becomes free. Another important variant of CSMA is the `non-persistent CSMA` [KT1975]_. The main difference between persistent and non-persistent CSMA described in the pseudo-code below is that a non-persistent CSMA node does not continuously listen to the channel to determine when it becomes free. When a non-persistent CSMA terminal senses the transmission channel to be busy, it waits for a random time before sensing the channel again. This improves channel utilization compared to persistent CSMA. With persistent CSMA, when two terminals sense the channel to be busy, they will both transmit (and thus cause a collision) as soon as the channel becomes free. With non-persistent CSMA, this synchronization does not occur, as the terminals wait a random time after having sensed the transmission channel. However, the higher channel utilization achieved by non-persistent CSMA comes at the expense of a slightly higher waiting time in the terminals when the network is lightly loaded.
[KT1975]_ analyzes in detail the performance of several CSMA variants. Under some assumptions about the transmission channel and the traffic, the analysis compares ALOHA, slotted ALOHA, persistent and non-persistent CSMA. Under these assumptions, ALOHA achieves a channel utilization of only 18.4% of the channel capacity. Slotted ALOHA is able to use 36.6% of this capacity. Persistent CSMA improves the utilization by reaching 52.9% of the capacity while non-persistent CSMA achieves 81.5% of the channel capacity.
Carrier Sense Multiple Access with Collision Detection
CSMA improves channel utilization compared to ALOHA. However, the performance can still be improved, especially in wired networks. Consider the situation of two terminals that are connected to the same cable. This cable could, for example, be a coaxial cable as in the early days of Ethernet [Metcalfe1976]_. It could also be built with twisted pairs. Before extending CSMA, it is useful to understand, more intuitively, how frames are transmitted in such a network and how collisions can occur. The figure below illustrates the physical transmission of a frame on such a cable. To transmit its frame, host A must send an electrical signal on the shared medium. The first step is thus to begin the transmission of the electrical signal. This is point `(1)` in the figure below. This electrical signal will travel along the cable. Although electrical signals travel fast, we know that information cannot travel faster than the speed of light (i.e. 300.000 kilometers/second). On a coaxial cable, an electrical signal is slightly slower than the speed of light and 200.000 kilometers per second is a reasonable estimation. This implies that if the cable has a length of one kilometer, the electrical signal will need 5 microseconds to travel from one end of the cable to the other. The ends of coaxial cables are equipped with termination points that ensure that the electrical signal is not reflected back to its source. This is illustrated at point `(3)` in the figure, where the electrical signal has reached the left endpoint and host B. At this point, B starts to receive the frame being transmitted by A. Notice that there is a delay between the transmission of a bit on host A and its reception by host B. If there were other hosts attached to the cable, they would receive the first bit of the frame at slightly different times. As we will see later, this timing difference is a key problem for MAC algorithms. At point `(4)`, the electrical signal has reached both ends of the cable and occupies it completely. Host A continues to transmit the electrical signal until the end of the frame. As shown at point `(5)`, when the sending host stops its transmission, the electrical signal corresponding to the end of the frame leaves the coaxial cable. The channel becomes empty again once the entire electrical signal has been removed from the cable.
Frame transmission on a shared bus
Now that we have looked at how a frame is actually transmitted as an electrical signal on a shared bus, it is interesting to look in more detail at what happens when two hosts transmit a frame at almost the same time. This is illustrated in the figure below, where hosts A and B start their transmission at the same time (point `(1)`). At this time, if host C senses the channel, it will consider it to be free. This will not last a long time and at point `(2)` the electrical signals from both host A and host B reach host C. The combined electrical signal (shown graphically as the superposition of the two curves in the figure) cannot be decoded by host C. Host C detects a collision, as it receives a signal that it cannot decode. Since host C cannot decode the frames, it cannot determine which hosts are sending the colliding frames. Note that host A (and host B) will detect the collision after host C (point `(3)` in the figure below).
Frame collision on a shared bus
As shown above, hosts detect collisions when they receive an electrical signal that they cannot decode. In a wired network, a host is able to detect such a collision both while it is listening (e.g. like host C in the figure above) and also while it is sending its own frame. When a host transmits a frame, it can compare the electrical signal that it transmits with the electrical signal that it senses on the wire. At points `(1)` and `(2)` in the figure above, host A senses only its own signal. At point `(3)`, it senses an electrical signal that differs from its own signal and can thus detects the collision. At this point, its frame is corrupted and it can stop its transmission. The ability to detect collisions while transmitting is the starting point for the `Carrier Sense Multiple Access with Collision Detection (CSMA/CD)` Medium Access Control algorithm, which is used in Ethernet networks [Metcalfe1976]_ [IEEE802.3]_ . When an Ethernet host detects a collision while it is transmitting, it immediately stops its transmission. Compared with pure CSMA, CSMA/CD is an important improvement since when collisions occur, they only last until colliding hosts have detected it and stopped their transmission. In practice, when a host detects a collision, it sends a special jamming signal on the cable to ensure that all hosts have detected the collision.
To better understand these collisions, it is useful to analyze what would be the worst collision on a shared bus network. Let us consider a wire with two hosts attached at both ends, as shown in the figure below. Host A starts to transmit its frame and its electrical signal is propagated on the cable. Its propagation time depends on the physical length of the cable and the speed of the electrical signal. Let us use :math:`\tau` to represent this propagation delay in seconds. Slightly less than :math:`\tau` seconds after the beginning of the transmission of A's frame, B decides to start transmitting its own frame. After :math:`\epsilon` seconds, B senses A's frame, detects the collision and stops transmitting. The beginning of B's frame travels on the cable until it reaches host A. Host A can thus detect the collision at time :math:`\tau-\epsilon+\tau \approx 2\times\tau`. An important point to note is that a collision can only occur during the first :math:`2\times\tau` seconds of its transmission. If a collision did not occur during this period, it cannot occur afterwards since the transmission channel is busy after :math:`\tau` seconds and CSMA/CD hosts sense the transmission channel before transmitting their frame.
The worst collision on a shared bus
Furthermore, on the wired networks where CSMA/CD is used, collisions are almost the only cause of transmission errors that affect frames. Transmission errors that only affect a few bits inside a frame seldom occur in these wired networks. For this reason, the designers of CSMA/CD chose to completely remove the acknowledgment frames in the datalink layer. When a host transmits a frame, it verifies whether its transmission has been affected by a collision. If not, given the negligible Bit Error Ratio of the underlying network, it assumes that the frame was received correctly by its destination. Otherwise the frame is retransmitted after some delay.
Removing acknowledgments is an interesting optimization as it reduces the number of frames that are exchanged on the network and the number of frames that need to be processed by the hosts. However, to use this optimization, we must ensure that all hosts will be able to detect all the collisions that affect their frames. The problem is important for short frames. Let us consider two hosts, A and B, that are sending a small frame to host C as illustrated in the figure below. If the frames sent by A and B are very short, the situation illustrated below may occur. Hosts A and B send their frame and stop transmitting (point `(1)`). When the two short frames arrive at the location of host C, they collide and host C cannot decode them (point `(2)`). The two frames are absorbed by the ends of the wire. Neither host A nor host B have detected the collision. They both consider their frame to have been received correctly by its destination.
The short-frame collision problem
To solve this problem, networks using CSMA/CD require hosts to transmit for at least :math:`2\times\tau` seconds. Since the network transmission speed is fixed for a given network technology, this implies that a technology that uses CSMA/CD enforces a minimum frame size. In the most popular CSMA/CD technology, Ethernet, :math:`2\times\tau` is called the `slot time` [#fslottime]_.
The last innovation introduced by CSMA/CD is the computation of the retransmission timeout. As for ALOHA, this timeout cannot be fixed, otherwise hosts could become synchronized and always retransmit at the same time. Setting such a timeout is always a compromise between the network access delay and the amount of collisions. A short timeout would lead to a low network access delay but with a higher risk of collisions. On the other hand, a long timeout would cause a long network access delay but a lower risk of collisions. The `binary exponential back-off` algorithm was introduced in CSMA/CD networks to solve this problem.
To understand `binary exponential back-off`, let us consider a collision caused by exactly two hosts. Once it has detected the collision, a host can either retransmit its frame immediately or defer its transmission for some time. If each colliding host flips a coin to decide whether to retransmit immediately or to defer its retransmission, four cases are possible :
Both hosts retransmit immediately and a new collision occurs

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