Building a network¶

Warning

This is an unpolished draft of the second edition of this ebook. If you find any error or have suggestions to improve the text, please create an issue via https://github.com/obonaventure/cnp3/issues?milestone=2

In the previous section, we have explained how reliable protocols allow hosts to exchange data reliably even if the underlying physical layer is imperfect and thus unreliable. Connecting two hosts together through a wire is the first step to build a network. However, this is not sufficient. Hosts usually need to interact with remote hosts that are not directly connected through a direct physical layer link. This can be achieved by adding one layer above the datalink layer : the network layer.

The main objective of the network layer is to allow endsystems, connected to different networks, to exchange information through intermediate systems called router. The unit of information in the network layer is called a packet.

Before explaining the network layer in detail, it is useful to remember the characteristics of the service provided by the datalink layer. There are many variants of the datalink layer. Some provide a reliable service while others do not provide any guarantee of delivery. The reliable datalink layer services are popular in environments such as wireless networks were transmission errors are frequent. On the other hand, unreliable services are usually used when the physical layer provides an almost reliable service (i.e. only a negligible fraction of the frames are affected by transmission errors). Such almost reliable services are frequently in wired and optical networks. In this chapter, we will assume that the datalink layer service provides an almost reliable service since this is both the most general one and also the most widely deployed one.

The second type of datalink layer is the one used in Local Area Networks (LAN). Conceptually, a LAN is a set of communicating devices such that any two devices can directly exchange frames through the datalink layer. Both endsystems and routers can be connected to a LAN. Some LANs only connect a few devices, but there are LANs that can connect hundreds or even thousands of devices. In this chapter, we focus on the utilization of point-to-point datalink layers. We will describe later the organisation and the operation of Local Area Networks and their impact on the network layer.

Even if we only consider the point-to-point datalink layers, there is an important characteristics of these layers that we cannot ignore. No datalink layer is able to send frames of unlimited size. Each datalink layer is characterized by a maximum frame size. There are more than a dozen different datalink layers and unfortunately most of them use a different maximum frame size. This heterogeneity in the maximum frame sizes will cause problems when we will need to exchange data between hosts attached to different types of datalink layers.

As a first step, let us assume that we only need to exchange small amount of data. In this case, there is no issue with the maximum length of the frames. However, there are other more interesting problems that we need to tackle. To understand these problems, let us consider the network represented in the figure below.

This network contains two types of devices. The end hosts, represented with circles and the routers, represented as boxes. An endhost is a device which is able to send and receive data for its own usage in contrast with routers that most of the time forward data towards their final destination. Routers have multiple links to neighbouring routers or endhosts. Endhosts are usually attached via a single link to the network. Nowadays, with the growth of wireless networks, more and more endhosts are equipped with several physical interfaces. These endhosts are often called multihomed. Still, using several interfaces at the same time often leads to practical issues that are beyond the scope of this document. For this reason, we will only consider single-homed hosts in this ebook.

To understand the key principles behind the operation of a network, let us analyse all the operations that need to be performed to allow host A in the above network to send one byte to host B. Thanks to the datalink layer used above the A-R1 link, host A can easily send a byte to router R1 inside a frame. However, upon reception of this frame, router R1 needs to understand that the byte is destined to host B and not to itself. This is the objective of the network layer.

The network layer enables the transmission of information between hosts that are not directly connected through intermediate routers. This transmission is carried out by putting the information to be transmitted inside a data structure which is called a packet. Like a frame that contains useful data and control information, a packet also contains useful data and control information. An important issue in the network layer is the ability to identify a node (host or router) inside the network. This identification is performed by associating an address to each node. An address is usually represented as a sequence of bits. Most networks use fixed-length addresses. At this stage, let us simply assume that each of the nodes in the above network has an address which corresponds to the binary representation on its name on the figure.

To send one byte of information to host B, host A needs to place this information inside a packet. In addition to the data being transmitted, the packet must also contain either the addresses of the source and the destination nodes or information that indicates the path that needs to be followed to reach the destination.

There are two possible organisations for the network layer :

• datagram
• virtual circuits

The datagram organisation¶

The first and most popular organisation of the network layer is the datagram organisation. This organisation is inspired by the organisation of the postal service. Each host is identified by a network layer address. To send information to a remote host, a host creates a packet that contains :

• the network layer address of the destination host
• its own network layer address
• the information to be sent

To understand the datagram organisation, let us consider the figure below. A network layer address, represented by a letter, has been assigned to each host and router. To send some information to host J, host A creates a packet containing its own address, the destination address and the information to be exchanged.

A simple internetwork

With the datagram organisation, routers use hop-by-hop forwarding. This means that when a router receives a packet that is not destined to itself, it looks up the destination address of the packet in its forwarding table. A forwarding table is a data structure that maps each destination address (or set of destination addresses) to the outgoing interface over which a packet destined to this address must be forwarded to reach its final destination. The router consults its forwarding table for each packet that it handles.

The figure illustrates some possible forwarding tables in this network. By inspecting the forwarding tables of the different routers, one can find the path followed by packets sent from a source to a particular destination. In the example above, host A sends its packet to router R1. R1 consults its routing table and forwards the packet towards R2. Based on its own routing table, R2 decides to forward the packet to R5 that can deliver it to its destination. Thus, the path from A to J is A -> R1 -> R2 -> R5 -> J.

The computation of the forwarding tables of all the routers inside a network is a key element for the correct operation of the network. This computation can be carried out in different ways and it is possible to use both distributed and centralized algorithms. These algorithms provide different performance, may lead to different types of paths, but their composition must lead to valid path.

In a network, a path can be defined as the list of all intermediate routers for a given source destination pair. For a given source/destination pair, the path can be derived by first consulting the forwarding table of the router attached to the source to determine the next router on the path towards the chosen destination. Then, the forwarding table of this router is queried for the same destination... The queries continue until the destination is reached. In a network that has valid forwarding tables, all the paths between all source/destination pairs contain a finite number of intermediate routers. However, if forwarding tables have not been correctly computed, two types of invalid path can occur.

A path may lead to a black hole. In a network, a black hole is a router that receives packets for at least one given source/destination pair but does not have any entry inside its forwarding table for this destination. Since it does not know how to reach the destination, the router cannot forward the received packets and must discard them. Any centralized or distributed algorithm that computes forwarding tables must ensure that there are not black holes inside the network.

A second type of problem may exist in networks using the datagram organisation. Consider a path that contains a cycle. For example, router R1 sends all packets towards destination D via router R2, router R2 forwards these packets to router R3 and finally router R3‘s forwarding table uses router R1 as its nexthop to reach destination D. In this case, if a packet destined to D is received by router R1, it will loop on the R1 -> R2 -> R3 -> R1 cycle and will never reach its final destination. As in the black hole case, the destination is not reachable from all sources in the network. However, in practice the loop problem is worse than the black hole problem because when a packet is caught in a forwarding loop, it unnecessarily consumes bandwidth. In the black hole case, the problematic packet is quickly discarded. We will see later that network layer protocols include techniques to minimize the impact of such forwarding loops.

Any solution which is used to compute the forwarding tables of a network must ensure that all destinations are reachable from any source. This implies that it must guarantee the absence of black holes and forwarding loops.

The forwarding tables and the precise format of the packets that are exchanged inside the network are part of the data plane of the network. This data plane contains all the protocols and algorithms that are used by hosts and routers to create and process the packets that contain user data. On high-end routers, the data plane is often implemented in hardware for performance reasons.

Besides the data plane, a network is also characterized by its control plane. The control plane includes all the protocols and algorithms (often distributed) that are used to compute the forwarding tables that are installed on all routers inside the network. While there is only one possible data plane for a given networking technology, different networks using the same technology may use different control planes. The simplest control plane for a network is always to compute manually the forwarding tables of all routers inside the network. This simple control plane is sufficient when the network is (very) small, usually up to a few routers.

In most networks, manual forwarding tables are not a solution for two reasons. First, most networks are too large to enable a manual computation of the forwarding tables. Second, with manually computed forwarding tables, it is very difficult to deal with link and router failures. Networks need to operate 24h a day, 365 days per year. During the lifetime of a network, many events can affect the routers and links that it contains. Link failures are regular events in deployed networks. Links can fail for various reasons, including electromagnetic interference, fiber cuts, hardware or software problems on the terminating routers, ... Some links also need to be added to the network or removed because their utilisation is too low or their cost is too high. Similarly, routers also fail. There are two types of failures that affect routers. A router may stop forwarding packets due to hardware or software problem (e.g. due to a crash of its operating system). A router may also need to be halted from time to time (e.g. to upgrade its operating system to fix some bugs). These planned and unplanned events affect the set of links and routers that can be used to forward packets in the network. Still, most network users expect that their network will continue to correctly forward packets despite all these events. With manually computed forwarding tables, it is usually impossible to precompute the forwarding tables while taking into account all possible failure scenarios.

An alternative to manually computed forwarding tables is to use a network management platform that tracks the network status and can push new forwarding tables on the routers when it detects any modification to the network topology. This solution gives some flexibility to the network managers in computing the paths inside their network. However, this solution only works if the network management platform is always capable of reaching all routers even when the network topology changes. This may require a dedicated network that allows the management platform to push information on the forwarding tables.

Another interesting point that is worth being discussed is when the forwarding tables are computed. A widely used solution is to compute the entries of the forwarding tables for all destinations on all routers. This ensures that each router has a valid route towards each destination. These entries can be updated when an event occurs and the network topology changes. A drawback of this approach is that the forwarding tables can become large in large networks since each router must maintain one entry for each destination at all times inside its forwarding table.

Some networks use the arrival of packets as the trigger to compute the corresponding entries in the forwarding tables. Several technologies have been built upon this principle. When a packet arrives, the router consults its forwarding table to find a path towards the destination. If the destination is present in the forwarding table, the packet is forwarded. Otherwise, the router needs to find a way to forward the packet and update its forwarding table.

Computing forwarding tables¶

Several techniques to update the forwarding tables upon the arrival of a packet have been used in deployed networks. In this section, we briefly present the principles that underly three of these techniques.

The first technique assumes that the underlying network topology is a tree. A tree is the simplest network to be considered when forwarding packets. The main advantage of using a tree is that there is only one path between any pair of nodes inside the network. Since a tree does not contain any cycle, it is impossible to have forwarding loops in a tree-shaped network.

To understand the operation of the port-address table, let us consider the example network shown in the figure below. This network contains three hosts : A, B and C and five nodes, R1 to R5. When the network boots, all the forwarding tables of the nodes are empty.

Host A sends a packet towards B. When receiving this packet, R1 learns that A is reachable via its North interface. Since it does not have an entry for destination B in its port-address table, it forwards the packet to both R2 and R3. When R2 receives the packet, it updates its own forwarding table and forward the packet to C. Since C is not the intended recipient, it simply discards the received packet. Node R3 also received the packet. It learns that A is reachable via its North interface and broadcasts the packet to R4 and R5. R5 also updates its forwarding table and finally forwards it to destination B.Let us now consider what happens when B sends a reply to A. R5 first learns that B is attached to its South port. It then consults its port-address table and finds that A is reachable via its North interface. The packet is then forwarded hop-by-hop to A without any broadcasting. If C sends a packet to B, this packet will reach R1 that contains a valid forwarding entry in its forwarding table.

By inspecting the source and destination addresses of packets, network nodes can automatically derive their forwarding tables. As we will discuss later, this technique is used in Ethernet networks. Despite being widely used, it has two important drawbacks. First, packets sent to unknown destinations are broadcasted in the network even if the destination is not attached to the network. Consider the transmission of ten packets destined to Z in the network above. When a node receives a packet towards this destination, it can only broadcast the packet. Since Z is not attached to the network, no node will ever receive a packet whose source is Z to update its forwarding table. The second and more important problem is that few networks have a tree-shaped topology. It is interesting to analyze what happens when a port-address table is used in a network that contains a cycle. Consider the simple network shown below with a single host.

Another technique can be used to automatically compute forwarding tables. It has been used in interconnecting Token Ring networks and in some wireless networks. Intuitively, Source routing enables a destination to automatically discover the paths from a given source towards itself. This technique requires nodes to change some information inside some packets. For simplicity, let us assume that the data plane supports two types of packets :

• the data packets
• the control packets

Data packets are used to exchange data while control packets are used to discover the paths between endhosts. With Source routing, network nodes can be kept as simple as possible and all the complexity is placed on the endhosts. This is in contrast with the previous technique where the nodes had to maintain a port-address and a forwarding table while the hosts simply sent and received packets. Each node is configured with one unique address and there is one identifier per outgoing link. For simplicity and to avoid cluttering the figures with those identifiers, we will assume that each node uses as link identifiers north, west, south, ... In practice, a node would associate one integer to each outgoing link.

In the network above, node R2 is attached to two outgoing links. R2 is connected to both R1 and R3. R2 can easily determine that it is connected to these two nodes by exchanging packets with them or observing the packets that it receives over each interface. Assume for example that when a host or node starts, it sends a special control packet over each of its interfaces to advertise its own address to its neighbors. When a host or node receives such a packet, it automatically replies with its own address. This exchange can also be used to verify whether a neighbor, either node or host, is still alive. With source routing, the data plane packets include a list of identifiers. This list is called a source route and indicates the path to be followed by the packet as a sequence of link identifiers. When a node receives such a data plane packet, it first checks whether the packet’s destination is direct neighbor. In this case, the packet is forwarded to the destination. Otherwise, the node extracts the next address from the list and forwards it to the neighbor. This allows the source to specify the explicit path to be followed for each packet. For example, in the figure above there are two possible paths between A and B. To use the path via R2, A would send a packet that contains R1,R2,R3 as source route. To avoid going via R2, A would place R1,R3 as the source route in its transmitted packet. If A knows the complete network topology and all link identifiers, it can easily compute the source route towards each destination. If needed, it could even use different paths, e.g. for redundancy, to reach a given destination. However, in a real network hosts do not usually have a map of the entire network topology.

In networks that rely on source routing, hosts use control packets to automatically discover the best path(s). In addition to the source and destination addresses, control packets contain a list that records the intermediate nodes. This list is often called the record route because it allows to record the route followed by a given packet. When a node receives a control packet, it first checks whether its address is included in the record route. If yes, the control packet is silently discarded. Otherwise, it adds its own address to the record route and forwards the packet to all its interfaces, except the interface over which the packet has been received. Thanks to this, the control packet will be able to explore all paths between a source and a given destination.

For example, consider again the network topology above. A sends a control packet towards B. The initial record route is empty. When R1 receives the packet, it adds its own address to the record route and forwards a copy to R2 and another to R3. R2 receives the packet, adds itself to the record route and forwards it to R3. R3 receives two copies of the packet. The first contains the [R1,R2] record route and the second [R1]. In the end, B will receive two control packets containing [R1,R2,R3,R4] and [R1,R3,R4] as record routes. B can keep these two paths or select the best one and discard the second. A popular heuristic is to select the record route of the first received packet as being the best one since this likely corresponds to the shortest delay path.

With the received record route, B can send a data packet to A. For this, it simply reverses the chosen record route. However, we still need to communicate the chosen path to A. This can be done by putting the record route inside a control packet which is sent back to A over the reverse path. An alternative is to simply send a data packet back to A. This packet will travel back to A. To allow A to inspect the entire path followed by the data packet, its source route must contain all intermediate routers when it is received by A. This can be achieved by encoding the source route using a data structure that contains an index and the ordered list of node addresses. The index always points to the next address in the source route. It is initialized at 0 when a packet is created and incremented by each intermediate node.

The last, but important, point to discuss about the data plane of the networks that rely on the datagram mode is their addressing scheme. In the examples above, we have used letters to represent the addresses of the hosts and network nodes. In practice, all addresses are encoded as a bit string. Most network technologies use a fixed size bit string to represent source and destination address. These addresses can be organized in two different ways.

With flat addressing the lookup operation in the forwarding table can be implemented as an exact match. The forwarding table contains the (sorted) list of all known destination addresses. When a packet arrives, a network node only needs to check whether this address is part of the forwarding table or not. In software, this is an O(log(n)) operation if the list is sorted. In hardware, Content Addressable Memories can perform this lookup operation efficiently, but their size is usually limited.

A drawback of the flat addressing scheme is that the forwarding tables grow linearly with the number of hosts and nodes in the network. With this addressing scheme, each forwarding table must contain an entry that points to every address reachable inside the network. Since large networks can contain tens of millions or more of hosts, this is a major problem on network nodes that need to be able to quickly forward packets. As an illustration, it is interesting to consider the case of an interface running at 10 Gbps. Such interfaces are found on high-end servers and in various network nodes today. Assuming a packet size of 1000 bits, a pretty large and conservative number, such interface must forward ten million packets every second. This implies that a network node that receives packets over such a link must forward one 1000 bits packet every 100 nanoseconds. This is the same order of magnitude as the memory access times of old DRAMs.

A widely used alternative to the flat addressing scheme is the hierarchical addressing scheme. This addressing scheme builds upon the fact that networks usually contain much more hosts than network nodes. In this case, a first solution to reduce the size of the forwarding tables is to create a hierarchy of addresses. This is the solution chosen by the post office were addresses contain a country, sometimes a state or province, a city, a street and finally a street number. When an enveloppe is forwarded by a postoffice in a remote country, it only looks at the destination country, while a post office in the same province will look at the city information. Only the post office responsible for a given city will look at the street name and only the postman will use the street number. Hierarchical addresses provide a similar solution for network addresses. For example, the address of an Internet host attached to a campus network could contain in the high-order bits an identification of the Internet Service Provider (ISP) that serves the campus network. Then, a subsequent block of bits identifies the campus network which is one of the customers from the ISP. Finally, the low order bits of the address identify the host in the campus network.

This hierarchical allocation of addresses can be applied in any type of network. In practice, the allocation of the addresses must follow the network topology. Usually, this is achieved by dividing the addressing space in consecutive blocks and then allocating these blocks to different parts of the network. In a small network, the simplest solution is to allocate one block of addresses to each network node and assign the host addresses from the attached node.

In the above figure, assume that the network uses 16 bits addresses and that the prefix 01001010 has been assigned to the entire network. Since the network contains four routers, the network operator could assign one block of sixty-four addresses to each router. R1 would use address 0100101000000000 while A could use address 0100101000000001. R2 could be assigned all adresses from 0100101001000000 to 0100101001111111. R4 could then use 0100101011000000 and assign 0100101011000001 to B. Other allocation schemes are possible. For example, R3 could be allocated a larger block of addresses than R2 and R4 could use a sub-block from R3 ‘s address block.

The main advantage of hierarchical addresses is that it is possible to significantly reduce the size of the forwarding tables. In many networks, the number of nodes can be several orders of magnitude smaller than the number of hosts. A campus network may contain a few dozen of network nodes for thousands of hosts. The largest Internet Services Providers typically contain no more than a few tens of thousands of network nodes but still serve tens or hundreds of millions of hosts.

Despite their popularity, hierarchical addresses have some drawbacks. Their first drawback is that a lookup in the forwarding table is more complex than when using flat addresses. For example, on the Internet, network nodes have to perform a longest-match to forward each packet. This is partially compensated by the reduction in the size of the forwarding tables, but the additional complexity of the lookup operation has been a difficulty to implement hardware support for packet forwarding. A second drawback of the utilisation of hierarchical addresses is that when a host connects for the first time to a network, it must contact one network node to determine its own address. This requires some packet exchanges between the host and some network nodes. Furthermore, if a host moves and is attached to another network node, its network address will change. This can be an issue with some mobile hosts.

Virtual circuit organisation¶

The second organisation of the network layer, called virtual circuits, has been inspired by the organisation of telephone networks. Telephone networks have been designed to carry phone calls that usually last a few minutes. Each phone is identified by a telephone number and is attached to a telephone switch. To initiate a phone call, a telephone first needs to send the destination’s phone number to its local switch. The switch cooperates with the other switches in the network to create a bi-directional channel between the two telephones through the network. This channel will be used by the two telephones during the lifetime of the call and will be released at the end of the call. Until the 1960s, most of these channels were created manually, by telephone operators, upon request of the caller. Today’s telephone networks use automated switches and allow several channels to be carried over the same physical link, but the principles remain roughly the same.

In a network using virtual circuits, all hosts are also identified with a network layer address. However, packet forwarding is not performed by looking at the destination address of each packet. With the virtual circuit organisation, each data packet contains one label [1]. A label is an integer which is part of the packet header. Network nodes implement label switching to forward labelled data packet. Upon reception of a packet, a network nodes consults its label forwarding table to find the outgoing interface for this packet. In contrast with the datagram mode, this lookup is very simple. The label forwarding table is an array stored in memory and the label of the incoming packet is the index to access this array. This implies that the lookup operation has an O(1) complexity in contrast with other packet forwarding techniques. To ensure that on each node the packet label is an index in the label forwarding table, each network node that forwards a packet replaces the label of the forwarded packet with the label found in the label forwarding table. Each entry of the label forwarding table contains two pieces of information :

• the outgoing interface for the packet
• the label for the outgoing packet

For example, consider the label forwarding table of a network node below.

 index outgoing interface label 0 South 7 1 none none 2 West 2 3 East 2

If this node receives a packet with label=2, it forwards the packet on its West interface and sets the label of the outgoing packet to 2. If the received packet’s label is set to 3, then the packet is forwarded over the East interface and the label of the outgoing packet is set to 2. If a packet is received with a label field set to 1, the packet is discarded since the corresponding label forwarding table entry is invalid.

Label switching enables a full control over the path followed by packets inside the network. Consider the network below and assume that we want to use two virtual circuits : R1->R3->R4->R2->R5 and R2->R1->R3->R4->R5.

To create these virtual circuits, we need to configure the label forwarding tables of all network nodes. For simplicity, assume that a label forwarding table only contains two entries. Assume that R5 wants to receive the packets from the virtual circuit created by R1 (resp. R2) with label=1 (label=0). R4 could use the following label forwarding table:

 index outgoing interface label 0 ->R2 1 1 ->R5 0

Since a packet received with label=1 must be forwarded to R5 with label=1, R2‘s label forwarding table could contain :

 index outgoing interface label 0 none none 1 ->R5 1

Two virtual circuits pass through R3. They both need to be forwarded to R4, but R4 expects label=1 for packets belonging to the virtual circuit originated by R2 and label=0 for packets belonging to the other virtual circuit. R3 could choose to leave the labels unchanged.

 index outgoing interface label 0 ->R4 0 1 ->R4 1

With the above label forwarding table, R1 needs to originate the packets that belong to the R1->R3->R4->R2->R5 with label=1. The packets received from R2 and belonging to the R2->R1->R3->R4->R5 would then use label=0 on the R1-R3 link. R1 ‘s label forwarding table could be built as follows :

 index outgoing interface label 0 ->R3 0 1 none 1

The figure below shows the path followed by the packets on the R1->R3->R4->R2->R5 path in red with on each arrow the label used in the packets.

Multi-Protocol Label Switching (MPLS) is the example of a deployed networking technology that relies on label switching. MPLS is more complex than the above description because it has been designed to be easily integrated with datagram technologies. However, the principles remain. Asynchronous Transfer Mode (ATM) and Frame Relay are other examples of technologies that rely on label switching.

Nowadays, most deployed networks rely on distributed algorithms, called routing protocols, to compute the forwarding tables that are installed on the network nodes. These distributed algorithms are part of the control plane. They are usually implemented in software and are executed on the main CPU of the network nodes. There are two main families of routing protocols : distance vector routing and link state routing. Both are capable of discovering autonomously the network and react dynamically to topology changes.

Footnotes

 [1] We will see later a more detailed description of Multiprotocol Label Switching, a networking technology that is capable of using one or more labels.

The control plane¶

One of the objectives of the control plane in the network layer is to maintain the routing tables that are used on all routers. As indicated earlier, a routing table is a data structure that contains, for each destination address (or block of addresses) known by the router, the outgoing interface over which the router must forward a packet destined to this address. The routing table may also contain additional information such as the address of the next router on the path towards the destination or an estimation of the cost of this path.

In this section, we discuss the main techniques that can be used to maintain the forwarding tables in a network.

Distance vector routing¶

Distance vector routing is a simple distributed routing protocol. Distance vector routing allows routers to automatically discover the destinations reachable inside the network as well as the shortest path to reach each of these destinations. The shortest path is computed based on metrics or costs that are associated to each link. We use l.cost to represent the metric that has been configured for link l on a router.

Each router maintains a routing table. The routing table R can be modelled as a data structure that stores, for each known destination address d, the following attributes :

• R[d].link is the outgoing link that the router uses to forward packets towards destination d
• R[d].cost is the sum of the metrics of the links that compose the shortest path to reach destination d
• R[d].time is the timestamp of the last distance vector containing destination d

A router that uses distance vector routing regularly sends its distance vector over all its interfaces. The distance vector is a summary of the router’s routing table that indicates the distance towards each known destination. This distance vector can be computed from the routing table by using the pseudo-code below.

Every N seconds:
v=Vector()
for d in R[]:
# add destination d to vector
for i in interfaces
# send vector v on this interface
send(v,interface)


When a router boots, it does not know any destination in the network and its routing table only contains itself. It thus sends to all its neighbours a distance vector that contains only its address at a distance of 0. When a router receives a distance vector on link l, it processes it as follows.

# V : received Vector
for d in V[]
if not (d in R[]) :
# new route
R[d].cost=V[d].cost+l.cost
R[d].time=now
else :
# existing route, is the new better ?
if ( ((V[d].cost+l.cost) < R[d].cost) or ( R[d].link == l) )  :
# Better route or change to current route
R[d].cost=V[d].cost+l.cost
R[d].time=now


The router iterates over all addresses included in the distance vector. If the distance vector contains an address that the router does not know, it inserts the destination inside its routing table via link l and at a distance which is the sum between the distance indicated in the distance vector and the cost associated to link l. If the destination was already known by the router, it only updates the corresponding entry in its routing table if either :

• the cost of the new route is smaller than the cost of the already known route ( (V[d].cost+l.cost) < R[d].cost)
• the new route was learned over the same link as the current best route towards this destination ( R[d].link == l)

The first condition ensures that the router discovers the shortest path towards each destination. The second condition is used to take into account the changes of routes that may occur after a link failure or a change of the metric associated to a link.

To understand the operation of a distance vector protocol, let us consider the network of five routers shown below.

Operation of distance vector routing in a simple network

Assume that A is the first to send its distance vector [A=0].

• B and D process the received distance vector and update their routing table with a route towards A.
• D sends its distance vector [D=0,A=1] to A and E. E can now reach A and D.
• C sends its distance vector [C=0] to B and E
• E sends its distance vector [E=0,D=1,A=2,C=1] to D, B and C. B can now reach A, C, D and E
• B sends its distance vector [B=0,A=1,C=1,D=2,E=1] to A, C and E. A, B, C and E can now reach all destinations.
• A sends its distance vector [A=0,B=1,C=2,D=1,E=2] to B and D.

At this point, all routers can reach all other routers in the network thanks to the routing tables shown in the figure below.

Routing tables computed by distance vector in a simple network

To deal with link and router failures, routers use the timestamp stored in their routing table. As all routers send their distance vector every N seconds, the timestamp of each route should be regularly refreshed. Thus no route should have a timestamp older than N seconds, unless the route is not reachable anymore. In practice, to cope with the possible loss of a distance vector due to transmission errors, routers check the timestamp of the routes stored in their routing table every N seconds and remove the routes that are older than $$3 \times N$$ seconds. When a router notices that a route towards a destination has expired, it must first associate an $$\infty$$ cost to this route and send its distance vector to its neighbours to inform them. The route can then be removed from the routing table after some time (e.g. $$3 \times N$$ seconds), to ensure that the neighbouring routers have received the bad news, even if some distance vectors do not reach them due to transmission errors.

Consider the example above and assume that the link between routers A and B fails. Before the failure, A used B to reach destinations B, C and E while B only used the A-B link to reach A. The affected entries timeout on routers A and B and they both send their distance vector.

• A sends its distance vector $$[A=0,B=\infty,C=\infty,D=1,E=\infty]$$. D knows that it cannot reach B anymore via A
• D sends its distance vector $$[D=0,B=\infty,A=1,C=2,E=1]$$ to A and E. A recovers routes towards C and E via D.
• B sends its distance vector $$[B=0,A=\infty,C=1,D=2,E=1]$$ to E and C. C learns that there is no route anymore to reach A via B.
• E sends its distance vector $$[E=0,A=2,C=1,D=1,B=1]$$ to D, B and C. D learns a route towards B. C and B learn a route towards A.

At this point, all routers have a routing table allowing them to reach all another routers, except router A, which cannot yet reach router B. A recovers the route towards B once router D sends its updated distance vector $$[A=1,B=2,C=2,D=1,E=1]$$. This last step is illustrated in figure Routing tables computed by distance vector after a failure, which shows the routing tables on all routers.

Routing tables computed by distance vector after a failure

Consider now that the link between D and E fails. The network is now partitioned into two disjoint parts : (A , D) and (B, E, C). The routes towards B, C and E expire first on router D. At this time, router D updates its routing table.

If D sends $$[D=0, A=1, B=\infty, C=\infty, E=\infty]$$, A learns that B, C and E are unreachable and updates its routing table.

Unfortunately, if the distance vector sent to A is lost or if A sends its own distance vector ( $$[A=0,D=1,B=3,C=3,E=2]$$ ) at the same time as D sends its distance vector, D updates its routing table to use the shorter routes advertised by A towards B, C and E. After some time D sends a new distance vector : $$[D=0,A=1,E=3,C=4,B=4]$$. A updates its routing table and after some time sends its own distance vector $$[A=0,D=1,B=5,C=5,E=4]$$, etc. This problem is known as the count to infinity problem in networking literature. Routers A and D exchange distance vectors with increasing costs until these costs reach $$\infty$$. This problem may occur in other scenarios than the one depicted in the above figure. In fact, distance vector routing may suffer from count to infinity problems as soon as there is a cycle in the network. Cycles are necessary to have enough redundancy to deal with link and router failures. To mitigate the impact of counting to infinity, some distance vector protocols consider that $$16=\infty$$. Unfortunately, this limits the metrics that network operators can use and the diameter of the networks using distance vectors.

This count to infinity problem occurs because router A advertises to router D a route that it has learned via router D. A possible solution to avoid this problem could be to change how a router creates its distance vector. Instead of computing one distance vector and sending it to all its neighbors, a router could create a distance vector that is specific to each neighbour and only contains the routes that have not been learned via this neighbour. This could be implemented by the following pseudocode.

Every N seconds:
# one vector for each interface
for l in interfaces:
v=Vector()
for d in R[]:
v=v+Pair(d,R[d.cost])
send(v)
# end for d in R[]
#end for l in interfaces


This technique is called split-horizon. With this technique, the count to infinity problem would not have happened in the above scenario, as router A would have advertised $$[A=0]$$, since it learned all its other routes via router D. Another variant called split-horizon with poison reverse is also possible. Routers using this variant advertise a cost of $$\infty$$ for the destinations that they reach via the router to which they send the distance vector. This can be implemented by using the pseudo-code below.

Every N seconds:
for l in interfaces:
# one vector for each interface
v=Vector()
for d in R[]:
v=v+Pair(d,R[d.cost])
else:
v=v+Pair(d,infinity);
send(v)
# end for d in R[]
#end for l in interfaces


Unfortunately, split-horizon, is not sufficient to avoid all count to infinity problems with distance vector routing. Consider the failure of link A-B in the network of four routers below.

Count to infinity problem

After having detected the failure, router B sends its distance vectors :

• $$[A=\infty,B=0,C=\infty,E=1]$$ to router C
• $$[A=\infty,B=0,C=1,E=\infty]$$ to router E

If, unfortunately, the distance vector sent to router C is lost due to a transmission error or because router C is overloaded, a new count to infinity problem can occur. If router C sends its distance vector $$[A=2,B=1,C=0,E=\infty]$$ to router E, this router installs a route of distance 3 to reach A via C. Router E sends its distance vectors $$[A=3,B=\infty,C=1,E=1]$$ to router B and $$[A=\infty,B=1,C=\infty,E=0]$$ to router C. This distance vector allows B to recover a route of distance 4 to reach A.

Note

Forwarding tables versus routing tables

Routers usually maintain at least two data structures that contain information about the reachable destinations. The first data structure is the routing table. The routing table is a data structure that associates a destination to an outgoing interface or a nexthop router and a set of additional attributes. Different routing protocols can associate different attributes for each destination. Distance vector routing protocols will store the cost to reach the destination along the shortest path. Other routing protocols may store information about the number of hops of the best path, its lifetime or the number of sub paths. A routing table may store multipath paths towards a given destination and flag one of them as the best one. The routing table is a software data structure which is updated by (one or more) routing protocols. The routing table is usually not directly used when forwarding packets. Packet forwarding relies on a more compact data structure which is the forwarding table. On high-end routers, the forwarding table is implemented directly in hardware while lower performance routers will use a software implementation. A forwarding table contains a subset of the information found in the routing table. It only contains the paths that are used to forward packets and no attributes. A forwarding table will typically associate each destination to an outgoing interface or nexthop router.