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.

In a tree-shaped network, it is relatively simple for each node to automatically compute its forwarding table by inspecting the packets that it receives. For this, each node uses the source and destination addresses present inside each packet. The source address allows to learn the location of the different sources inside the network. Each source has a unique address. When a node receives a packet over a given interface, it learns that the source (address) of this packet is reachable via this interface. The node maintains a data structure that maps each known source address to an incoming interface. This data structure is often called the port-address table since it indicates the interface (or port) to reach a given address. Learning the location of the sources is not sufficient, nodes also need to forward packets towards their destination. When a node receives a packet whose destination address is already present inside its port-address table, it simply forwards the packet on the interface listed in the port-address table. In this case, the packet will follow the port-address table entries in the downstream nodes and will reach the destination. If the destination address is not included in the port-address table, the node simply forwards the packet on all its interfaces, except the interface from which the packet was received. Forwarding a packet over all interfaces is usually called broadcasting in the terminology of computer networks. Sending the packet over all interfaces except one is a costly operation since the packet will be sent over links that do not reach the destination. Given the tree-shape of the network, the packet will explore all downstream branches of the tree and will thus finally reach its destination. In practice, the broadcasting operation does not occur too often and its cost is limited.

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.

Assume that the network has started and all port-station and forwarding tables are empty. Host A sends a packet towards B. Upon reception of this packet, R1 updates its port-address table. Since B is not present in the port-address table, the packet is broadcasted. Both R2 and R3 receive a copy of the packet sent by A. They both update their port-address table. Unfortunately, they also both broadcast the received packet. B receives a first copy of the packet, but R3 and R2 receive it again. R3 will then broadcast this copy of the packet to B and R1 while R2 will broadcast its copy to R1. Although B has already received two copies of the packet, it is still inside the network and will continue to loop. Due to the presence of the cycle, a single packet towards an unknown destination generates copies of this packet that loop and will saturate the network bandwidth. Network operators who are using port-address tables to automatically compute the forwarding tables also use distributed algorithms to ensure that the network topology is always a tree.

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.

Flat or hierarchical addresses¶

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.

The first organisation, which is the one that we have implicitly assumed until now, is the flat addressing scheme. Under this scheme, each host and network node has a unique address. The unicity of the addresses is important for the operation of the network. If two hosts have the same address, it can become difficult for the network to forward packets towards this destination. Flat addresses are typically used in situations where network nodes and hosts need to be able to communicate immediately with unique addresses. These flat addresses are often embedded inside the hardware of network interface cards. The network card manufacturer creates one unique address for each interface and this address is stored in the read-only memory of the interface. An advantage of this addressing scheme is that it easily supports ad-hoc and mobile networks. When a host moves, it can attach to another network and remain confident that its address is unique and enables it to communicate inside the new network.

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.

Dealing with heterogeneous datalink layers¶

Sometimes, the network layer needs to deal with heterogenous datalink layers. For example, two hosts connected to different datalink layers exchange packets via routers that are using other types of datalink layers. Thanks to the network layer, this exchange of packets is possible provided that each packet can be placed inside a datalink layer frame before being transmitted. If all datalink layers support the same frame size, this is simple. When a node receives a frame, it decapsulate the packet that it contains, checks the header and forwards it, encapsulated inside another frame, to the outgoing interface. Unfortunately, the encapsulation operation is not always possible. Each datalink layer is characterized by the maximum frame size that it supports. Datalink layers typically support frames containing up to a few hundreds or a few thousands of bytes. The maximum frame size that a given datalink layer supports depends on its underlying technology and unfortunately, most datalink layers support a different maximum frame size. This implies that when a host sends a large packet inside a frame to its nexthop router, there is a risk that this packet will have to traverse a link that is not capable of forwarding the packet inside a single frame. In principle, there are three possibilities to solve this problem. We will discuss them by considering a simpler scenario with two hosts connected to a router as shown in the figure below.

Considering in the network above that host A wants to send a 900 bytes packet (870 bytes of payload and 30 bytes of header) to host B via router R1. Host A encapsulates this packet inside a single frame. The frame is received by router R1 which extracts the packet. Router R1 has three possible options to process this packet.

1. The packet is too large and router R1 cannot forward it to router R2. It rejects the packet and sends a control packet back to the source (host A) to indicate that it cannot forward packets longer than 500 bytes (minus the packet header). The source will have to react to this control packet by retransmitting the information in smaller packets.
2. The network layer is able to fragment a packet. In our example, the router could fragment the packet in two parts. The first part contains the beginning of the payload and the second the end. There are two possible ways to achieve this fragmentation.

1. Router R1 fragments the packet in two fragments before transmitting them to router R2. Router R2 reassembles the two packet fragments in a larger packet before transmitting them on the link towards host B.
2. Each of the packet fragments is a valid packet that contains a header with the source (host A) and destination (host B) addresses. When router R2 receives a packet fragment, it treats this packet as a regular packet and forwards it to its final destination (host B). Host B reassembles the received fragments.

These three solutions have advantages and drawbacks. With the first solution, routers remain simple and do not need to perform any fragmentation operation. This is important when routers are implemented mainly in hardware. However, hosts are more complex since they need to store the packets that they produce if they need to pass through a link that does not support large packets. This increases the buffering required on the end hosts. Furthermore, a single large packet may potentially need to be retransmitted several times. Consider for example a network similar to the one shown above but with four routers. Assume that the link R1->R2 supports 1000 bytes packets, link R2->R3 800 bytes packets and link R3->R4 600 bytes packets. A host attached to R1 that sends large packet will have to first try 1000 bytes, then 800 bytes and finally 600 bytes. Fortunately, this scenario does not occur very often in practice and this is the reason why this solution is used in real networks.

Fragmenting packets on a per-link basis, as presented for the second solution, can minimize the transmission overhead since a packet is only fragmented on the links where fragmentation is required. Large packets can continue to be used downstream of a link that only accepts small packets. However, this reduction of the overhead comes with two drawbacks. First, fragmenting packets, potentially on all links, increases the processing time and the buffer requirements on the routers. Second, this solution leads to a longer end-to-end delay since the downstream router has to reassemble all the packet fragments before forwarding the packet.

The last solution is a compromise between the two others. Routers need to perform fragmentation but they do not need to reassemble packet fragments. Only the hosts need to have buffers to reassemble the received fragments. This solution has a lower end-to-end delay and requires fewer processing time and memory on the routers.

The first solution to the fragmentation problem presented above suggests the utilization of control packets to inform the source about the reception of a too long packet. This is only one of the functions that are performed by the control protocol in the network layer. Other functions include :

• sending a control packet back to the source if a packet is received by a router that does not have a valid entry in its forwarding table
• sending a control packet back to the source if a router detects that a packet is looping inside the network
• verifying that packets can reach a given destination

We will discuss these functions in more details when we will describe the protocols that are used in the network layer of the TCP/IP protocol suite.

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
    v.add(Pair(d,R[d].cost))
 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
# l : link over which vector is received
def received(V,l):
   # received vector from link l
   for d in V[]
     if not (d in R[]) :
        # new route
        R[d].cost=V[d].cost+l.cost
        R[d].link=l
        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].link=l
             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[]:
     if (R[d].link != l) :
        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[]:
     if (R[d].link != l) :
        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.

Link state routing¶

Link state routing is the second family of routing protocols. While distance vector routers use a distributed algorithm to compute their routing tables, link-state routers exchange messages to allow each router to learn the entire network topology. Based on this learned topology, each router is then able to compute its routing table by using a shortest path computation [Dijkstra1959].

For link-state routing, a network is modelled as a directed weighted graph. Each router is a node, and the links between routers are the edges in the graph. A positive weight is associated to each directed edge and routers use the shortest path to reach each destination. In practice, different types of weight can be associated to each directed edge :

• unit weight. If all links have a unit weight, shortest path routing prefers the paths with the least number of intermediate routers.
• weight proportional to the propagation delay on the link. If all link weights are configured this way, shortest path routing uses the paths with the smallest propagation delay.
• \(weight=\frac{C}{bandwidth}\) where C is a constant larger than the highest link bandwidth in the network. If all link weights are configured this way, shortest path routing prefers higher bandwidth paths over lower bandwidth paths

Usually, the same weight is associated to the two directed edges that correspond to a physical link (i.e. \(R1 \rightarrow R2\) and \(R2 \rightarrow R1\)). However, nothing in the link state protocols requires this. For example, if the weight is set in function of the link bandwidth, then an asymmetric ADSL link could have a different weight for the upstream and downstream directions. Other variants are possible. Some networks use optimisation algorithms to find the best set of weights to minimize congestion inside the network for a given traffic demand [FRT2002].

When a link-state router boots, it first needs to discover to which routers it is directly connected. For this, each router sends a HELLO message every N seconds on all of its interfaces. This message contains the router’s address. Each router has a unique address. As its neighbouring routers also send HELLO messages, the router automatically discovers to which neighbours it is connected. These HELLO messages are only sent to neighbours who are directly connected to a router, and a router never forwards the HELLO messages that they receive. HELLO messages are also used to detect link and router failures. A link is considered to have failed if no HELLO message has been received from the neighbouring router for a period of \(k \times N\) seconds.

The exchange of HELLO messages

Once a router has discovered its neighbours, it must reliably distribute its local links to all routers in the network to allow them to compute their local view of the network topology. For this, each router builds a link-state packet (LSP) containing the following information :

• LSP.Router : identification (address) of the sender of the LSP
• LSP.age : age or remaining lifetime of the LSP
• LSP.seq : sequence number of the LSP
• LSP.Links[] : links advertised in the LSP. Each directed link is represented with the following information : - LSP.Links[i].Id : identification of the neighbour - LSP.Links[i].cost : cost of the link

These LSPs must be reliably distributed inside the network without using the router’s routing table since these tables can only be computed once the LSPs have been received. The Flooding algorithm is used to efficiently distribute the LSPs of all routers. Each router that implements flooding maintains a link state database (LSDB) containing the most recent LSP sent by each router. When a router receives an LSP, it first verifies whether this LSP is already stored inside its LSDB. If so, the router has already distributed the LSP earlier and it does not need to forward it. Otherwise, the router forwards the LSP on all links except the link over which the LSP was received. Flooding can be implemented by using the following pseudo-code.

# links is the set of all links on the router
# Router R's LSP arrival on link l
if newer(LSP, LSDB(LSP.Router)) :
  LSDB.add(LSP)
  for i in links :
    if i!=l :
       send(LSP,i)
else:
 # LSP has already been flooded

In this pseudo-code, LSDB(r) returns the most recent LSP originating from router r that is stored in the LSDB. newer(lsp1,lsp2) returns true if lsp1 is more recent than lsp2. See the note below for a discussion on how newer can be implemented.

def newer( lsp1, lsp2 ):
  return ( ( ( lsp1.seq > lsp2.seq) and ( (lsp1.seq-lsp2.seq)<=32) ) or
          ( ( lsp1.seq < lsp2.seq) and ( (lsp2.seq-lsp1.seq)> 32) )    )

Flooding is illustrated in the figure below. By exchanging HELLO messages, each router learns its direct neighbours. For example, router E learns that it is directly connected to routers D, B and C. Its first LSP has sequence number 0 and contains the directed links E->D, E->B and E->C. Router E sends its LSP on all its links and routers D, B and C insert the LSP in their LSDB and forward it over their other links.

Flooding : example

Flooding allows LSPs to be distributed to all routers inside the network without relying on routing tables. In the example above, the LSP sent by router E is likely to be sent twice on some links in the network. For example, routers B and C receive E‘s LSP at almost the same time and forward it over the B-C link. To avoid sending the same LSP twice on each link, a possible solution is to slightly change the pseudo-code above so that a router waits for some random time before forwarding a LSP on each link. The drawback of this solution is that the delay to flood an LSP to all routers in the network increases. In practice, routers immediately flood the LSPs that contain new information (e.g. addition or removal of a link) and delay the flooding of refresh LSPs (i.e. LSPs that contain exactly the same information as the previous LSP originating from this router) [FFEB2005].

To ensure that all routers receive all LSPs, even when there are transmissions errors, link state routing protocols use reliable flooding. With reliable flooding, routers use acknowledgements and if necessary retransmissions to ensure that all link state packets are successfully transferred to all neighbouring routers. Thanks to reliable flooding, all routers store in their LSDB the most recent LSP sent by each router in the network. By combining the received LSPs with its own LSP, each router can compute the entire network topology.

Link state databases received by all routers

When a link fails, the two routers attached to the link detect the failure by the lack of HELLO messages received in the last \(k \times N\) seconds. Once a router has detected a local link failure, it generates and floods a new LSP that no longer contains the failed link and the new LSP replaces the previous LSP in the network. As the two routers attached to a link do not detect this failure exactly at the same time, some links may be announced in only one direction. This is illustrated in the figure below. Router E has detected the failures of link E-B and flooded a new LSP, but router B has not yet detected the failure.

The two-way connectivity check

When a link is reported in the LSP of only one of the attached routers, routers consider the link as having failed and they remove it from the directed graph that they compute from their LSDB. This is called the two-way connectivity check. This check allows link failures to be flooded quickly as a single LSP is sufficient to announce such bad news. However, when a link comes up, it can only be used once the two attached routers have sent their LSPs. The two-way connectivity check also allows for dealing with router failures. When a router fails, all its links fail by definition. Unfortunately, it does not, of course, send a new LSP to announce its failure. The two-way connectivity check ensures that the failed router is removed from the graph.

When a router has failed, its LSP must be removed from the LSDB of all routers [2]. This can be done by using the age field that is included in each LSP. The age field is used to bound the maximum lifetime of a link state packet in the network. When a router generates a LSP, it sets its lifetime (usually measured in seconds) in the age field. All routers regularly decrement the age of the LSPs in their LSDB and a LSP is discarded once its age reaches 0. Thanks to the age field, the LSP from a failed router does not remain in the LSDBs forever.

To compute its forwarding table, each router computes the spanning tree rooted at itself by using Dijkstra’s shortest path algorithm [Dijkstra1959]. The forwarding table can be derived automatically from the spanning as shown in the figure below.

Computation of the forwarding table

Footnotes