Routing Principles

Networking Basics

Routing can be compared with the kind of routing we would do when we try to travel to another city by car. We need to figure out which way to take, we need to get a new route when something on our normal route is blocked, etc.

In computer networks routing is needed in lots of different situation. For example in a circuit switched network (like the phone network) a connection needs to be established at the beginning and it remains static till the end of the conversation. In a packed switched network (like the internet), each packet (chunk of information) gets routed seperately, so the decision which way to take needs to be performed way more often. This decision happens on special hardware, so called routers.

The routers build a topology map of the network where each router represents a node. Nodes in the network can be added or removed, therefore the routing needs to adjust dynamically to changes of the network topology. Routing algorithms calculate the ways we can take through a network on demand and save or update them to routing tables.

Common routing protocols are based on two algorithms:

• Global information, where all routers know the whole topology of the network and calculate the routing tables with a link state algorithm.

• Decentralized information, where the routers only know their directly connected neighbors and calculate their routing tables with a distance vector algorithm.

Link State Routing

Link state routing was invented by John McQuillan in 1978 and used in the early days of the ARPANET. Known protocols that implement link stare algorithms are OSPF or ISIS.

Every link between two nodes has costs, these can be configured as any metric at choice (eg. delay). Link state algorithms are based on global information, that means that every node knows all the other nodes (the whole network topology) and the link costs to them. Using Dijkstra's algorithm it then computes the least cost paths to all nodes other and store that information in the routing table.

To build the whole topology map each node first checks the links to its directly connected neighbors. Then it sends a so called link state advertisements through the network with all the information about its neighbors. From all the received advertisements each node can now compute the topology.

Dijkstra's Algorithm

To calculate the routing table from the computed topology map, link state protocols perform Dijkstra's shortest path first algorithm. In small graphs the shortest path (the one with the least costs) is easy to see, like in the graph below, but in more complex networks an algorithm is needed to compute it.

      3
   A-----B
   |     |
 2 |     | 4
   |     |
   C-----D
      1

Obviously the shortest path from A to D in this graph would be via C. Following the algorithm we would compute that as follows:

For node A:

• for all nodes, if node adjacent to A set known costs, else set infinity

 N'  D(B)  D(C)  D(D)
 ------------------------------
 A   3     2     infinity

• take the next node (which is not in N') and has the minimum costs (in our example C)
• check all neighbors of this node, update costs if they are less via C (or replace infinity)

 N'  D(B)  D(C)  D(D)
 ------------------------------
 A   3     2     infinity
 AC  3     -     3

• loop last 2 steps until all nodes in N'

Now we can compute the routing table (or next hop table) for node A:

 Destination  Next-Hop
 ------------------------------
 B           B
 C           C
 D           C

OSPF

OSPR (Open Shortest Path First) is an interior gateway protocol which uses the link state algorithm to compute the routing table. It is one example for an implementation of the link state algorithm. It doesn't send all link state advertisements over and over again, but sends out incremental updates after a link state change.

It checks the link state by sending Hello packets periodically. If one neighbor doesn't respond the network gets flooded with an update (to a multicast address). The updates must be acknowledged by the recipients to ensure identical maps at each node.

Distance Vector Routing

Distance Vector routing protocols use the Bellman-Ford algorithm to calculate the paths in the network. The first implementation was used in the ARPANET as early as 1969.

Each node keeps a routing table with an entry for each destination in the network. This entry consists of the distance to the destination and the first hop on the path to the destination. Nodes inform their neighbours of their routing tables, so that they can update their own entries.

Bellman-Ford Algorithm

The Bellman-Ford algorithm computes single-source shortest paths in a directed graph. Unlike Dijkstra's algorithm it is compatible with negative edge-weights.

The basic idea is to repeatedly check each edge of the graph to determine if there is a shorter path (than the one already found) to the edge's destination by using the edge. Of course this has to be done often enough, so that the shortest path is found.

The input of the Algorithm is a directed weighted graph G and a vertex of this graph as source. The algorithm computes the distances to all other vertices in three steps.

procedure BellmanFord(list vertices, list edges, vertex source)
   // This implementation takes in a graph, represented as lists of vertices
   // and edges, and modifies the vertices so that their distance and
   // predecessor attributes store the shortest paths.

   // Step 1: Initialize graph
   for each vertex v in vertices:
       if v is source then v.distance := 0
       else v.distance := infinity
       v.predecessor := null
   
   // Step 2: relax edges repeatedly
   for i from 1 to size(vertices):       
       for each edge uv in edges:
           u := uv.source
           v := uv.destination             // uv is the edge from u to v
           if v.distance > u.distance + uv.weight:
               v.distance := u.distance + uv.weight
               v.predecessor := u

   // Step 3: check for negative-weight cycles
   for each edge uv in edges:
       u := uv.source
       v := uv.destination
       if v.distance > u.distance + uv.weight:
           error "Graph contains a negative-weight cycle"

It can be proven that the algorithm always finds the shortest paths from the source to each node of the graph. The time needed is bound by O(n*m) where n is the number of vertices and m is the number of edges in the graph.

Routing Information Protocol

RIP is an implementation of a distance vector routing protocol that was proposed in 1988 (RFC 1058). Later revisions include RIP2 (1994) and RIPng(1997).

RIP uses a basic metric to measure the distance between nodes: The number of links to traverse (i.e. hops).

The routing table entries in RIP consist of

• Address: destination IP
• Gateway: first hop on the path to the destination
• Interface: hardware interface to use
• Metric: number of hops to the destination
• Timer: time of last update

Each node of the network has to relay it's full routing table to each of it's neighbours regularly. If a node recieves an update it will compare the contained metric plus one to it's own stored metric and update the routing table if needed. If a node wants to send a packet to a destination it looks up the gateway in the routing table. The node has no need of full information about the topology of the network as it only cares about the first hop, i.e. who to send the packet to. The recieving gateway then refers to it's own routing table to determine the next hop and so on.

Network Failures

If a link or node in the network goes down, no further updates are send. After three update cycles have completed, without receiving routing information from another node it is considered dead. The routing table is updated to the metric ∞ (implemented by RIP as 16). Consider the case of three nodes in a line

 A ----- B ----- C 

The routing entries for C in the tables of A and B are as follows:

 Node  Gateway to C  #hops to C  
 ------------------------------
 A         B            2
 B         C            1

If C goes down, B will update it's routing table accordingly.

 Node  Gateway to C  #hops to C  
 ------------------------------
 A         B            2
 B         ~           16

But at the same time A offers a route to C with the metric 2 that is clearly shorter than 16. B will therefore update it's entry to metric 3.

 Node  Gateway to C  #hops to C  
 ------------------------------
 A         B            2
 B         A            3

This will cause A to update the metric to 4 and so on, until both nodes reach the maximum of 16. This problem is called Counting to Infinity and it is the reason for choosing 16 as the representation of ∞ in RIP. While A and B are counting to 16, packets are routed in a loop.

To avoid this problem RIP implements Split Horizon. This means that nodes do not advertise routes to the nodes they have stored as gateways. Poisoned Reverse is an extension that causes nodes to advertise routes to the gateways with the metric ∞. This helps resolving loops in complex situations faster. But routing loops cannot be avoided altogether by RIP.

Border Gateway Protocol

BGP is the de facto standard for routing between autonomous systems in the Internet. It is often referred to as a path vector protocol as the routing table entries contain the whole path to the destination and not only the first hop as in "true" distance vector routing protocols. The advantage is loop detection on the one hand and the possibility to implement policies at the nodes (meaning a node will prefer paths using certain nodes over others).

Destination-Sequenced Distance-Vector Routing

DSDV is a proposition by C. Perkins and P. Bhagwat for using distance vector routing in mobile ad-hoc networks. The algorithm was presented in 1994, but it was never implemented.

Using distance vector routing in ad-hoc networks is problematic because of the rapid topology changes and the fact that mobile networks use a broadcast instead of a point-to-point medium, so the standard loop-prevention techniques cannot be used. The idea in DSDV is then to let each node number it's outgoing update packets to differentiate between new and stale routes. These sequence numbers get propagated through the route. Nodes can therefore discard updates with older numbers they receive.

Sources

• McQuillan, John M. et al. "The New Routing Algorithm for the ARPANET" (1980)
• Perkins, Charles E. and Bhagwat, Pravin. "Highly Dynamic Destination-Sequenced Distance-Vector Routing (DSDV) for Mobile Computers" (1994)
• Distance Vector Routing: RIPv1 (RFC1058), RIPv2 (RFC2453)
• Bellman-Ford algorithm at wikipedia.org