# 3.4 Routing¶

So far in this chapter we have assumed that the switches and routers have enough knowledge of the network topology so they can choose the right port onto which each packet should be output. In the case of virtual circuits, routing is an issue only for the connection request packet; all subsequent packets follow the same path as the request. In datagram networks, including IP networks, routing is an issue for every packet. In either case, a switch or router needs to be able to look at a destination address and then to determine which of the output ports is the best choice to get a packet to that address. As we saw in an earlier section, the switch makes this decision by consulting a forwarding table. The fundamental problem of routing is how switches and routers acquire the information in their forwarding tables.

Key Takeaway

We restate an important distinction, which is often neglected, between forwarding and routing. Forwarding consists of receiving a packet, looking up its destination address in a table, and sending the packet in a direction determined by that table. We saw several examples of forwarding in the preceding section. It is a simple and well-defined process performed locally at each node, and is often referred to as the network’s data plane. Routing is the process by which forwarding tables are built. It depends on complex distributed algorithms, and is often referred to as the network’s control plane. [Next]

While the terms forwarding table and routing table are sometimes used interchangeably, we will make a distinction between them here. The forwarding table is used when a packet is being forwarded and so must contain enough information to accomplish the forwarding function. This means that a row in the forwarding table contains the mapping from a network prefix to an outgoing interface and some MAC information, such as the Ethernet address of the next hop. The routing table, on the other hand, is the table that is built up by the routing algorithms as a precursor to building the forwarding table. It generally contains mappings from network prefixes to next hops. It may also contain information about how this information was learned, so that the router will be able to decide when it should discard some information.

Whether the routing table and forwarding table are actually separate data structures is something of an implementation choice, but there are numerous reasons to keep them separate. For example, the forwarding table needs to be structured to optimize the process of looking up an address when forwarding a packet, while the routing table needs to be optimized for the purpose of calculating changes in topology. In many cases, the forwarding table may even be implemented in specialized hardware, whereas this is rarely if ever done for the routing table.

Table 14 gives an example of a row from a routing table, which tells us that network prefix 18/8 is to be reached by a next hop router with the IP address 171.69.245.10

Table 14. Example row from a routing table.
Prefix/Length Next Hop
18/8 171.69.245.10

In contrast, Table 15 gives an example of a row from a forwarding table, which contains the information about exactly how to forward a packet to that next hop: Send it out interface number 0 with a MAC address of 8:0:2b:e4:b:1:2. Note that the last piece of information is provided by the Address Resolution Protocol.

Table 15. Example row from a forwarding table.
Prefix/Length Interface MAC Address
18/8 if0 8:0:2b:e4:b:1:2

Before getting into the details of routing, we need to remind ourselves of the key question we should be asking anytime we try to build a mechanism for the Internet: “Does this solution scale?” The answer for the algorithms and protocols described in this section is “not so much.” They are designed for networks of fairly modest size—up to a few hundred nodes, in practice. However, the solutions we describe do serve as a building block for a hierarchical routing infrastructure that is used in the Internet today. Specifically, the protocols described in this section are collectively known as intradomain routing protocols, or interior gateway protocols (IGPs). To understand these terms, we need to define a routing domain. A good working definition is an internetwork in which all the routers are under the same administrative control (e.g., a single university campus, or the network of a single Internet Service Provider). The relevance of this definition will become apparent in the next chapter when we look at interdomain routing protocols. For now, the important thing to keep in mind is that we are considering the problem of routing in the context of small to midsized networks, not for a network the size of the Internet.

## Network as a Graph¶

Routing is, in essence, a problem of graph theory. Figure 84 shows a graph representing a network. The nodes of the graph, labeled A through F, may be hosts, switches, routers, or networks. For our initial discussion, we will focus on the case where the nodes are routers. The edges of the graph correspond to the network links. Each edge has an associated cost, which gives some indication of the desirability of sending traffic over that link. A discussion of how edge costs are assigned is given in a later section.

Note that the example networks (graphs) used throughout this chapter have undirected edges that are assigned a single cost. This is actually a slight simplification. It is more accurate to make the edges directed, which typically means that there would be a pair of edges between each node—one flowing in each direction, and each with its own edge cost.

Figure 84. Network represented as a graph.

The basic problem of routing is to find the lowest-cost path between any two nodes, where the cost of a path equals the sum of the costs of all the edges that make up the path. For a simple network like the one in Figure 84, you could imagine just calculating all the shortest paths and loading them into some nonvolatile storage on each node. Such a static approach has several shortcomings:

• It does not deal with node or link failures.
• It does not consider the addition of new nodes or links.
• It implies that edge costs cannot change, even though we might reasonably wish to have link costs change over time (e.g., assigning high cost to a link that is heavily loaded).

For these reasons, routing is achieved in most practical networks by running routing protocols among the nodes. These protocols provide a distributed, dynamic way to solve the problem of finding the lowest-cost path in the presence of link and node failures and changing edge costs. Note the word distributed in the previous sentence; it is difficult to make centralized solutions scalable, so all the widely used routing protocols use distributed algorithms.

The distributed nature of routing algorithms is one of the main reasons why this has been such a rich field of research and development—there are a lot of challenges in making distributed algorithms work well. For example, distributed algorithms raise the possibility that two routers will at one instant have different ideas about the shortest path to some destination. In fact, each one may think that the other one is closer to the destination and decide to send packets to the other one. Clearly, such packets will be stuck in a loop until the discrepancy between the two routers is resolved, and it would be good to resolve it as soon as possible. This is just one example of the type of problem routing protocols must address.

To begin our analysis, we assume that the edge costs in the network are known. We will examine the two main classes of routing protocols: distance vector and link state. In a later section, we return to the problem of calculating edge costs in a meaningful way.

## Distance-Vector (RIP)¶

The idea behind the distance-vector algorithm is suggested by its name. (The other common name for this class of algorithm is Bellman-Ford, after its inventors.) Each node constructs a one-dimensional array (a vector) containing the “distances” (costs) to all other nodes and distributes that vector to its immediate neighbors. The starting assumption for distance-vector routing is that each node knows the cost of the link to each of its directly connected neighbors. These costs may be provided when the router is configured by a network manager. A link that is down is assigned an infinite cost.

Figure 85. Distance-vector routing: an example network.

Table 16. Initial Distances Stored at Each Node (Global View).
A B C D E F G
A 0 1 1 1 1
B 1 0 1
C 1 1 0 1
D 1 0 1
E 1 0
F 1 0 1
G 1 1 0

To see how a distance-vector routing algorithm works, it is easiest to consider an example like the one depicted in Figure 85. In this example, the cost of each link is set to 1, so that a least-cost path is simply the one with the fewest hops. (Since all edges have the same cost, we do not show the costs in the graph.) We can represent each node’s knowledge about the distances to all other nodes as a table like Table 16. Note that each node knows only the information in one row of the table (the one that bears its name in the left column). The global view that is presented here is not available at any single point in the network.

We may consider each row in Table 16 as a list of distances from one node to all other nodes, representing the current beliefs of that node. Initially, each node sets a cost of 1 to its directly connected neighbors and ∞ to all other nodes. Thus, A initially believes that it can reach B in one hop and that D is unreachable. The routing table stored at A reflects this set of beliefs and includes the name of the next hop that A would use to reach any reachable node. Initially, then, A’s routing table would look like Table 17.

Table 17. Initial Routing Table at Node A.
Destination Cost NextHop
B 1 B
C 1 C
D
E 1 E
F 1 F
G

The next step in distance-vector routing is that every node sends a message to its directly connected neighbors containing its personal list of distances. For example, node F tells node A that it can reach node G at a cost of 1; A also knows it can reach F at a cost of 1, so it adds these costs to get the cost of reaching G by means of F. This total cost of 2 is less than the current cost of infinity, so A records that it can reach G at a cost of 2 by going through F. Similarly, A learns from C that D can be reached from C at a cost of 1; it adds this to the cost of reaching C (1) and decides that D can be reached via C at a cost of 2, which is better than the old cost of infinity. At the same time, A learns from C that B can be reached from C at a cost of 1, so it concludes that the cost of reaching B via C is 2. Since this is worse than the current cost of reaching B (1), this new information is ignored. At this point, A can update its routing table with costs and next hops for all nodes in the network. The result is shown in Table 18.

Table 18. Final Routing Table at Node A.
Destination Cost NextHop
B 1 B
C 1 C
D 2 C
E 1 E
F 1 F
G 2 F

In the absence of any topology changes, it takes only a few exchanges of information between neighbors before each node has a complete routing table. The process of getting consistent routing information to all the nodes is called convergence. Table 19 shows the final set of costs from each node to all other nodes when routing has converged. We must stress that there is no one node in the network that has all the information in this table—each node only knows about the contents of its own routing table. The beauty of a distributed algorithm like this is that it enables all nodes to achieve a consistent view of the network in the absence of any centralized authority.

Table 19. Final Distances Stored at Each Node (Global View).
A B C D E F G
A 0 1 1 2 1 1 2
B 1 0 1 2 2 2 3
C 1 1 0 1 2 2 2
D 2 2 1 0 3 2 1
E 1 2 2 3 0 2 3
F 1 2 2 2 2 0 1
G 2 3 2 1 3 1 0

There are a few details to fill in before our discussion of distance-vector routing is complete. First we note that there are two different circumstances under which a given node decides to send a routing update to its neighbors. One of these circumstances is the periodic update. In this case, each node automatically sends an update message every so often, even if nothing has changed. This serves to let the other nodes know that this node is still running. It also makes sure that they keep getting information that they may need if their current routes become unviable. The frequency of these periodic updates varies from protocol to protocol, but it is typically on the order of several seconds to several minutes. The second mechanism, sometimes called a triggered update, happens whenever a node notices a link failure or receives an update from one of its neighbors that causes it to change one of the routes in its routing table. Whenever a node’s routing table changes, it sends an update to its neighbors, which may lead to a change in their tables, causing them to send an update to their neighbors.

Now consider what happens when a link or node fails. The nodes that notice first send new lists of distances to their neighbors, and normally the system settles down fairly quickly to a new state. As to the question of how a node detects a failure, there are a couple of different answers. In one approach, a node continually tests the link to another node by sending a control packet and seeing if it receives an acknowledgment. In another approach, a node determines that the link (or the node at the other end of the link) is down if it does not receive the expected periodic routing update for the last few update cycles.

To understand what happens when a node detects a link failure, consider what happens when F detects that its link to G has failed. First, F sets its new distance to G to infinity and passes that information along to A. Since A knows that its 2-hop path to G is through F, A would also set its distance to G to infinity. However, with the next update from C, A would learn that C has a 2-hop path to G. Thus, A would know that it could reach G in 3 hops through C, which is less than infinity, and so A would update its table accordingly. When it advertises this to F, node F would learn that it can reach G at a cost of 4 through A, which is less than infinity, and the system would again become stable.

Unfortunately, slightly different circumstances can prevent the network from stabilizing. Suppose, for example, that the link from A to E goes down. In the next round of updates, A advertises a distance of infinity to E, but B and C advertise a distance of 2 to E. Depending on the exact timing of events, the following might happen: Node B, upon hearing that E can be reached in 2 hops from C, concludes that it can reach E in 3 hops and advertises this to A; node A concludes that it can reach E in 4 hops and advertises this to C; node C concludes that it can reach E in 5 hops; and so on. This cycle stops only when the distances reach some number that is large enough to be considered infinite. In the meantime, none of the nodes actually knows that E is unreachable, and the routing tables for the network do not stabilize. This situation is known as the count to infinity problem.

There are several partial solutions to this problem. The first one is to use some relatively small number as an approximation of infinity. For example, we might decide that the maximum number of hops to get across a certain network is never going to be more than 16, and so we could pick 16 as the value that represents infinity. This at least bounds the amount of time that it takes to count to infinity. Of course, it could also present a problem if our network grew to a point where some nodes were separated by more than 16 hops.

One technique to improve the time to stabilize routing is called split horizon. The idea is that when a node sends a routing update to its neighbors, it does not send those routes it learned from each neighbor back to that neighbor. For example, if B has the route (E, 2, A) in its table, then it knows it must have learned this route from A, and so whenever B sends a routing update to A, it does not include the route (E, 2) in that update. In a stronger variation of split horizon, called split horizon with poison reverse, B actually sends that route back to A, but it puts negative information in the route to ensure that A will not eventually use B to get to E. For example, B sends the route (E, ∞) to A. The problem with both of these techniques is that they only work for routing loops that involve two nodes. For larger routing loops, more drastic measures are called for. Continuing the above example, if B and C had waited for a while after hearing of the link failure from A before advertising routes to E, they would have found that neither of them really had a route to E. Unfortunately, this approach delays the convergence of the protocol; speed of convergence is one of the key advantages of its competitor, link-state routing, the subject of a later section.

### Implementation¶

The code that implements this algorithm is very straightforward; we give only some of the basics here. Structure Route defines each entry in the routing table, and constant MAX_TTL specifies how long an entry is kept in the table before it is discarded.

#define MAX_ROUTES      128     /* maximum size of routing table */
#define MAX_TTL         120     /* time (in seconds) until route expires */

typedef struct {
NodeAddr  Destination;    /* address of destination */
NodeAddr  NextHop;        /* address of next hop */
int        Cost;          /* distance metric */
u_short   TTL;            /* time to live */
} Route;

int      numRoutes = 0;
Route    routingTable[MAX_ROUTES];


The routine that updates the local node’s routing table based on a new route is given by mergeRoute. Although not shown, a timer function periodically scans the list of routes in the node’s routing table, decrements the TTL (time to live) field of each route, and discards any routes that have a time to live of 0. Notice, however, that the TTL field is reset to MAX_TTL any time the route is reconfirmed by an update message from a neighboring node.

void
mergeRoute (Route *new)
{
int i;

for (i = 0; i < numRoutes; ++i)
{
if (new->Destination == routingTable[i].Destination)
{
if (new->Cost + 1 < routingTable[i].Cost)
{
/* found a better route: */
break;
} else if (new->NextHop == routingTable[i].NextHop) {
/* metric for current next-hop may have changed: */
break;
} else {
/* route is uninteresting---just ignore it */
return;
}
}
}
if (i == numRoutes)
{
/* this is a completely new route; is there room for it? */
if (numRoutes < MAXROUTES)
{
++numRoutes;
} else {
/* cant fit this route in table so give up */
return;
}
}
routingTable[i] = *new;
/* reset TTL */
routingTable[i].TTL = MAX_TTL;
/* account for hop to get to next node */
++routingTable[i].Cost;
}


Finally, the procedure updateRoutingTable is the main routine that calls mergeRoute to incorporate all the routes contained in a routing update that is received from a neighboring node.

void
updateRoutingTable (Route *newRoute, int numNewRoutes)
{
int i;

for (i=0; i < numNewRoutes; ++i)
{
mergeRoute(&newRoute[i]);
}
}


### Routing Information Protocol (RIP)¶

One of the more widely used routing protocols in IP networks is the Routing Information Protocol (RIP). Its widespread use in the early days of IP was due in no small part to the fact that it was distributed along with the popular Berkeley Software Distribution (BSD) version of Unix, from which many commercial versions of Unix were derived. It is also extremely simple. RIP is the canonical example of a routing protocol built on the distance-vector algorithm just described.

Routing protocols in internetworks differ very slightly from the idealized graph model described above. In an internetwork, the goal of the routers is to learn how to forward packets to various networks. Thus, rather than advertising the cost of reaching other routers, the routers advertise the cost of reaching networks. For example, in Figure 86, router C would advertise to router A the fact that it can reach networks 2 and 3 (to which it is directly connected) at a cost of 0, networks 5 and 6 at cost 1, and network 4 at cost 2.

Figure 86. Example network running RIP.

Figure 87. RIPv2 packet format.

We can see evidence of this in the RIP (version 2) packet format in Figure 87. The majority of the packet is taken up with (address, mask, distance) triples. However, the principles of the routing algorithm are just the same. For example, if router A learns from router B that network X can be reached at a lower cost via B than via the existing next hop in the routing table, A updates the cost and next hop information for the network number accordingly.

RIP is in fact a fairly straightforward implementation of distance-vector routing. Routers running RIP send their advertisements every 30 seconds; a router also sends an update message whenever an update from another router causes it to change its routing table. One point of interest is that it supports multiple address families, not just IP—that is the reason for the Family part of the advertisements. RIP version 2 (RIPv2) also introduced the subnet masks described in an earlier section, whereas RIP version 1 worked with the old classful addresses of IP.

As we will see below, it is possible to use a range of different metrics or costs for the links in a routing protocol. RIP takes the simplest approach, with all link costs being equal to 1, just as in our example above. Thus, it always tries to find the minimum hop route. Valid distances are 1 through 15, with 16 representing infinity. This also limits RIP to running on fairly small networks—those with no paths longer than 15 hops.

## Metrics¶

The ARPANET was the testing ground for a number of different approaches to link-cost calculation. (It was also the place where the superior stability of link-state over distance-vector routing was demonstrated; the original mechanism used distance vector while the later version used link state.) The following discussion traces the evolution of the ARPANET routing metric and, in so doing, explores the subtle aspects of the problem.

The original ARPANET routing metric measured the number of packets that were queued waiting to be transmitted on each link, meaning that a link with 10 packets queued waiting to be transmitted was assigned a larger cost weight than a link with 5 packets queued for transmission. Using queue length as a routing metric did not work well, however, since queue length is an artificial measure of load—it moves packets toward the shortest queue rather than toward the destination, a situation all too familiar to those of us who hop from line to line at the grocery store. Stated more precisely, the original ARPANET routing mechanism suffered from the fact that it did not take either the bandwidth or the latency of the link into consideration.

A second version of the ARPANET routing algorithm took both link bandwidth and latency into consideration and used delay, rather than just queue length, as a measure of load. This was done as follows. First, each incoming packet was timestamped with its time of arrival at the router (ArrivalTime); its departure time from the router (DepartTime) was also recorded. Second, when the link-level ACK was received from the other side, the node computed the delay for that packet as

Delay = (DepartTime - ArrivalTime) + TransmissionTime + Latency


where TransmissionTime and Latency were statically defined for the link and captured the link’s bandwidth and latency, respectively. Notice that in this case, DepartTime - ArrivalTime represents the amount of time the packet was delayed (queued) in the node due to load. If the ACK did not arrive, but instead the packet timed out, then DepartTime was reset to the time the packet was retransmitted. In this case, DepartTime - ArrivalTime` captures the reliability of the link—the more frequent the retransmission of packets, the less reliable the link, and the more we want to avoid it. Finally, the weight assigned to each link was derived from the average delay experienced by the packets recently sent over that link.

Although an improvement over the original mechanism, this approach also had a lot of problems. Under light load, it worked reasonably well, since the two static factors of delay dominated the cost. Under heavy load, however, a congested link would start to advertise a very high cost. This caused all the traffic to move off that link, leaving it idle, so then it would advertise a low cost, thereby attracting back all the traffic, and so on. The effect of this instability was that, under heavy load, many links would in fact spend a great deal of time being idle, which is the last thing you want under heavy load.

A third approach addressed these problems. The major changes were to compress the dynamic range of the metric considerably, to account for the link type, and to smooth the variation of the metric with time.

The smoothing was achieved by several mechanisms. First, the delay measurement was transformed to a link utilization, and this number was averaged with the last reported utilization to suppress sudden changes. Second, there was a hard limit on how much the metric could change from one measurement cycle to the next. By smoothing the changes in the cost, the likelihood that all nodes would abandon a route at once is greatly reduced.

The compression of the dynamic range was achieved by feeding the measured utilization, the link type, and the link speed into a function that is shown graphically in Figure 92. below. Observe the following:

Figure 92. Revised ARPANET routing metric versus link utilization.

• A highly loaded link never shows a cost of more than three times its cost when idle.
• The most expensive link is only seven times the cost of the least expensive.
• A high-speed satellite link is more attractive than a low-speed terrestrial link.
• Cost is a function of link utilization only at moderate to high loads.

All of these factors mean that a link is much less likely to be universally abandoned, since a threefold increase in cost is likely to make the link unattractive for some paths while letting it remain the best choice for others. The slopes, offsets, and breakpoints for the curves in Figure 92 were arrived at by a great deal of trial and error, and they were carefully tuned to provide good performance.

Despite all these improvements, it turns out that in the majority of real-world network deployments, metrics change rarely if at all and only under the control of a network administrator, not automatically as described above. The reason for this is partly that conventional wisdom now holds that dynamically changing metrics are too unstable, even though this probably need not be true. Perhaps more significantly, many networks today lack the great disparity of link speeds and latencies that prevailed in the ARPANET. Thus, static metrics are the norm. One common approach to setting metrics is to use a constant multiplied by (1/link_bandwidth).

Key Takeaway

Why do we still tell the story about a decades old algorithm that’s no longer in use? Because it perfectly illustrates two valuable lessons. The first is that computer systems are often designed iteratively based on experience. We seldom get it right the first time, so it’s important to deploy a simple solution sooner rather than later, and expect to improve it over time. Staying stuck in the design phase indefinitely is usually not a good plan. The second is the well-know KISS principle: Keep it Simple, Stupid. When building a complex system, less is often more. Opportunities to invent sophisticated optimizations are plentiful, and it’s a tempting opportunity to pursue. While such optimizations sometimes have short-term value, it is shocking how often a simple approach proves best over time. This is because when a system has many moving parts, as the Internet most certainly does, keeping each part as simple as possible is usually the best approach. [Next]