At the heart of any routing protocol is the algorithm (the routing algorithm) that determines the path for a packet. The purpose of a routing algorithm is simple: given a set of routers, with links connecting the routers, a routing algorithm finds a "good" path from source to destination. Typically, a "good" path is one that has "least cost." We'll see, however, that in practice, real-world concerns such as policy issues (for example, a rule such as "router X, belonging to organization Y should not forward any packets originating from the network owned by organization Z") also come into play to complicate the conceptually simple and elegant algorithms whose theory underlies the practice of routing in today's networks. 

The graph abstraction used to formulate routing algorithms is shown in Figure 4.4. To view some graphs representing real network maps, see [Dodge 1999]; for a discussion of how well different graph-based models model the Internet, see [Zegura 1997]. Here, nodes in the graph represent routers--the points at which packet routing decisions are made--and the lines ("edges" in graph theory terminology) connecting these nodes represent the physical links between these routers. A link also has a value representing the "cost" of sending a packet across the link. The cost may reflect the level of congestion on that link (for example, the current average delay for a packet across that link) or the physical distance traversed by that link (for example, a transoceanic link might have a higher cost than a short-haul terrestrial link). For our current purposes, we'll simply take the link costs as a given and won't worry about how they are determined. 

Given the graph abstraction, the problem of finding the least-cost path from a source to a destination requires identifying a series of links such that: 

• the first link in the path is connected to the source 
• the last link in the path is connected to the destination 
• for all i, the i and i-1st link in the path are connected to the same node 
• for the least-cost path, the sum of the cost of the links on the path is the minimum over all possible paths between the source and destination. Note that if all link costs are the same, the least-cost path is also the shortest path (that is, the path crossing the smallest number of links between the source and the destination).

As a simple exercise, try finding the least-cost path from nodes A to F, and reflect for a moment on how you calculated that path. If you are like most people, you found the path from A to F by examining Figure 4.4, tracing a few routes from A to F, and somehow convincing yourself that the path you had chosen had the least cost among all possible paths. (Did you check all of the 12 possible paths between A and F? Probably not!) Such a calculation is an example of a centralized routing algorithm--the routing algorithm was run in one location, your brain, with complete information about the network. Broadly, one way in which we can classify routing algorithms is according to whether they are global or decentralized: 

• A global routing algorithm computes the least-cost path between a source and destination using complete, global knowledge about the network. That is, the algorithm takes the connectivity between all nodes and all link costs as inputs. This then requires that the algorithm somehow obtain this information before actually performing the calculation. The calculation itself can be run at one site (a centralized global routing algorithm) or replicated at multiple sites. The key distinguishing feature here, however, is that a global algorithm has complete information about connectivity and link costs. In practice, algorithms with global state information are often referred to as link state algorithms, since the algorithm must be aware of the cost of each link in the network. We will study a global link state algorithm in Section 4.2.1. 
• In a decentralized routing algorithm, the calculation of the least-cost path is carried out in an iterative, distributed manner. No node has complete information about the costs of all network links. Instead, each node begins with only the knowledge of the costs of its own directly attached links. Then, through an iterative process of calculation and exchange of information with its neighboring nodes (that is, nodes that are at the "other end" of links to which it itself is attached), a node gradually calculates the least-cost path to a destination or set of destinations. We will study a decentralized routing algorithm known as a distance vector algorithm in Section 4.2.2. It is called a distance vector algorithm because a node never actually knows a complete path from source to destination. Instead, it only knows the neighbor to which it should forward a packet in order to reach a given destination along the least-cost path, and the cost of that path from itself to the destination. 

Only two types of routing algorithms are typically used in the Internet: a dynamic global link state algorithm, and a dynamic decentralized distance vector algorithm. We cover these algorithms in Section 4.2.1 and 4.2.2, respectively. Other routing algorithms are surveyed briefly in Section 4.2.3. 

4.2.1: A Link State Routing Algorithm

The link state algorithm we present below is known as Dijkstra's algorithm, named after its inventor. A closely related algorithm is Prim's algorithm; see [Corman 1990] for a general discussion of graph algorithms. Dijkstra's algorithm computes the least-cost path from one node (the source, which we will refer to as A) to all other nodes in the network. Dijkstra's algorithm is iterative and has the property that after the kth iteration of the algorithm, the least-cost paths are known to k destination nodes, and among the least-cost paths to all destination nodes, these k paths will have the k smallest costs. Let us define the following notation: 

• c(i,j): link cost from node i to node j. If nodes i and j are not directly connected, then c(i,j) = . We will assume for simplicity that c(i,j) equals c(j,i). 
• D(v): cost of the path from the source node to destination v that has currently (as of this iteration of the algorithm) the least cost 
• p(v): previous node (neighbor of v) along the current least-cost path from the source to v 
• N: set of nodes whose least-cost path from the source is definitively known

Link State (LS) Algorithm:

1 Initialization:

2  N = {A}

3  for all nodes v

4   if v adjacent to A

5    then D(v) = c(A,v)

6    else D(v) = 

7

8 Loop

9  find w not in N such that D(w) is a minimum

10  add w to N

11  update D(v) for all v adjacent to w and not in N:

12   D(v) = min( D(v), D(w) + c(w,v) )

13  /* new cost to v is either old cost to v or known

14   shortest path cost to w plus cost from w to v */

15 until all nodes in N

Table 4.2: Running the link state algorithm on the network in Figure 4.4

step	N	D(B),p(B)	D(C),p(C)	D(D),p(D)	D(E),p(E)	D(F),p(F)
0	A	2,A	5,A	1,A
1	AD	2,A	4,D		2,D
2	ADE	2,A	3,E			4,E
3	ADEB		3,E			4,E
4	ADEBC					4,E
5	ADEBCF

Let's consider the few first steps in detail:

• In the initialization step, the currently known least-cost path from A to its directly attached neighbors, B, C, and D are initialized to 2, 5, and 1 respectively. Note in particular that the cost to C is set to 5 (even though we will soon see that a lesser-cost path does indeed exist) since this is the cost of the direct (one hop) link from A to C. The costs to E and F are set to infinity because they are not directly connected to A. 
• In the first iteration, we look among those nodes not yet added to the set N and find that node with the least cost as of the end of the previous iteration. That node is D, with a cost of 1, and thus D is added to the set N. Line 12 of the LS algorithm is then performed to update D(v) for all nodes v, yielding the results shown in the second line (step 1) in Table 4.2. The cost of the path to B is unchanged. The cost of the path to C (which was 5 at the end of the initialization) through node D is found to have a cost of 4. Hence this lower cost path is selected and C's predecessor along the shortest path from A is set to D. Similarly, the cost to E (through D) is computed to be 2, and the table is updated accordingly. 
• In the second iteration, nodes B and E are found to have the least path costs (2), and we break the tie arbitrarily and add E to the set N so that N now contains A, D, and E. The cost to the remaining nodes not yet in N, that is, nodes B, C, and F, are updated via line 12 of the LS algorithm, yielding the results shown in the third row in the Table 4.2. 
• and so on...

What is the computational complexity of this algorithm? That is, given n nodes (not counting the source), how much computation must be done in the worst case to find the least-cost paths from the source to all destinations? In the first iteration, we need to search through all n nodes to determine the node, w, not in N that has the minimum cost. In the second iteration, we need to check n - 1 nodes to determine the minimum cost; in the third iteration n - 2 nodes, and so on. Overall, the total number of nodes we need to search through over all the iterations is n(n + 1)/2, and thus we say that the above implementation of the link state algorithm has worst-case complexity of order n squared: O(n²). (A more sophisticated implementation of this algorithm, using a data structure known as a heap, can find the minimum in line 9 in logarithmic rather than linear time, thus reducing the complexity.) 

Before completing our discussion of the LS algorithm, let us consider a pathology that can arise. Figure 4.5 shows a simple network topology where link costs are equal to the load carried on the link, for example, reflecting the delay that would be experienced. In this example, link costs are not symmetric, that is, c(A,B) equals c(B,A) only if the load carried on both directions on the AB link is the same. In this example, node D originates a unit of traffic destined for A, node B also originates a unit of traffic destined for A, and node C injects an amount of traffic equal to e, also destined for A. The initial routing is shown in Figure 4.5(a) with the link costs corresponding to the amount of traffic carried. 

When the LS algorithm is next run, node C determines (based on the link costs shown in Figure 4.5a) that the clockwise path to A has a cost of 1, while the counterclockwise path to A (which it had been using) has a cost of 1 + e. Hence C's least-cost path to A is now clockwise. Similarly, B determines that its new least-cost path to A is also clockwise, resulting in costs shown in Figure 4.5b. When the LS algorithm is run next, nodes B, C, and D all detect a zero-cost path to A in the counterclockwise direction, and all route their traffic to the counterclockwise routes. The next time the LS algorithm is run, B, C, and D all then route their traffic to the clockwise routes. 

What can be done to prevent such oscillations (which can occur in any algorithm that uses a congestion or delay-based link metric). One solution would be to mandate that link costs not depend on the amount of traffic carried--an unacceptable solution since one goal of routing is to avoid highly congested (for example, high-delay) links. Another solution is to ensure that all routers do not run the LS algorithm at the same time. This seems a more reasonable solution, since we would hope that even if routers run the LS algorithm with the same periodicity, the execution instance of the algorithm would not be the same at each node. Interestingly, researchers have recently noted that routers in the Internet can self-synchronize among themselves [Floyd Synchronization 1994]. That is, even though they initially execute the algorithm with the same period but at different instants of time, the algorithm execution instance can eventually become, and remain, synchronized at the routers. One way to avoid such self-synchronization is to purposefully introduce randomization into the period between execution instants of the algorithm at each node. 

Having now studied the link state algorithm, let's next consider the other major routing algorithm that is used in practice today--the distance vector routing algorithm. 

4.2.2: A Distance Vector Routing Algorithm

The principal data structure in the DV algorithm is the distance table maintained at each node. Each node's distance table has a row for each destination in the network and a column for each of its directly attached neighbors. Consider a node X that is interested in routing to destination Y via its directly attached neighbor Z. Node X's distance table entry, D^x(Y,Z) is the sum of the cost of the direct one-hop link between X and Z, c(X,Z), plus neighbor Z's currently known minimum-cost path from itself (Z) to Y. That is: 

The min_w term in the equation is taken over all of Z's directly attached neighbors (including X, as we shall soon see). 

The equation suggests the form of the neighbor-to-neighbor communication that will take place in the DV algorithm--each node must know the cost of each of its neighbors' minimum-cost path to each destination. Thus, whenever a node computes a new minimum cost to some destination, it must inform its neighbors of this new minimum cost. 

Before presenting the DV algorithm, let's consider an example that will help clarify the meaning of entries in the distance table. Consider the network topology and the distance table shown for node E in Figure 4.6. This is the distance table in node E once the DV algorithm has converged. Let's first look at the row for destination A. 

• Clearly the cost to get to A from E via the direct connection to A has a cost of 1. Hence D^E(A,A) = 1. 
• Let's now consider the value of D^E(A,D)--the cost to get from E to A, given that the first step along the path is D. In this case, the distance table entry is the cost to get from E to D (a cost of 2) plus whatever the minimum cost it is to get from D to A. Note that the minimum cost from D to A is 3--a path that passes right back through E! Nonetheless, we record the fact that the minimum cost from E to A given that the first step is via D has a cost of 5. We're left, though, with an uneasy feeling that the fact that the path from E via D loops back through E may be the source of problems down the road (it will!). 
• Similarly, we find that the distance table entry via neighbor B is D^E(A,B) = 14. Note that the cost is not 15. (Why?) 

In discussing the distance table entries for node E above, we informally took a global view, knowing the costs of all links in the network. The distance vector algorithm we will now present is decentralized and does not use such global information. Indeed, the only information a node will have are the costs of the links to its directly attached neighbors, and information it receives from these directly attached neighbors. The distance vector algorithm we will study is also known as the Bellman-Ford algorithm, after its inventors. It is used in many routing protocols in practice, including: Internet BGP, ISO IDRP, Novell IPX, and the original ARPAnet. 

Distance Vector (DV) algorithm

At each node, X:

1 Initialization:

2  for all adjacent nodes v:

3   DX (*,v) =        /* the * operator means "for all rows" */

4   DX (v,v) = c(X,v)

5  for all destinations, y

6   send minwD(y,w) to each neighbor  /* w over all X's neighbors */

7

8 loop

9   wait (until I see a link cost change to neighbor V

10       or until I receive an update from neighbor V)

11

12  if (c(X,V) changes by d)

13    /* change cost to all dest's via neighbor v by d */

14    /* note: d could be positive or negative */

15    for all destinations y: DX (y,V) = DX (y,V) + d

16

17  else if (update received from V wrt destination Y)

18    /* shortest path from V to some Y has changed */

19    /* V has sent a new value for its minw DV (Y,w) */

20    /* call this received new value "newval" */

21    for the single destination y: DX (Y,V) = c(X,V) + newval

22

23  if we have a new minw DX (Y,w)for any destination Y

24    send new value of minw DX (Y,w) to all neighbors

25

26 forever

Figure 4.7 illustrates the operation of the DV algorithm for the simple three node network shown at the top of the figure. The operation of the algorithm is illustrated in a synchronous manner, where all nodes simultaneously receive messages from their neighbors, compute new distance table entries, and inform their neighbors of any changes in their new least path costs. After studying this example, you should convince yourself that the algorithm operates correctly in an asynchronous manner as well, with node computations and update generation/reception occurring at any times. 

The circled distance table entries in Figure 4.7 show the current minimum path cost to a destination. A double-circled entry indicates that a new minimum cost has been computed (in either line 4 of the DV algorithm (initialization) or line 21). In such cases an update message will be sent (line 24 of the DV algorithm) to the node's neighbors as represented by the arrows between columns in Figure 4.7. 

The leftmost column in Figure 4.7 shows the distance table entries for nodes X, Y, and Z after the initialization step. 

Let's now consider how node X computes the distance table shown in the middle column of Figure 4.7 after receiving updates from nodes Y and Z. As a result of receiving the updates from Y and Z, X computes in line 21 of the DV algorithm: 

DX(Y,Z)	= c(X,Z) + minw DZ(Y,w)  = 7 + 1  = 8
DX(Z,Y)	= c(X,Y) + minw DY(Z,w)  = 2 + 1  = 3

It is important to note that the only reason that X knows about the terms min_w D^Z(Y,w) and min_w D^Y(Z,w) is because nodes Z and Y have sent those values to X (and are received by X in line 10 of the DV algorithm). As an exercise, verify the distance tables computed by Y and Z in the middle column of Figure 4.7. 

The value D^X(Z,Y) = 3 means that X's minimum cost to Z has changed from 7 to 3. Hence, X sends updates to Y and Z informing them of this new least cost to Z. Note that X need not update Y and Z about its cost to Y since this has not changed. Note also that although Y's recomputation of its distance table in the middle column of Figure 4.7 does result in new distance entries, it does not result in a change of Y's least-cost path to nodes X and Z. Hence Y does not send updates to X and Z. 

The process of receiving updated costs from neighbors, recomputation of distance table entries, and updating neighbors of changed costs of the least-cost path to a destination continues until no update messages are sent. At this point, since no update messages are sent, no further distance table calculations will occur and the algorithm enters a quiescent state; that is, all nodes are performing the wait in line 9 of the DV algorithm. The algorithm would remain in the quiescent state until a link cost changes, as discussed below. 

The Distance Vector Algorithm: Link Cost Changes and Link Failure

When a node running the DV algorithm detects a change in the link cost from itself to a neighbor (line 12), it updates its distance table (line 15) and, if there's a change in the cost of the least-cost path, updates its neighbors (lines 23 and 24). Figure 4.8 illustrates this behavior for a scenario where the link cost from Y to X changes from 4 to 1. We focus here only on Y and Z's distance table entries to destination (row) X. 

• At time t₀, Y detects the link-cost change (the cost has changed from 4 to 1) and informs its neighbors of this change since the cost of the minimum cost path has changed. 
• At time t₁, Z receives the update from Y and then updates its table. Since it computes a new least cost to X (it has decreased from a cost of 5 to a cost of 2), it informs its neighbors. 
• At time t₂, Y receives Z's update and updates its distance table. Y's least costs have not changed (although its cost to X via Z has changed) and hence Y does not send any message to Z. The algorithm comes to a quiescent state.

Let's now consider what can happen when a link cost increases. Suppose that the link cost between X and Y increases from 4 to 60 as shown in Figure 4.9. 

• At time t₀, Y detects the link-cost change (the cost has changed from 4 to 60). Y computes its new minimum cost path to X to have a cost of 6 via node Z. Of course, with our global view of the network, we can see that this new cost via Z is wrong. But the only information node Y has is that its direct cost to X is 60 and that Z has last told Y that Z could get to X with a cost of 5. So in order to get to X, Y would now route through Z, fully expecting that Z will be able to get to X with a cost of 5. As of t₁ we have a routing loop--in order to get to X, Y routes through Z, and Z routes through Y. A routing loop is like a black hole--a packet arriving at Y or Z as of t₁ and destined for X, will bounce back and forth between these two nodes forever (or until the routing tables are changed). 
• Since node Y has computed a new minimum cost to X, it informs Z of this new cost at time t₁. 
• Sometime after t₁, Z receives the new least cost to X via Y (Y has told Z that Y's new minimum cost is 6). Z knows it can get to Y with a cost of 1 and hence computes a new least cost to X (still via Y) of 7. Since Z's least cost to X has increased, it then informs Y of its new cost at t₂. 
• In a similar manner, Y then updates its table and informs Z of a new cost of 8. Z then updates its table and informs Y of a new cost of 9, etc.

Distance Vector Algorithm: Adding Poisoned Revers

The specific looping scenario illustrated in Figure 4.9 can be avoided using a technique known as poisoned reverse. The idea is simple--if Z routes through Y to get to destination X, then Z will advertise to Y that its (Z's) distance to X is infinity. Z will continue telling this little "white lie" to Y as long as it routes to X via Y. Since Y believes that Z has no path to X, Y will never attempt to route to X via Z, as long as Z continues to route to X via Y (and lies about doing so). 

Figure 4.10 illustrates how poisoned reverse solves the particular looping problem we encountered before in Figure 4.9. As a result of the poisoned reverse, Y's distance table indicates an infinite cost when routing to X via Z (the result of Z having informed Y that Z's cost to X was infinity). When the cost of the XY link changes from 4 to 60 at time t₀, Y updates its table and continues to route directly to X, albeit at a higher cost of 60, and informs Z of this change in cost. After receiving the update at t₁, Z immediately shifts its route to X to be via the direct ZX link at a cost of 50. Since this is a new least-cost to X, and since the path no longer passes through Y, Z informs Y of this new least-cost path to X at t₂. After receiving the update from Z, Y updates its distance table to route to X via Z at a least cost of 51. Also, since Z is now on Y's least-cost path to X, Y poisons the reverse path from Z to X by informing Z at time t₃ that it (Y) has an infinite cost to get to X. The algorithm becomes quiescent after t₄, with distance table entries for destination X shown in the rightmost column in Figure 4.10. 

Does poison reverse solve the general count-to-infinity problem? It does not. You should convince yourself that loops involving three or more nodes (rather than simply two immediately neighboring nodes, as we saw in Figure 4.10) will not be detected by the poison reverse technique. 

A Comparison of Link State and Distance Vector Routing Algorithms

Let's conclude our study of link state and distance vector algorithms with a quick comparison of some of their attributes.

• Message complexity. We have seen that LS requires each node to know the cost of each link in the network. This requires O(nE) messages to be sent, where n is the number of nodes in the network and E is the number of links. Also, whenever a link cost changes, the new link cost must be sent to all nodes. The DV algorithm requires message exchanges between directly connected neighbors at each iteration. We have seen that the time needed for the algorithm to converge can depend on many factors. When link costs change, the DV algorithm will propagate the results of the changed link cost only if the new link cost results in a changed least-cost path for one of the nodes attached to that link. 
• Speed of convergence. We have seen that our implementation of LS is an O(n²) algorithm requiring O(nE) messages, and that it potentially suffers from oscillations. The DV algorithm can converge slowly (depending on the relative path costs, as we saw in Figure 4.10) and can have routing loops while the algorithm is converging. DV also suffers from the count-to-infinity problem.
• Robustness. What can happen if a router fails, misbehaves, or is sabotaged? Under LS, a router could broadcast an incorrect cost for one of its attached links (but no others). A node could also corrupt or drop any LS broadcast packets it receives as part of a link state broadcast. But an LS node is only computing its own routing tables; other nodes are performing the similar calculations for themselves. This means route calculations are somewhat separated under LS, providing a degree of robustness. Under DV, a node can advertise incorrect least-cost paths to any/all destinations. (Indeed, in 1997, a malfunctioning router in a small ISP provided national backbone routers with erroneous routing tables. This caused other routers to flood the malfunctioning router with traffic and caused large portions of the Internet to become disconnected for up to several hours [Neumann 1997].) More generally, we note that at each iteration, a node's calculation in DV is passed on to its neighbor and then indirectly to its neighbor's neighbor on the next iteration. In this sense, an incorrect node calculation can be diffused through the entire network under DV. 

4.2.3: Other Routing Algorithms

Nonetheless, many routing algorithms have been proposed by researchers over the past 30 years, ranging from the extremely simple to the very sophisticated and complex. One of the simplest routing algorithms proposed is hot potato routing. The algorithm derives its name from its behavior--a router tries to get rid of (forward) an outgoing packet as soon as it can. It does so by forwarding it on any outgoing link that is not congested, regardless of destination. 

Another broad class of routing algorithms are based on viewing packet traffic as flows between sources and destinations in a network. In this approach, the routing problem can be formulated mathematically as a constrained optimization problem known as a network flow problem [Bertsekas 1991]. Let us define _ij as the amount of traffic (for example, in packets/sec) entering the network for the first time at node i and destined for node j. The set of flows, {_ij} for all i,j, is sometimes referred to as the network traffic matrix. In a network flow problem, traffic flows must be assigned to a set of network links subject to constraints such as:

• The sum of the flows between all source destination pairs passing though link m must be less than the capacity of link m. 
• The amount of _ij traffic entering any router r (either from other routers, or directly entering that router from an attached host) must equal the amount of _ij traffic leaving the router either via one of r's outgoing links or to an attached host at that router. This is a flow conservation constraint.

Let us define  _ij^m as the amount of source i, destination j traffic passing through link m. The optimization problem then is to find the set of link flows, {_ij^m} for all links m and all sources, i, and destinations, j, that satisfies the constraints above and optimizes a performance measure that is a function of {_ij^m}. The solution to this optimization problem then defines the routing used in the network. For example, if the solution to the optimization problem is such that _ij^m = _ij for some link m, then all i-to-j traffic will be routed over link m. In particular, if link m is attached to node i, then m is the first hop on the optimal path from source i to destination j. 

But what performance function should be optimized? There are many possible choices. If we make certain assumptions about the size of packets and the manner in which packets arrive at the various routers, we can use the so-called M/M/1 queuing theory formula [Kleinrock 1975] to express the average delay at link m as: 

where R_m is link m's capacity (measured in terms of the average number of packets/sec it can transmit) and _ijij^m is the total arrival rate of packets (in packets/ sec) that arrive to link m. The overall network-wide performance measure to be optimized might then be the sum of all link delays in the network, or some other suitable performance metric. A number of elegant distributed algorithms exist for computing the optimum link flows (and hence the routing paths, as discussed above). The reader is referred to [Bertsekas 1991] for a detailed study of these algorithms. 

The final set of routing algorithms we mention here are those derived from the telephony world. These circuit-switched routing algorithms are of interest to packet-switched data networking in cases where per-link resources (for example, buffers, or a fraction of the link bandwidth) are to be reserved for each connection that is routed over the link. While the formulation of the routing problem might appear quite different from the least-cost routing formulation we have seen in this chapter, we will see that there are a number of similarities, at least as far as the path finding algorithm (routing algorithm) is concerned. Our goal here is to provide a brief introduction for this class of routing algorithms. The reader is referred to [Ash 1998; Ross 1995; Girard 1990] for a detailed discussion of this active research area. 

The circuit-switched routing problem formulation is illustrated in Figure 4.11. Each link has a certain amount of resources (for example, bandwidth). The easiest (and a quite accurate) way to visualize this is to consider the link to be a bundle of circuits, with each call that is routed over the link requiring the dedicated use of one of the link's circuits. A link is thus characterized both by its total number of circuits, as well as the number of these circuits currently in use. In Figure 4.11, all links except AB and BD have 20 circuits; the number to the left of the number of circuits indicates the number of circuits currently in use. 

Suppose now that a call arrives at node A, destined to node D. What path should be taken? In shortest path first (SPF) routing, the shortest path (least number of links traversed) is taken. We have already seen how the Dijkstra LS algorithm can be used to find shortest-path routes. In Figure 4.11, either the ABD or ACD path would thus be taken. In least loaded path (LLP) routing, the load at a link is defined as the ratio of the number of used circuits at the link and the total number of circuits at that link. The path load is the maximum of the loads of all links in the path. In LLP routing, the path taken is that with the smallest path load. In Figure 4.11, the LLP path is ABCD. In maximum free circuit (MFC) routing, the number of free circuits associated with a path is the minimum of the number of free circuits at each of the links on a path. In MFC routing, the path with the maximum number of free circuits is taken. In Figure 4.11, the path ABD would be taken with MFC routing. 

Given these examples from the circuit-switching world, we see that the path selection algorithms have much the same flavor as LS routing. All nodes have complete information about the network's link states. Note, however, that the potential consequences of old or inaccurate state information are more severe with circuit-oriented routing--a call may be routed along a path only to find that the circuits it had been expecting to be allocated are no longer available. In such a case, the call setup is blocked and another path must be attempted. Nonetheless, the main differences between connection-oriented, circuit-switched routing and connectionless packet-switched routing come not in the path-selection mechanism, but rather in the actions that must be taken when a connection is set up, or torn down, from source to destination.