Routing in packet switched networks involves selecting the optimal path between end nodes across the network. Adaptive routing is commonly used, where routing decisions dynamically change in response to network conditions like failures or congestion. Key algorithms for computing optimal paths include Dijkstra's algorithm and Bellman-Ford algorithm, which calculate the shortest or least-cost path between all nodes based on link costs.

1. Data and ComputerData and Computer
CommunicationsCommunications
Eighth EditionEighth Edition
by William Stallingsby William Stallings
Lecture slides by Lawrie BrownLecture slides by Lawrie Brown
Chapter 12 –Chapter 12 – Routing in SwitchedRouting in Switched
NetworksNetworks

2. Routing in Switched NetworksRouting in Switched Networks
"I tell you," went on Syme with passion, "that every"I tell you," went on Syme with passion, "that every
time a train comes in I feel that it has broken pasttime a train comes in I feel that it has broken past
batteries of besiegers, and that man has won a battlebatteries of besiegers, and that man has won a battle
against chaos. You say contemptuously that when oneagainst chaos. You say contemptuously that when one
has left Sloane Square one must come to Victoria. Ihas left Sloane Square one must come to Victoria. I
say that one might do a thousand things instead, andsay that one might do a thousand things instead, and
that whenever I really come there I have the sense ofthat whenever I really come there I have the sense of
hairbreadth escape. And when I hear the guard shouthairbreadth escape. And when I hear the guard shout
out the word 'Victoria', it is not an unmeaning word.out the word 'Victoria', it is not an unmeaning word.
It is to me the cry of a herald announcing conquest. ItIt is to me the cry of a herald announcing conquest. It
is to me indeed 'Victoria'; it is the victory of Adam."is to me indeed 'Victoria'; it is the victory of Adam."
——The Man Who Was ThursdayThe Man Who Was Thursday, G.K. Chesterton, G.K. Chesterton

3. RoutingRouting in Packet Switchedin Packet Switched
NetworkNetwork
 key design issue for (packet) switched networkskey design issue for (packet) switched networks
 select route across network between end nodesselect route across network between end nodes
 characteristics required:characteristics required:

correctnesscorrectness

simplicitysimplicity

robustnessrobustness

stabilitystability

fairnessfairness

optimalityoptimality

efficiencyefficiency

4. Performance CriteriaPerformance Criteria
 used for selection of routeused for selection of route
 simplest is “minimum hop”simplest is “minimum hop”
 can be generalized as “least cost”can be generalized as “least cost”

5. Example Packet SwitchedExample Packet Switched
NetworkNetwork

6. Decision Time and PlaceDecision Time and Place
 timetime

packet or virtual circuit basispacket or virtual circuit basis

fixed or dynamically changingfixed or dynamically changing
 placeplace

distributed - made by each nodedistributed - made by each node

centralizedcentralized

sourcesource

7. Network Information SourceNetwork Information Source
and Update Timingand Update Timing
 routing decisions usually based on knowledge ofrouting decisions usually based on knowledge of
network (not always)network (not always)

distributed routingdistributed routing
• using local knowledge, info from adjacent nodes, info from allusing local knowledge, info from adjacent nodes, info from all
nodes on a potential routenodes on a potential route

central routingcentral routing
• collect info from all nodescollect info from all nodes
 issue of update timingissue of update timing

when is network info held by nodes updatedwhen is network info held by nodes updated

fixed - never updatedfixed - never updated

adaptive - regular updatesadaptive - regular updates

8. Routing Strategies - FixedRouting Strategies - Fixed
RoutingRouting
 use a single permanent route for eachuse a single permanent route for each
source to destination pairsource to destination pair
 determined using a least cost algorithmdetermined using a least cost algorithm
 route is fixedroute is fixed

at least until a change in network topologyat least until a change in network topology

hence cannot respond to traffic changeshence cannot respond to traffic changes
 advantage is simplicityadvantage is simplicity
 disadvantage is lack of flexibilitydisadvantage is lack of flexibility

9. FixedFixed
RoutingRouting
TablesTables

10. Routing Strategies - FloodingRouting Strategies - Flooding
 packet sent by node to every neighborpacket sent by node to every neighbor
 eventually multiple copies arrive at destinationeventually multiple copies arrive at destination
 no network info requiredno network info required
 each packet is uniquely numbered so duplicateseach packet is uniquely numbered so duplicates
can be discardedcan be discarded
 need some way to limit incessant retransmissionneed some way to limit incessant retransmission

nodes can remember packets already forwarded tonodes can remember packets already forwarded to
keep network load in boundskeep network load in bounds

or include a hop count in packetsor include a hop count in packets

11. FloodingFlooding
ExampleExample

12. Properties of FloodingProperties of Flooding
 all possible routes are triedall possible routes are tried

very robustvery robust
 at least one packet will have takenat least one packet will have taken
minimum hop count routeminimum hop count route

can be used to set up virtual circuitcan be used to set up virtual circuit
 all nodes are visitedall nodes are visited

useful to distribute information (eg. routing)useful to distribute information (eg. routing)
 disadvantage is high traffic load generateddisadvantage is high traffic load generated

13. Routing Strategies - RandomRouting Strategies - Random
RoutingRouting
 simplicity of flooding with much less loadsimplicity of flooding with much less load
 node selects one outgoing path fornode selects one outgoing path for
retransmission of incoming packetretransmission of incoming packet
 selection can be random or round robinselection can be random or round robin
 a refinement is to select outgoing path based ona refinement is to select outgoing path based on
probability calculationprobability calculation
 no network info neededno network info needed
 but a random route is typically neither least costbut a random route is typically neither least cost
nor minimum hopnor minimum hop

14. Routing Strategies - AdaptiveRouting Strategies - Adaptive
RoutingRouting
 used by almost all packet switching networksused by almost all packet switching networks
 routing decisions change as conditions on therouting decisions change as conditions on the
network change due to failure or congestionnetwork change due to failure or congestion
 requires info about networkrequires info about network
 disadvantages:disadvantages:

decisions more complexdecisions more complex

tradeoff between quality of network info and overheadtradeoff between quality of network info and overhead

reacting too quickly can cause oscillationreacting too quickly can cause oscillation

reacting too slowly means info may be irrelevantreacting too slowly means info may be irrelevant

15. Adaptive Routing -Adaptive Routing -
AdvantagesAdvantages
 improved performanceimproved performance
 aid congestion controlaid congestion control
 but since is a complex system, may notbut since is a complex system, may not
realize theoretical benefitsrealize theoretical benefits

cf. outages on many packet-switched netscf. outages on many packet-switched nets

16. Classification of AdaptiveClassification of Adaptive
Routing StartegiesRouting Startegies
 based on information sourcesbased on information sources

local (isolated)local (isolated)
• route to outgoing link with shortest queueroute to outgoing link with shortest queue
• can include bias for each destinationcan include bias for each destination
• Rarely used - does not make use of available infoRarely used - does not make use of available info

adjacent nodesadjacent nodes
• takes advantage on delay / outage infotakes advantage on delay / outage info
• distributed or centralizeddistributed or centralized

all nodesall nodes
• like adjacentlike adjacent

17. Isolated Adaptive RoutingIsolated Adaptive Routing

18. ARPANET Routing StrategiesARPANET Routing Strategies
1st Generation1st Generation
 19691969
 distributed adaptive using estimated delaydistributed adaptive using estimated delay

queue length used as estimate of delayqueue length used as estimate of delay
 using Bellman-Ford algorithmusing Bellman-Ford algorithm
 node exchanges delay vector with neighborsnode exchanges delay vector with neighbors
 update routing table based on incoming infoupdate routing table based on incoming info
 problems:problems:

doesn't consider line speed, just queue lengthdoesn't consider line speed, just queue length

queue length not a good measurement of delayqueue length not a good measurement of delay

responds slowly to congestionresponds slowly to congestion

19. ARPANET Routing StrategiesARPANET Routing Strategies
2nd Generation2nd Generation
 19791979
 distributed adaptive using measured delaydistributed adaptive using measured delay

using timestamps of arrival, departure & ACK timesusing timestamps of arrival, departure & ACK times
 recomputes average delays every 10secsrecomputes average delays every 10secs
 any changes are flooded to all other nodesany changes are flooded to all other nodes
 recompute routing using Dijkstra’s algorithmrecompute routing using Dijkstra’s algorithm
 good under light and medium loadsgood under light and medium loads
 under heavy loads, little correlation betweenunder heavy loads, little correlation between
reported delays and those experiencedreported delays and those experienced

20. ARPANET Routing StrategiesARPANET Routing Strategies
3rd Generation3rd Generation
 19871987
 link cost calculations changedlink cost calculations changed

to damp routing oscillationsto damp routing oscillations

and reduce routing overheadand reduce routing overhead
 measure average delay over last 10 secs andmeasure average delay over last 10 secs and
transform into link utilization estimatetransform into link utilization estimate
 normalize this based on current value andnormalize this based on current value and
previous resultsprevious results
 set link cost as function of average utilizationset link cost as function of average utilization

21. Least Cost AlgorithmsLeast Cost Algorithms
 basis for routing decisionsbasis for routing decisions

can minimize hop with each link cost 1can minimize hop with each link cost 1

or have link value inversely proportional to capacityor have link value inversely proportional to capacity
 dedefines cost of path between two nodes as sumfines cost of path between two nodes as sum
of costs of links traversedof costs of links traversed

in network of nodes connected by bi-directional linksin network of nodes connected by bi-directional links

where ewhere each link has a cost in each directionach link has a cost in each direction
 for each pair of nodes, find path with least costfor each pair of nodes, find path with least cost

link costs in different directions may be differentlink costs in different directions may be different
 alternatives:alternatives: Dijkstra or Bellman-Ford algorithmsDijkstra or Bellman-Ford algorithms

22. Dijkstra’s AlgorithmDijkstra’s Algorithm
 finds shortest paths from given sourcefinds shortest paths from given source
nodenode ss to all other nodesto all other nodes
 by developing paths in order of increasingby developing paths in order of increasing
path lengthpath length
 algorithm runs in stages (next slide)algorithm runs in stages (next slide)

each time adding node with next shortest patheach time adding node with next shortest path
 algorithmalgorithm terminates when all nodes processedterminates when all nodes processed
by algorithm (in set T)by algorithm (in set T)

23. Dijkstra’s Algorithm MethodDijkstra’s Algorithm Method
 Step 1Step 1 [Initialization][Initialization]

T = {s}T = {s} SSet of nodes so far incorporatedet of nodes so far incorporated

L(n) = w(s, n) for n ≠ sL(n) = w(s, n) for n ≠ s

initialinitial path costs to neighboring nodes are simply link costspath costs to neighboring nodes are simply link costs
 StepStep 22 [Get Next Node][Get Next Node]

find neighboring node not in Tfind neighboring node not in T withwith least-cost path from sleast-cost path from s

inincorporate node into Tcorporate node into T

also incorporate the edge that is incident on that node and aalso incorporate the edge that is incident on that node and a
node in T that contributes to the pathnode in T that contributes to the path
 StepStep 33 [Update Least-Cost Paths][Update Least-Cost Paths]

L(n) = min[L(n), L(x) + w(x, n)]L(n) = min[L(n), L(x) + w(x, n)] for all nfor all n ∉∉ TT

if latter term is minimum, path from s to n is path from s to xif latter term is minimum, path from s to n is path from s to x
concatenated with edge from x to nconcatenated with edge from x to n

24. Dijkstra’s Algorithm ExampleDijkstra’s Algorithm Example

25. Dijkstra’s Algorithm ExampleDijkstra’s Algorithm Example
Iter T L(2) Path L(3) Path L(4) Path L(5) Path L(6
)
Path
1 {1} 2 1–2 5 1-3 1 1–4 ∞ - ∞ -
2 {1,4} 2 1–2 4 1-4-3 1 1–4 2 1-4–5 ∞ -
3 {1, 2, 4} 2 1–2 4 1-4-3 1 1–4 2 1-4–5 ∞ -
4 {1, 2, 4,
5}
2 1–2 3 1-4-5–3 1 1–4 2 1-4–5 4 1-4-5–6
5 {1, 2, 3,
4, 5}
2 1–2 3 1-4-5–3 1 1–4 2 1-4–5 4 1-4-5–6
6 {1, 2, 3,
4, 5, 6}
2 1-2 3 1-4-5-3 1 1-4 2 1-4–5 4 1-4-5-6

26. Bellman-Ford AlgorithmBellman-Ford Algorithm
 find shortest paths from given nodefind shortest paths from given node
subject to constraint that paths contain atsubject to constraint that paths contain at
most one linkmost one link
 findfind the shortest paths with a constraint ofthe shortest paths with a constraint of
paths of at most two linkspaths of at most two links
 andand so onso on

27. Bellman-Ford AlgorithmBellman-Ford Algorithm
 stepstep 1 [Initialization]1 [Initialization]
 LL00(n) =(n) = ∞∞, for all n, for all n ≠≠ ss
 LLhh(s) = 0, for all h(s) = 0, for all h
 stepstep 2 [Update]2 [Update]

for each successive hfor each successive h ≥≥ 00
• for each n ≠ s, compute:for each n ≠ s, compute: LLh+1h+1((nn)=)=minmin
jj[[LLhh((jj)+)+ww((j,nj,n)])]

connect n with predecessor node j that gives minconnect n with predecessor node j that gives min

eliminateeliminate any connection of n with differentany connection of n with different
predecessor node formed during an earlier iterationpredecessor node formed during an earlier iteration

pathpath from s to n terminates with link from j to nfrom s to n terminates with link from j to n

28. Example of Bellman-FordExample of Bellman-Ford
AlgorithmAlgorithm

29. Results of Bellman-FordResults of Bellman-Ford
ExampleExampleh Lh(2) Path Lh(3) Path Lh(4) Path Lh(5) Path Lh(6) Path
0 ∞ - ∞ - ∞ - ∞ - ∞ -
1 2 1-2 5 1-3 1 1-4 ∞ - ∞ -
2 2 1-2 4 1-4-3 1 1-4 2 1-4-5 10 1-3-6
3 2 1-2 3 1-4-5-3 1 1-4 2 1-4-5 4 1-4-5-6
4 2 1-2 3 1-4-5-3 1 1-4 2 1-4-5 4 1-4-5-6

30. ComparisonComparison
 results from two algorithms agreeresults from two algorithms agree
 Bellman-FordBellman-Ford

calculation for node n needs link cost to neighbouringcalculation for node n needs link cost to neighbouring
nodes plus total cost to each neighbour from snodes plus total cost to each neighbour from s

each node can maintain set of costs and paths foreach node can maintain set of costs and paths for
every other nodeevery other node

can exchange information with direct neighborscan exchange information with direct neighbors

can update costs and paths based on informationcan update costs and paths based on information
from neighbors and knowledge of link costsfrom neighbors and knowledge of link costs
 DijkstraDijkstra

each node needs complete topologyeach node needs complete topology

must know link costs of all links in networkmust know link costs of all links in network

must exchange information with all other nodesmust exchange information with all other nodes

31. EvaluationEvaluation
 dependent ondependent on

processing time of algorithmsprocessing time of algorithms

amount of information required from other nodesamount of information required from other nodes
 implementation specificimplementation specific
 both converge under static topology and costsboth converge under static topology and costs
 both converge to same solutionboth converge to same solution
 if link costs change, algs attempt to catch upif link costs change, algs attempt to catch up
 if link costs depend on traffic, which depends onif link costs depend on traffic, which depends on
routes chosen, may have feedback instabilityroutes chosen, may have feedback instability

32. SummarySummary
 routing in packet-switched networksrouting in packet-switched networks
 routing strategiesrouting strategies

fixed, flooding, random,adaptivefixed, flooding, random,adaptive
 ARPAnet examplesARPAnet examples
 least-cost algorithmsleast-cost algorithms

Dijkstra, Bellman-FordDijkstra, Bellman-Ford