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routing

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network layer in context• layer 1: physical (PHY) layer• layer 2: datalink layer and MAC sublayer

– transmits frames (containing packets) between adjacent nodes, arbitrates access within collision domains

• layer 3: network layer– routes packets between endpoints– “end to end”, “source to destination”, “source to sink”

• transport layer– cooperates with transport layer on node at other end to

manage streams of traffic supporting app layer comms

• (layers above 1, 2, 3 differ by network protocol stack)

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challenges in internetworking

• heterogeneity– many different kinds of networks: Ethernets,

wireless, pt-to-pt links, switched rings, etc

• scale– Internet doubled each year for the last 20 years– which paths, thru millions/billions of nodes?

• efficient, loop-free

– unambiguous addressing of all these nodes?

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store-and-forward packet switching

data network --- environment:

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store-and-forward packet switching

• routers perform store-and-forward• receive packet, do checksum, [queue,]

compute egress link, transmit over egress link• routers are aware of each other on the

network layer, but the transport layer is not aware of routers

• what is the transport layer aware of?– a few generic system calls

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network services for transport layer

• ideals

– transport layer makes generic system calls to network• transport layer otherwise ignorant of what goes on in network

– network shows tech-neutral face to transport layer• whether connection-oriented or connectionless

– global network addresses

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network layer in a nutshell

• “datagram subnet”, “packet-switched network”, “statistically multiplexed network”

• Internet Protocol, ATM, others

• for each generic router:– routing computations initialize & renew forwarding table– forwarding table (“next hop” table):

• {(destination, egress line, <protocol specific>)}

– receive packet, [checksum,] [queue,] route toward sink

• next router does the same

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connectionless service

routing within a packet-switching network

(sink, next hop)

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routing algorithms

• the Optimality Principle• shortest path routing• flooding• Distance Vector Routing (DVR)• Link State Routing (LSR)• hierarchical routing• broadcast routing• multicast routing• routing for mobile hosts• routing in ad hoc networks

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graph theory and the network layer

• like a horse and carriage

• set N of nodes, set E of edges– edges are full duplex, arcs are simplex

• graph G = (N,E)

• N = (a,b,c,d)

• E = ((a,b), (a,c), (b,c), (b,c))

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graph theory

• walk: a sequence of adjacent nodes

• path: a walk with no node repeated

• cycle: walk (n1, n

2, ..., n

n), only n

1 & n

n the same

• connected graph

• unconnected graph components

• acyclic graph

• tree: acyclic connected graph – cardinality(E) = cardinality(N) - 1

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subgraph

• subgraph G' = (N',E')– G' is a graph, N' ⊆N, E' ⊆E

• let spanning tree T be a subgraph ofG– where T is a tree and N' = N

• broadcast routing– with tree: n transmits on all adjacent edges e ∈ E'

• other nodes relay on each non-ingress adjacent e ∈ E' 

– flood: n transmits on all adjacent edges, other nodes relay on each non-ingress adjacent e ∈ E

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flooding algorithms

• send packets everywhere, “flood” the network• static algorithm

– receive flooding packet on one link– transmit flooding packet out on all other links

• robust: if paths exist, flooding finds shortest• benchmark for other routing algorithms

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challenges in flooding

• cycles/loops• massive packet duplication• how to make it stop?

– hop count field in flood packets• hop count “too high”, discard packet

– Selective flooding (only in “right direction”)– only forward “new” packets (higher seq#s) – reverse path forwarding: only accept packets from

source that arrive on the forwarding link to source

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uses for flooding

• downside: very high overhead• good for:

– high risk environment, unreliable nodes• battlefield, ad hoc networks

– distributed databases• concurrent global update

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distributed spanning tree algorithms

• where do you start? stop? is it biased? not?• minimum spanning tree (MST) algorithms

– fragment: a component of MST, a “subtree”– generic MST: given a set of fragments, add a min

weight edge to some fragment (no cycles)– Prim-Dijkstra: some node is first fragment; add min

weight adjacent edge– Kruskal: all nodes are fragments; add min weight

edge

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Prim-Dijkstra

graph slides adapted from E. Modiano, MIT

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routing algorithms

• network layer routes from source to sink

• routing algorithm

– computation of output line per sink

– building lookup table: {(sink, output line)}

• forwarding: using lookup table

• ideal routing algorithms:

– simple, stable, fair, efficient

– cope well with changes in topology and load

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tuning the network layer

• min( hop count ) => less delay, bandwidth

• packet delay v. overall network tput/capacity• fairness v. overall nwk capacity (optimality)

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optimality v. fairness

Conflict between fairness and optimality.

at max subnet throughput, path x → x’ is starved

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optimality principle

• IF node j is on an optimal path (OP), i→k,– THEN an OP j→k is a subset of OP i→k

• the union of OPs for all nodes to a given sink is a sink tree

• routing algorithms seek to discover (or approximate) the sink trees of every sink in the subnet

• sink trees: max network capacity, min delay

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shortest path (least cost) routing

• ways to measure path goodness (or “cost”):– hop length– mean queuing delay (higher with higher loads)– link latency/distance– capacity

• actual hop cost is abstracted as “distance”• routers choose shortest available path,

whether explicitly, or implicitly

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static routing

• non-adaptive

• routes are computed in advance

• routes are optimal (global knowledge)

• routes do not change in response to topology and traffic pattern changes

• static routing used for:

– long-lasting topologies

– topologies with assigned PHY layer protection

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Dijkstra (1959)

• static algorithm for shortest path (optimal sink tree)• G(N,E)

– set of nodes N; set of (edge, edge length) pairs E

• mark source node permanent, others temporary• source becomes working node• for each working node

– label each node adjacent to a permanent node as (predicate, distance to source)

– of all temps, choose temp with least distance to source– mark temp permanent– temp becomes next working node, until sink is reached

worst case complexity of this algorithm? why?

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shortest path computationfirst 5 steps to compute the shortest path from A to D

(arrows indicate working node)

first working node

(a) input to Dijkstra algorithm; (c) illustration for proof by contradiction

Tanenbaum, Computer Networks, 2003, p. 354

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why is Dijkstra correct?

• in (c) above, E is now permanent• could some AXYZE be shorter than ABE?

– if Z permanent, ZE already rejected– if Z temp, and Z(dist to src) >= E(dist to src)

• then AXYZE is not shorter than ABE

– if Z temp, and Z(dist to src) < E(dist to src)• then Z would be permanent before E• why?

• {perms} = source• REPEAT {perms} += closest temp UNTIL sink added

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• a link to a scan of the hand-drawn image used in class to support the previous illustration of the Dijkstra proof has been placed on the class webpage, and leads to the following file.

• dijkstra-pf.pdf

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dynamic routing

• decisions made on-line• reacts to changes in topology, traffic, delays • dynamic routing algorithms

– distance vector– link state

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distance vector routing

• aka: Routing Information Protocol (RIP), Bellman-Ford algorithm

• iterative, self-terminating, asynchronous, distributed

• nodes maintain adjacent link costs• nodes exchange info, build forwarding tables

– estimated distance to each node

• forwarding table: {(node, line, distance)}

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Bellman-Ford equation

dx(y) = minv{ c(x,v) + dv(y) },

for all nodes y in N,

for all neighbors v of x

dx(y): cost of least-cost path from x to y

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distance vector implementation

• data structures:– cost vector: cost to each direct (adjacent) neighbor– distance vector: estimated cost to each node in N– distance vector of each direct neighbor

• algorithm:– each node regularly sends DV to neighbors– upon DV receipt, each node:

• saves neighbor’s DV• updates own DV using Bellman-Ford equation• if own DV changes, send it out to all neighbors

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distance vector routing example(a) subnet; (b) input for J from A, H, I, K; new routing table for J

Jneighbor links

link delays

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distance vector routing fatal flaw

A goes down; B believes C

fast convergence to shorter path

count-to-infinity problem

A comes up; B propagates

DVR: “where is it now?”

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link state routing

- best-known implementation: OSPF

each router must:• discover each neighbor (globally unique nwk ID)• measure the delay or cost to each neighbor• build packet: neighbor IDs, costs• send packet to all other subnet routers• compute shortest path to every other router

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link state routing implementation

• HELLO– neighbor/address discovery

• ECHO– delay/cost to reach neighbor– queueing delay?

• realistic estimate of fully-loaded delay• risk of oscillation

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building link state (update) packets

• update packet contents– source ID– sequence #– TTL– neighbor list: {(neighbor ID, delay)}

• when to send updates?– triggered by state change– on regular schedule (timer)

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link state packets

(a) subnet; (b) link state packets for subnet

(note: these are symmetric links)

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reliable link state packet distribution• source seq# in each update

– increment seq# each update– higher seq# is more recent

• each router maintains seq# list– for each other router: (router ID, seq#)

• for each update arriving from router X:– if update seq# <= list seq#

• update packet is a duplicate, discard it

– if update seq# > list seq#• copy new seq# to list• forward update packet to remaining adjacent routers (flooding)• update own routing table

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link state packet age

• each update packet includes age of packet– TTL field: time to live– TTL initialized to some reasonable value– TTL “aged” by each router before relaying onward– TTL periodically decremented (e.g., each second)

• when TTL reaches 0, packet is discarded– prevents old info from wandering around forever

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link state update refinements

• update holding time– wait to see if duplicate or fresher updates come in

• ACKs– all update packets are ACKed

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where to relay, where to ACK

packet buffer for router B

(see prev. graph) each row indexes an update packet, ready for processing

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computing routes from link state updates

• global state info– cooperative state distribution– local computation

• routing computation– aggregate link state info of all subnet routers– shortest path or all-pairs-shortest-paths algorithm– update local forwarding table

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DV versus LS Routing

1. only neighbor-to-neighbor info exchange about what each has learned - low overhead

2. link costs: simple hop counts

3. nodes have no idea of globaltopology

4. protocol convergence is slow- count-to-infinity problem

5. due to 3 & 4, routingloops can occur

1. each node gives info to all other nodes (only verified info)

2. link costs: delay, bandwidth, link reliability, distance, etc.

3. each node can contruct global topology from the info it receives from others

4. protocol convergence is fast

5. due to 3 & 4, routing loops do not occur

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hierarchical routing

• link state routing tax on subnet resources– for n routers, averaging k neighbors– memory footprint grows as kn– bandwidth overhead grows as kn– CPU cycles overhead grow as kn

• so, partition the overall subnet into much smaller, more manageable chunks (“regions”)

• delegate regional routing to the much smaller number of routers actually in that region

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the tradeoff

• with small regions, and limited connections into the next level of the hierarchy, routers gain much smaller, more manageable data structures

• the more levels, the longer the hop length of the average path

• for an N node subnet, (ln N) levels are optimal, with (e ln N) table entries per node

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hierarchical routing example

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broadcast routing: data to each host

• unicast to each host– source sends N flows, one to each address

• flood– still uses a lot of bandwidth

• multidestination routing– packet has list of all sinks, parsed by each router

• sink tree routing– each node must know current, global sink tree

... bullets in order of what?

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broadcast routing

• reverse path forwarding– approximate sink tree forwarding– for each broadcast routed packet received, a

router • checks which node sent the packet• checks current forwarding table• if packet comes in on the line going out to the source

– send copies out only on all other lines• if packet comes in on any other line

– drop it

• no extra packet info, no state, self-terminating• simple, easy, effective, efficient• Radia Perlman

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reverse path forwarding example

(a)subnet; (b) sink tree; (c) tree built by reverse path forwarding

sink tree: max 4 hops, 14 packets

reverse path forwarding: max 5 hops, 24 packets ...

... depending on what?

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multicast routing

• sending identical flows to network subset

• what is the great virtue of multicast?

• senders to group use a discrete group address

• group management (using, e.g., IGMP)– group creation, destruction

– dynamic membership

– local process discovers group out-of-band

– host learns group membership from local process

– routers learn group memberships from hosts

– routers tell other routers, maintain state

• registry of which groups are reachable through which routers (here is hierarchical addressing again)

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multicast and distance vector routing

• idea: “simulate” a spanning tree

• “flood and prune” protocols

• flood {(node, group)} info across internetwork

• routers prune themselves from “group tree”

– if no group host/router connections: send PRUNE msg

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DV multicast (DVMRP) in a nutshell

• each host in group G periodically says so to nwk• if group membership changed, router relays DVM

update packet: {(source, cost, {group})}• reverse path broadcast (RPB) updates• routers update forwarding table: {(group, {link})}• source-based “spanning trees” pruned de facto

– empty leaves/branches not in group forwarding tables• reverse path multicast (RPM)

– for G, forward on each listed link, except source link– why “source link”, why not just “arriving link”?

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spanning tree pruning example

(a) network (b) spanning tree for the leftmost router

(c) multicast tree for group 1 (d) multicast tree for group 2

(c) nodes do not have to be in group to be in pruned tree

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scaling issues for pruned spanning tree multicast

• group forwarding table and data structure growth of O(mn) on each router, for

– m, average number of group members

– n, average number of groups

• why?

– for each source, a “tree”

– for each group, m trees

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multicast and link state routing

• spanning tree computed locally with existing global link state

• each host in group G periodically says so to nwk

• group/router list applied to resulting spanning tree, going from each leaf to root

• if node is not in group, prune it from branch• if node is in group, so is its branch toward root

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core-based tree multicast

• each group designates a core node near the middle of the internetwork

• a single group spanning tree is computed, using the core as the root

• each group source sends its transmissions to the core, and thence along the single tree

• average path length is greater, but router overhead is reduced by factor of m

who might have a core-based tree, and where might its core be?

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protocol independent multicast (PIM-SM)

• (PIM dense mode, but prior protocols work)

• prior protocols do sparse mode poorly

– e.g., they broadcast updates by default

• PIM sparse mode (PIM-SM)

– routers explicitly join and leave groups, no global state

• “unicast routing protocol independent”

– PIM-SM depends on Internet Protocol

– particular unicast routing algorithm is irrelevant

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PIM-SM routing state maitenance

• well-known rendezvous point (RP) per group

• RP selection is complex

• router X tunnels Join message to RP

• RP unicasts Join message to router X– creates sender-specific state on router X branch– why?

• Prune culls unused branches, en route to RP

• result: unique, implicit, default, shared tree

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PIM-SM & PIM-SSM

• shared tree can be costly, if shorter paths exist between mcast source and some sinks

• source-specific tree for high-traffic source

• source-specific Join from sink to source creates source-specific tree

• resulting mcast route bypasses RP router

• PIM-SSM: source + group – allocated subset of mcast IP address space

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routing for mobile hosts

• stationary hosts• mobile hosts

– migratory hosts– roaming hosts

• for each host– permanent home location– permanent home address

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mobile host context

WAN, with LANs, MANs, and wireless cells attached

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how to find mobile hosts

• foreign agent in each geographical area– announces presence in area periodically– tracks all visiting mobile hosts

• home agent– tracks all mobile hosts that are away

• mobile host (MH) registers with foreign agent• foreign agent notifies home agent of MH• MH is now registered in foreign area

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routing for mobile hosts

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differences between mobile IP protocols

• protocol division between routers and hosts• host nwk stack layer responsible for protocol• intermediate router participation• host or foreign agent temporary address• forwarding by readdressing• forwarding by tunneling• security protocols

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Mobile Ad hoc NETworks (MANETs)• each node: mobile host/router combo• no infrastructure, cell tower, nor basestation• changing network membership, topology• lossy RF links (each node has antenna)

– links exist based on proximity, RF environment– fading, crosstalk, reflection, absorption, etc, etc

• mobile nodes provide all network services– routing– address assignment– name translation

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context of ad hoc networks

• military vehicles on battlefield– no infrastructure

• fleet of ships at sea– all moving, all the time

• emergency workers at earthquake– infrastructure destroyed

• gathering of people with notebook computers– “come as you are”

• sensor networks– self-organizing, not necessarily stationary

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example ad hoc networking algorithm: AODV

• Ad hoc On-demand Distance Vector routing• C. Perkins & E. Royer (1999, 2001)

• “mobile Bellman-Ford”• no full routing table update broadcasts• respects bandwidth, limited battery power• finds route to sink iff source actively seeking

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AODV route discovery

• link exists iff two nodes can hear each other• history table at each node: {(srcIP, reqID)}• routing table at each node:

– {(sink, next hop, <more>)}– all table info times out if not refreshed periodically

• if destination not in {(sink)}, then:– ROUTE REQUEST– (srcIP, reqID, sinkIP, src seq#, sink seq#, hop#)

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ROUTE REQUEST processing

• ROUTE REQUEST packet received• if (srcIP, reqID) in history table, drop packet

• if (local sink seq#) > (RTE REQ sink seq#)– send ROUTE REPLY (“this node is next hop”)

• else, increment RTE REQ hop#, enter route to src in own table, flood RTE REQ onward

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ROUTE REQUEST processing

• ROUTE REPLY– (srcIP, sinkIP, sink seq#, hop#, TTL)– sent back to neighbor RTE REQ came from– hop# reset, so src can know length of path– RTE REPLY follows (pruned) path of RTE REQ– nodes en route update info on route to sink

• side effect of ROUTE REQUEST flood– all nodes learn route to src, if not to sink

• TTL widening rings

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ROUTE REQUEST example

shaded nodes: new recipients; arrows: possible reverse routes

• (a) Range of A's broadcast.• (b) After B and D have received A's broadcast.• (c) After C, F, and G have received A's broadcast.• (d) After E, H, and I have received A's broadcast.

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AODV route maintenance

• HELLO (“I’m still alive”)• reply to HELLO (“me, too”)

• “disappeared” neighbors prompt table purge• routing table

– {(sinkIP, egress, #hops, {active neighbor}, <etc>)}– “active neighbor”: uses local node to get to sink

• purge proceeds through MANET recursively

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AODV route maintenance example

(a) D's routing table before G goes down

(b) graph after G goes down