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Routing algorithms. Yaakov (J) Stein Sept 2009 Chief Scientist RAD Data Communications. Outline. Control Plane principles of IP routing longest prefix match RIBs and FIBs Forwarding plane classification and lookup mechanisms switching fabrics.

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routing algorithms


Yaakov (J) Stein Sept 2009

Chief Scientist

RAD Data Communications


Control Plane

principles of IP routing

longest prefix match

RIBs and FIBs

Forwarding plane

classification and lookup mechanisms

switching fabrics


A router is a combination of hardware, software, and memory

that is responsible for forwarding packets towards their destinations

Routers generally work at ISO layer 3 (network layer)

but can also function at layer “2.5” (for MPLS)

and may inspect higher layers, but only for optimization

(QoS management, load balancing, etc.)

Note that Ethernet switches technically filter rather than forward

In order to correctly fulfill their function (i.e. to know where to forward)

routers usually run routing protocols

to exchange information between themselves

Ethernet switches do not need such protocols as they learn how to filter

So the router performs 2 distinct algorithms :

  • forwarding algorithm (forwarding component)
  • routing algorithm (control component)



what does a router do
What does a router do ?

Control plane (routing algorithm)

  • run routing protocols
  • identify interface and next hop L2 addresses
  • populate RIBs (if Link State, perform SPFs)
  • scan all RIBs, and produce FIB (entries map FEC to NH)

Data plane (forwarding algorithm)

  • deframing (CRC/checksum/defragmentation/reassembly/demapping…)
  • parsing (pulling values from appropriate fields – simple IPv4 DA, complex finding URL or MIB variable)
  • FEC classification (add metadata, based on DA, DA+ToS, MPLS, …)
  • lookup / search
  • packet modification and replication
  • framing
  • traffic management and queuing
  • compression, encryption, etc.
ip networks
IP networks

IP networks are made up of

  • hosts
  • middleboxes(e.g., firewalls, NATs, NAPTs, Application Layer GWs)
  • routers (obsolete terminology – gateways)

It will be useful to differentiate between

  • core routers (connect to other routers)
  • edge routers (connect to hosts)

We will see shortly that it is more complex than that

To understand how a router is different from other network elements

we need to know the basic principles the IP protocol architecture

We will mainly deal with IPv4 unicast forwarding

Routing Slide 6

the basics 1
The basics (1)

The first principle of IP is the end-to-end (E2E) principle

All functionality should be implemented only with the knowledge

and help of the application at the end points

The second principle is the hourglass model

  • IP (l3) is the common layer
  • below IP (L3) is not part of IP suite, above is

Thus :

  • most functionality and state is in the hosts
  • middlebox functionality is severely limited
  • routers are limited to forwarding packets

without extensive packet manipulation (exception - TTL)

The third principle is that forwarding is

  • connectionless
  • on a hop-by-hop basis

ftp, http, …



Ethernet, PPP

UTP, optic,


Routing Slide 7

the basics 2
The basics (2)

The fourth principle is that unicast IP forwarding is performed

based on a Destination Address (DA)

  • Addresses must usually be unique (end-to-end principle)
  • Hosts usually have a single IP address, routers have many addresses
  • It is the responsibility of a service provider (SP) to allocate addresses

IP addresses are not arbitrary, like Ethernet MAC addresses

The fifth principle is that IP addresses are aggregated into subnetworks

  • All addresses in a subnetwork share a common prefix
  • Subnetworks may be further aggregated

The sixth principle is that it is the responsibility of the router

to forward towards the host’s subnet

but it is not its responsibility to deliver the packet on the subnet

  • the IP suite starts above L2
  • subnet’s L2 (e.g., Ethernet, PPP) delivers the packet to the host
ip routing types
IP Routing types
  • Distance Vector(Bellman-Ford), e.g. RIP, RIPv2,


    • send <addr,cost> to neighbors
    • routers maintain cost to all destinations
    • need to solve “count to  problem“
  • Path Vector, e.g. BGP
    • send <addr,cost,path> to neighbors
    • similar to distance vector, but w/o “count to  problem“
    • like distance vector has slow convergence*
    • doesn’t require consistent topology
    • can support hierarchical topology => exterior protocol (EGP)
  • Link State, e.g. OSPF, IS-IS
    • send <neighbor-addr,cost> to all routers
    • determine entire flat network topology (SPF - Dijkstra’s algorithm)
    • fast convergence*, guaranteed loopless => interior routing protocol (IGP)

*convergence time is the time taken until all routers work consistently

before convergence is complete packets may be misforwarded, and there may be loops


Control Plane



Based on the 6 principles we can understand what a router does

  • The router looks at the packet’s DA
  • It deduces to which subnet the packet belongs
  • If the router can directly interface that subnet

it must use the appropriate L2 to send the packet to the host

  • Otherwise it must retrieve the next hop (router)

that sends the packet towards the subnet

  • The next router does the same
  • If routing has converged there will be no loops or black holes

but there may be during transients

The information needed by the router to properly forward packets

is stored in the Forwarding Information Base (FIB)

The FIB associates address prefixes with Next Hops (NHs)

(and, to save an additional lookup, usually with L2 addresses as well)

Do not confuse the FIB with a Routing Information Base (RIB)

more on fibs
More on FIBs

Simple (and primitive) routers have a routing table

modern large routers have several different databases

The FIB is designed to be fast to search

we will talk about its data structure later

RIBs are designed to be fast to update

which is quite a different structure

There may be many RIBs, one for each routing protocol running

and static routes may be entered into any of them

There are sometime other databases as well

for example – link state routing protocols require a LSDB

from which the RIB is built

The basic idea is that we build the FIB from the RIBs

router interfaces
Router interfaces

Routers connect to hosts and to other routers via interfaces

(from 1 to many thousands of interfaces per router)

Routers are responsible for forwarding packets

  • arriving at an ingress interface
  • to an egress interface

Interfaces have layer 3 and above properties

and also contain layer a and 2 properties (ports)

Each interface is assigned a unique IP address

Interfaces are grouped into subnetworks

All interfaces on a subnetwork share the same prefix







prefixes and masks
Prefixes and masks

Since 1993 (RFC 1519 - CIDR) subnets can have any length prefix

There are two ways of specifying the prefix length

  • slash notation, e.g.,

note – unspecified bits are set to zero

  • mask notation, e.g., with mask

Note that means all addresses

from through

Note that it contains,, etc.

since they are in the range and have longer prefixes (larger masks)

/32 are fully qualified IP addresses matches every IP address –

  • it is the default route

route taken when there is no matching entry in FIB

  • the gateway of last resort
prefix tables
Prefix tables

Note :

for /25 D=0 or 128

for /26 D= 0, 64, 128, or 192


special ip addresses
Special IP addresses

Some IP addresses are reserved for special purposes

they are not assigned by IANA

and may require special treatment by router

longest prefix match and fecs
Longest prefix match and FECs

To find the subnet, we need to look at the packet’s DA

  • and to find the best match for the DA that is known
  • find known the FIB entry that matches the longest prefix of the DA (LPM)

All packets that are forwarded in the same way are grouped

into a Forwarding Equivalence Class (FEC)

In the simplest case, a FEC is simply a known IP address prefix

i.e., the packet’s subnet

In more complex cases it might get more complex

for example, ToS field, source address, etc.

Every packet has to be looked up in the FIB and classified to a FEC

and this forwarding has to be done fast


Assume the following FIB

and let’s look up (last byte 10000011)

It matches the first entry with prefix length 0 (everything matches)

It matches the second with length 24 (first three bytes)

It matches the third entry with prefix length 25 (last byte 1xxxxxxx)

It does not match the fourth entry (11xxxxxx )

So the packet is forwarded to next hop C

packet processing time
Packet processing time

How much time do we have to process a packet ?

disregarding L2 overhead, IPGs, etc.

So the FIB data structure has to be optimized for fast look-up

policy and autonomy
Policy and autonomy

The FIB information is based on :

  • static routes
  • dynamic routes determined by routing protocols
  • gateway of last resort (default route)

In general we need to apply policy, since

  • there are conflicting sources of information
  • may not want to use, or even believe, information received from peers
  • it is all a matter of autonomy
  • an Autonomous System can request service from another

but can not force it to provide service

autonomous systems
Autonomous systems

Routers are grouped into Autonomous Systems (ASs)

ASs may be grouped into domains

AS look to the outside world as single entity (they usually have an AS ID)

Routers in the same AS obey a common policy, and trust each other

AS are truly autonomous

one AS can request another to forward a packet, but can not force it to

Inside ASs we run Internal Gateway Protocols (IGPs)

  • e.g. OSPF, IS-IS

Between ASs we run External Gateway Protocols (EGPs)

  • e.g., BGP

A router that runs both is called an ASBorder Router (ASBR)

more of the story
More of the story

Actually, it can get a lot more complicated

In general, a router will be running multiple routing protocols

For example :

  • one or more IGPs (RIP,OSPF, IS-IS) between routers in the same AS
  • internal BGP (iBGP) between routers in the same AS

(usually a full mesh, but when too complex we can use route reflectors)

  • external BGP (eBGP) between ASBRs in different ASs

How does a router know if a BGP session is iBGP or eBGP ?

  • by the AS number !

IGP is used to find a path to another router (including ASBR) in the same AS

eBGP is used by ASBRs to learn / distribute routes to other ASs

iBGP is used for ASBR to inform core routers of external routes

simplest example
Simplest example

Stub ASs (my home router)

  • single homed to outside world
  • single internal subnet, so don’t need IGP
  • single homed, so don’t need to run BGP to ISP
  • don’t need to have an AS number







more complex example
More complex example

Connecting to a server connected to another ISP with dual homing

  • Routers 3 and 6 learn from eBGP how to reach A.B.C.D
  • Policy determines that 3 will be used (see later)
  • Router 1 learns from iBGP session that A.B.C.D is reachable via router 3
  • Router 1 learns from IGP that router 3 is reachable via router 2
  • Router 2 knows how to directly reach router 3 because of IGP adjacency
  • Packet from a.b.c.d is forwarded via 1-2-3 to AS 2 and to A.B.C.D









AS 2

AS 1

eBGP sessions

Full mesh of iBGP sessions


even more complex example
Even more complex example

Three ASs, with one possibly acting as a transit domain

AS 2

AS 1

AS 1 would like to hand off the traffic to AS 2

AS 2 has no economic incentive to carry this traffic

But AS 2 gets the route from AS3

What can AS 2 do to stop this ? (remember autonomy!)

What can AS 1 then do ?


rules for customer ass
Rules for customer ASs

Stub AS

Single-homed AS does not need to learn routes from provider

It only has to send all traffic via its unique exit point (

Provider gets routes from static or IGP or private-AS eBGP

Multihomed Nontransit AS

AS advertises only its own routes to both SPs

AS filters out traffic for foreign routes that reach it via static/default routing

eBGP is not needed, but recommended for route propagation and filtering

Multihomed Transit AS

Uses eBGP to SPs and iBGP for transit traffic

bgp rules
BGP rules

There are :

  • internal routes
  • external routes
  • customer routes

When eBGP learns a route it is repeated via iBGP to all others in AS

thus all routers in AS learn it

When iBGP learns a route it is repeated only to externals via eBGP

since internals also get it directly

When there is another ASBR that can reach the same other AS

a second route is repeated by iBGP to the ASBR

The ASBR will then make the decision as to which to use !

igp rules
IGP rules

IGPs are used between routers in the same AS

  • so IGPs do not have sophisticated policy control
  • routers usually blindly accept all information received

For proper operation (no routing loops)

  • all routers in AS must have the same IGP RIB
  • for link state protocols (OSPF, IS-IS)

there is a Link State Data Base (LSDB)

from which IGP RIBs can be constructed (will be explained shortly)

Because all routers have the same LSDB

Although the forwarding is hop-by-hop

the result is the same as if there were coordination


  • do not scale to inifinity
  • require complete knowledge
  • are not suitable for interaction with non-trusted routers

since a single misconfiguration can be fatal


We said before that LS routing protocols have another database

LSDB contains representation of every router and link in the AS

implicitly holding the complete topology of the network

In addition, the LSDB associate costs (metric) with every link

  • RIP - the metric is always hop count, no non-trivial metric
  • OSPF - the metric is more general, for example link length

These costs form a matrix

The topology is symmetric, but the costs need not be

lsdbs and igp ribs

Each router can independently calculate the least-cost path

to every other router in the AS

A Shortest Path First (SPF) algorithm (e.g., Dijkstra’s algorithm)

is used to compute a tree of the shortest paths to all destinations

Each route in the SPF tree is an entire path

but for each router we can extract the next hop

and build the RIB for that router (each router has its own RIB)

From the RIBs we build the FIB needed for efficient forwarding of packets

graph search algorithms
Graph search algorithms

There are many algorithms for search on graphs :

  • Breadth first
    • Bellman-Ford
    • Iterative deepening
  • Depth first (backtracking)
    • Depth limited
  • Best first
    • Greedy algorithms
      • Dijkstra’s algorithm
    • Beam search
    • A*
    • B*

etc. etc.

We will discuss graphs, trees, etc. later on










dijkstra s algorithm
Dijkstra’s algorithm

Graph search algorithm first described by Edsger Dijkstra in 1959

It assumes additive, non-negative, costs for each link in graph

It is a best-first greedy algorithm

Think of a city street map

We want to from initial intersection to destination one with the least walking

Start at the initial intersection – its distance is zero

Measure and label the distances to all adjacent intersections (breadth first)

Choose the closest one (this is the greedy step)

Consider all the neighbors of the chosen intersection

If the distance (sum of the distance to the chosen intersection and the distance from chosen intersection to neighbor) is the shortest known way to get to that neighbor

then remember that distance (not a tree!)

Once you have considered all neighbors of the intersection

mark the chosen intersection as visited (its distance is now known)

Choose the unvisited intersection with shortest distance

Continue until all intersections have been visited

dijkstra s algorithm formal
Dijkstra’s algorithm - formal

Let's call the node we are starting with an initial node.

The COST of node X will be the distance from the initial node,

i.e., the sum of distances of all links along the path from the initial node to X


Set initial node’s COST to zero, all others to infinity

Set initial node as current, all other as unvisited

Main step

For all unvisited neighbours of current node :

Calculate their distances from the initial node as

COST(neighbor) = COST(current) + DIST(current to neighbor)

If this is less than what is presently marked, overwrite the marking

When all neighbors have been considered, mark current node as visited

(once visited, this node’s COST is final)


Select the unvisited node with the smallest COST as current node

Go to Main step

implementation issues
Implementation issues

If our graph has N nodes and L links

In a straightforward implementation of Dijkstra’s algorithm

  • finding the unvisited node with lowest cost takes O(N)
  • this is done N times
  • so the total computation for this is O(N2)
  • the computation of the distances to every node takes O(L)

since each link is followed once (to the node it lands on)

So the total complexity is O(N2 + L) ≈ O(N2)

By using more sophisticated data structures (Fibonacci heap)

this can be reduced to O(N log N + L) ≈ O(N log N)

ribs to fib

So we are finally ready to see how the FIB is populated

First rejection rules are applied, for example :

  • do not accept routes from ASs without agreements
  • do not accept routes that loop

(e.g., BGP advertisements with AS number in the AS-PATH)

Then install FIB entries according to policy, for example :

  • first install Static routes
  • then routes from IGP RIB
  • choose eBGP before iBGP (hot potato rule- get it out of my network - let someone else handle)
  • if there are different routes from BGP choose the route with highest local preference
  • if routes have equal local preference choose the route with the shortest AS-PATH
  • if routes have equal AS-PATHs choose the route with the lowest origin number
  • if still equal choose highest BGP peer address

Not everything received is accepted for inclusion in the FIB

Not everything accepted for inclusion in the FIB is further advertised

Never advertise information not accepted to FIB !

RIB in

RIB local

RIB out





Best path



Now that we have a FIB installed, let’s forward some packets !

There are main steps to forwarding :

  • classification
  • switching
  • misc. (scheduling, queuing, QoS, compression, encryption, …)

The operations

  • may be stateless vs. statefull
  • may change over time
  • may involve peeking into the packet (Deep Packet Inspection)
  • may be recursive

Packet forwarding can be done by SW or HW or some combination

We normally differentiate between

  • the fast path (simple forwarding)
  • the slow path (control protocol packets)
lookup and data structures
Lookup and data structures

Lookup comes in several varieties, such as :

  • Exact match (e.g., MAC addresses, VLANs, IP multicast)
  • Longest Prefix Matching (LPM) (needed for searching FIBs)
  • Range matching (e.g., ports, firewalls)

In order to optimize lookup, we use appropriate data structures

Wirth’s law Programs = algorithms + data structures

We need to perform the following on our data structures :

  • Insert
  • Delete
  • Modify
  • Search

and to check the following metrics :

  • Time complexity for each of the above
  • Size (spatial) efficiency
  • Scalability
lookup table
LookUp Table

The simplest (and fastest) data structure is the LookUp Table (LUT)

AKA indexed array, Location Addressable Memory (LAM)

The incoming address is used as an index to access the (NH) information

We can put in more info, e.g., L2 type and address, to save further lookups

Example :


  • only for exact match, not LPM
  • limitation only for small number of possible addresses, e.g. VLANs

We can use LUTs after other data structures that return a key as an index

hash tables
Hash tables

Hash tables enable handling a large number of potential addresses

A hashing function is a function

  • from a large variable (large number of bits or large number of bytes)
  • to a small variable (small number of bits or bytes)

which is white (small changes in the input create widely different outputs)

Hashing long addresses returns a short index

The problem is that the hashing function is not 1:1

so there will always be the probability of hash clashes (collisions)

Solutions :

  • perfect hashing – only when addresses are known ahead of time
  • index in table returns list of all addresses stored
  • multiple hashing – linear probing, quadratic probing

Hashing is very good for exact match (e.g. MAC addresses)

but is not suitable for LPM

hash implementation
Hash implementation

From an efficiency point of view

hash tables are between LUTs and search tables (to be discussed next)

To control collisions, we need a relatively large table (birthday paradox !)

Example :

99% probability of collision

when 3000 entries are put into a hash table of size 1 million

Using multiple hashing

average computational load is O(1 + keys/table-size)

A primitive hash function is the modulo hash

H(key) = addr mod table-size

table-size should be prime – must not be a power of 2 or close

A better hash function is (for appropriate integer m and fraction f)

H(key) = Trunc [ m Frac( f addr) ]

The quality of the hashing function depends on f

For Fibonacci hashing : f = 1 / γ

γ is the golden ratio ½ (√5 – 2) ≈ 1.618

23 people – ½

57 people – 99%

search table
Search table

The most spatially efficient data structure is the search table

It is similar to a LUT

but the addresses being looked up are not indexes

rather, we need to sequentially search the table for the address

We can reduce the search time by ordering the table

Search tables are good for LPM !

For example :

Order FIB from most specific (longest prefix) to least (

Loop through FIB list until find the first match

limitations of search tables
Limitations of search tables

Search tables are not limited in size like LUTs

but this comes at a price

  • it is expensive to search for an address
  • it is expensive to modify the information for an address
  • it is very expensive to insert or delete addresses (copy!)

Search table FIBs can be rebuilt from RIBs each time

For exact match it is possible to speed up by binary search

  • order by address
  • guess position in middle of table range where key should be
  • choose new range by comparison
linked lists
Linked lists

Search tables are hard to maintain

if we need to insert or delete an element we need extensive moving

Linked lists are designed to simplify mechanics of such updates

still need exhaustive search to find where to insert

Linked lists can be singly or doubly linked

Skip lists increase efficiency by enabling skipping over ranges





linked list implementation
Linked list implementation

If we already know where to insert or what to delete or whom to modify

then linked lists are very efficient

However, search is O(N) where N is the number of entries

worst case N

average case N / 2

Properly constructed multi-level skip lists take O(log N) on average

but are still O(N) in the worst case

But if we already need to use double pointers

then trees are better

tree structures
Tree structures

A graph is a collection of nodes and edges connecting them

In a directed graph the edges have direction

and so or every edge there is a father node and a child node

Nodes without children are called leaves

A forest is a directed graph without loops (only one path between 2 nodes)

A tree is a forest with a single root -- it thus defines a partial order

(it is conventional to draw the tree upsidedown)

A binary tree has no more than 2 output edges per node

Trees can be implemented using arrays, pointers (like linked lists), heaps, etc.





search trees
Search trees

Search trees may store data

  • in their nodes
  • in leaves only
  • on edges
  • combinations of the above

For general search trees searching can be breadth-first or depth-first


  • start at the root
  • find all children of root and check for desired data
  • if not found, find all children’s children
  • recurse

Depth first

  • start at the root
  • find first child and check for desired data
  • if not found, find first child of first child
  • recurse until data found or leaf
  • if leaf backtrack to father and try the next child
binary trees
Binary trees

Binary Search Trees simplify storage and manipulation

We call the children of a node – L and R

Perfect binary trees have exactly 2 children for each internal node

Thus there are exactly 2H leaves, where H is the height of the tree

Altogether there are (2H+1 – 1) nodes

To store keys in a binary search tree

  • place keys in all nodes
  • for every intermediate node N
    • key(L) < key(N)
    • key(R) > key(N)

To search for a key in a BST

  • start at root (set current node to root)
  • check if key is stored in current node
  • if not : if key < key(N) then set current to L else set current to R

In the worst case this takes only H comparisons (for perfect trees O(log N))




balanced binary trees
Balanced binary trees

Since the search complexity is proportional to the BST’s height H

we would like to use BSTs with minimal height

Balanced BSTs are not perfect BSTs, but as close as possible to perfect

It is more complex to build a balanced BST, but faster to search




















From retrieve, but usually pronounced try

A trie is an ordered tree with

  • subvalues on edges
  • values at leaves

Tries are related to prefix search representations

Tries were originally developed for exact match

Tries can be binary or not

Tries are good for all lexicographical searches O(log n)

but particularly efficient for LPM

Trie variants are the fastest known lookups - O(log log n)

  • LC-trie used in modern Linux router implementations
example trie
Example trie




Assume the following FIB :


in the plain trie,

all IP prefixes have the same length



















example compact trie
Example compact trie



Same FIB :

Now maximum length is 2

We could also save memory by exploiting common suffixes





more trie variants
More trie variants

Patricia trie

Practical Algorithm to Retrieve Information Coded in Alphanumeric

  • Binary trie which store in nodes the number of bits

to skip before next decision point

  • For LPM store prefixes in internal nodes

Bucket tries

  • Store multiple keys in leaves

Multibit tries (M-tries)

  • Fewer branching decisions than binary tries
  • Multibit strides (usually variable strides)

Level-compressed tries (LC-tries)

  • Replace perfect subtrees in binary trie with single degree 2k nodes
  • LPC trie – level and path compressed

And there are many more (Lulea, full-tree, …)

example lc trie
Example LC-trie

binary trie LC-trie

content addressable memory
Content Addressable Memory

CAM (AKA associative memory)

Addressable by content, rather than by location (LAM)

Special purpose hardware

  • Fastest possible lookup (essentially searches entire table in one clock)
  • but limited in size
  • usually drives regular memory for additional storage

Binary CAM (BCAM) stores 0 or 1 in each bit

Ternary CAM (TCAM) allows wildcards

  • Can be used for LPM
  • Can prioritize solution by
    • number of bits matched
    • order in table

CAM technology today

  • 32 to 144 bit keys
  • 128K – 512 K memories
  • hundreds of millions searches per second
example 3 bit bcam
Example – 3 bit BCAM











match lines

search lines

encode output

to access LAM

search word




other uses of lookup
Other uses of lookup

Deep Packet Inspection

  • URL lookup (often partial or with wildcards)
    • can use Trees and tries
  • XML information, patterns, etc.
  • multiple encapsulations
    • e.g. Ethernet in IP, MPLS over IP, etc.
    • there are special-purpose languages to describe such cases

Firewalls, Access Control

  • source/destination IP addresses + source/destination ports 4-tuples
  • TCP/UDP ports in ranges

Once the packet has been classified we need to properly forward it

The classifier result (the FEC) becomes a metadata field

that controls the switch

A switch fabric is combination of HW and SW components

that enable moving the packet from input interface to output interface

The metaphor is borrowed from woven material

At low packets per second (pps) switching can be all software

At high speeds highly parallel hardware is needed


The major design constraint in switches is blocking

Blocking occurs when some resource is being used

and the present packet can not be processed

We differentiate three types of blocking

  • Output blocking (the egress port is in use)
  • Internal blocking (some internal resource of the switch is in use)
  • Input (head of line) blocking (packet can not enter the switch)

A switch which is designed such that there is never internal blocking

is called a nonblocking switch

To alleviate blocking we can add buffers to store the waiting packets

According to the type of blocking we wish to avoid we have

  • output queues
  • internal buffers
  • input queues
switch types
Switch types

In the TDM days there were two switching mechanism types :

  • time domain switches (time slot interchange)
  • spatial domain switches

For packet networks there are no time slots

but time domain switching can still be used

  • shared memory switches (packets from all inputs placed in single memory)
  • shared bus switches (all inputs and outputs share a ring/hypercube, etc. )

In spatial switching

the packets destined for different output interfaces

travel different internal paths

The simplest spatial switch is the crossbar

invented for analog telephone circuits

does not scale well – O(N2) possible connections

Multilayer crossbars can scale better
















shared memory bus
Shared memory/bus

Shared memory switches are simple and cheap to implement

The memory is the heart of the fabric

it determines the throughput and delay

The memory must run N times faster than the ingress rates

Packets may be divided into frame buffers

Scalability can be achieved by parallelism (bit or byte slicing)

The architecture breaks down at high speeds

Shared bus switches are similar in principle to shared memory ones

The shared medium is the heart of the switch

and determines its characteristics

Scalability can be achieved by parallelism (parallel buses)

The architecture breaks down at high speeds

multistage crossbars
Multistage crossbars

Crossbars are fast, but

  • are not nonblocking
  • do not scale

These problems are solved by multistage crossbars

The only blocking of a single stage crossbar is output blocking

more than one packet needs to leave the egress interface

Time-space switches solve this by sorting the frames before switching

More complex architectures are time-space-time switches

There are many multistage solutions to the scaling problem …

1 2 3 4

1 2 3 4

2 3 4 1

2 3 14

3 4 1 2

3 4 1 2

4 1 2 3

4 1 2 3

clos network
Clos network

The Clos network is more efficient than a single N*N crossbar

We divide N into r groups of n N = n r

It has 3 stages of crossbars

  • the first stage has r groups of n*n crossbars
  • the second stage has n groups of r*r crossbars
  • the third stage has r groups of n*n crossbars

The shuffle rule : Xth output of Yth crossbar connects to Yth input of Xth crossbar

Instead of N2 = n2r2 connections

just r2 n + 2 r n2

For example:

if r = n = √N

then instead of n4 just 3n 3

a reduction by 3/n = 3 / √N



benes network
Benes network

The Benes network contains only 2*2 crossbars

and is built recursively

For N = 2n, the network has 2n-1 stages and 4 N log (N-1/2) connections

The shuffle rule is that 1st outputs go to the 1st block, 2nd to the 2nd



banyan network
Banyan network

The Banyan network is a binary tree of 2*2 crossbars

with exactly one path from each ingress interface to each egress interface

At each stage the next bit of the identifier determines the switching

Banyan switches are time and space efficient

  • O(log N) delay
  • ½ N log N 2*2 crossbars

The main problem is internal blocking at any of the crossbars

One way to relieve this is to speed up the crossbars and to add buffers



batcher s sort
Batcher’s sort

To prevent internal blocking in a Banyan switch

we can first sort the frames according to egress interface

When this is done with Batcher’s parallel sorter

½ log N ( log N + 1) stages of simple sorters

we get the Batcher-Banyan switch

to Banyan switch

4th order Batcher sorter