Routing

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Routing

• Routing in voice networks
• Routing in data networks
• Vector distance routing
• Link state routing
• Distributed Bellman-Ford algorithm
• Routing information protocol (RIP) and open
  shortest path first (OSPF) for the Internet

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ROUTING FUNCTIONS

• The major functions of a network is to enable
  different users to communicate with each other by
  making use of the network, as shown below

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• Through the routing function performed by the
  network, user1 is able to communicate with user2
  by
• setting up a circuit between user1 and user2, in
  the case of circuit-switched networks or
• exchanging data units (frames, cells, packets)
  between user1 and user2, in the case of data
  networks.
• The objectives of network design are to
  accommodate the expected user traffic under
  specified network conditions, this is done by
• producing a network topology at minimal equipment
  cost (e.g., minimum spanning tree, cheap access
  network)
• performing the routing functions

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Routing functions (cont.)

• There can be three major components of the
  routing function to be performed by a network
• Collecting and distributing of state information
  about the users and the network itself
• Determination of the route according to some
  criteria, this is the routing algorithm that
  determines the path between each pair of users
  usually an optimum criteria (such as least cost
  or shortest delay) is to be satisfied while the
  routes are to be determined, it is desirable for
  a routing algorithm to be

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Routing functions (cont.)

• correct -- user traffic are routed to the
  correct destination
• robust -- cope with changes in topology and,
  traffic
• stable -- convergence to an equilibrium
• simple -- easy implementation and maintenance
• fair -- every user is equal
• optimal -- the best use of the network is got.
• Forwarding the user traffic - mode of operation
  may be connection-oriented or connectionless.

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ROUTING IN VOICE NETWORKS

• in a circuit-switched network, two users are
  "connected up" together through a circuit so that
  they can communicate
• the telephone network is an example network of
  this kind
• routing is the selection of a path to connect two
  users
• the circuit between two users, once has been set
  up, is dedicated to their use until the circuit
  is disconnected

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• blocking occurs when a free user calls another
  free user but the circuit cannot be set up
  between them because of the network resource
  problem
• a major quality of service (QOS) is the blocking
  probability
• an example of blocking

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• when a path is to be set up between user 1 and
  user 2, the usual requirements are
• the path can be set up (otherwise the call is
  blocked)
• if there are many different ways to set up the
  path, it is preferable to set up the path such
  that it should not increase much the blocking
  probability for "future traffic" in other parts
  of the network
• since the traffic entering a telephone network
  changes according to the time of day, a dynamic
  routing algorithm, which can cope with traffic
  changes, will perform better

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Dynamic alternative routing (DAR)

• this is a routing algorithm for the telephone
  network developed by British Telecom
• the network model is

• when traffic between a node pair is offered to
  the network, the first-choice circuit is the
  direct link between the two nodes, through two
  directly connected parents

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• if no direct link is available, a two-link
  alternative is to be sought, since two links are
  engaged for this call, this will lessen the
  chance of establishing circuits for future calls
• the above problem can be alleviated by
  implementing a trunk reservation scheme with a
  trunk-reservation parameter r
• a two-link alternative is accepted only if more
  than r circuits are free for this two-link
  circuit
• under overload condition when there are not so
  many free circuits, the two-link alternative
  routes are effectively suppressed, thus
  preventing the spread of overload

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Dynamic nonhierarchical routing (DNHR)

• this is another dynamic routing algorithms for
  circuit-switched networks, which is employed in
  ATT's long-distance network
• similar to the network model for the DAR
  algorithm, there is a direct route between two
  switches, and several ordered alternate routes,
  which have been computed off-line with reference
  to network topology and traffic forecast

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• when the direct route is full, the ordered
  alternate routes are tried one-by-one until the
  call is connected
• if no alternative route is free, the call is
  blocked
• in the course of setting up the circuit, blocking
  may occur at any stage, in case that intermediate
  links are blocked, there can be different schemes
  to handle these situations, namely originating
  office control (OOC), sequential office control
  (SOC), and crank back

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Originating office control (OOC)

• according to OOC, in case that a chosen route is
  blocked, the choice of the next route to try is
  always made by the source node (i.e. the
  originating office)
• suppose that for a network as shown below

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• in this example, three routes have been computed
  for traffic from node A to node F, namely
  A-B-C-F, A-B-E-F, and A-D-E-F
• if a particular route is blocked, all the
  intermediate reserved links will be released and
  a blocking message is passed all the way back to
  node A, node A will then try another computed
  route
• disadvantage of this method
• A does not know where blocking occurs, from the
  given example, if A-B link is blocked, it is
  useless for A to try A-B-E-F in the second route

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Sequential office control (SOC)

• Also known as progressive control, sequential
  control, spill-forward without crankback
• to overcome a disadvantage of OOC, the SOC scheme
  allows intermediate nodes to react to blocking
• when blocking occurs, the intermediate node tries
  to set up the call on another link, if no links
  are available at an intermediate node, the call
  is blocked

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• an example

• each intermediate node will have a set of
  possible outgoing links to try
• if the link B-C is blocked, B is responsible to
  try B-E

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Crank back

• also called spill-forward with crank back
• this is an improvement over SOC, a blocked
  message is allowed to be sent back to the
  upstream nodes in the routing tree
• for example

• if the call request travels over A-B-E but B-E
• link is blocked, the blocking message is passed
  back to A, so that A may choose another route
  (e.g. maybe A-D-E)
• the call is blocked only when non of the paths
  defined in the routing tree are available, i.e.
  when A-D, D-E, and E-F are blocked

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ROUTING IN DATA NETWOKRS

• in data networks, user data are routed from
  source to destination along a path chosen by the
  routing algorithm
• the data are usually in the form of packets
• as far as a network node is concerned, the
  routing algorithm decides which output line an
  incoming packet should be transmitted on to, as
  shown in the following

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• if the total input rate to a node is ?., the
  output rates to the outgoing links may be denoted
  as ?1?, ?2?, ?3?
• if it is assumed that packets will not be created
  nor destroyed within a node, to maintain the
  continuity of traffic flow, for each node the
  following holds
• ?1 ?2 ?3 1, ?i ? 0
  for i1,2,3
• according to the way to choose the ?-variables,
  routing algorithms may be classified as
  centralized or distributed
• according to the time interval between updates of
  the ?-variables are made, routing algorithms may
  be classified as static or dynamic
• according to the range of possible values of the
  ?-variables, routing algorithms may be classified
  as fixed or alternate

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Centralized vs. distributed routing

• a centralized algorithm employs a central
  controller to determine the ?-variables for the
  entire network
• the central controller bases its decisions on
  global information about conditions everywhere in
  the network, such as the state of the network,
  and the state of the user traffic
• disadvantages of centralized routing
• requirement of central controller leads to single
  point of failure

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• traffic in the vicinity of the controller will be
  high
• not feasible for very large network (e.g. the
  Internet with many of hosts)
• a distributed algorithm requires that each
  individual node decide the values for its
  ?-variables without coordinating its decisions
  with those of other nodes, these decisions are
  taken on the basis of local information only
• some routing algorithms employ a mixture of
  centralized and distributed features, they are
  known as "hierarchical

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Static vs. dynamic

• a static routing algorithm chooses the values of
  the ?-variables once and for all, and stay
  constant throughout the life cycle of the
  network's operation
• a dynamic algorithm updates the ?-variables
  constantly to reflect the changes in network
  topology and traffic conditions
• many practical routing algorithms are dynamic in
  nature, adapting themselves to the changing
  environment to achieve optimum (or sub-optimum)
  performance
• intermediate algorithms are called "quasi-static"

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Fixed versus alternate

• a fixed routing algorithm constraints the values
  of ? to be either zero or 1, as a result between
  two update instants, all traffic received will be
  assigned to the same outgoing link if the node is
  not the destination node
• an alternate routing algorithm allows ? to take
  any value between 0 and 1 as a result traffic is
  split between alternate routes (perhaps
  probabilistically)
• an alternate routing algorithm is also known as
  bifurcated routing

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MINIMUM NETWORK--WIDE DELAY ROUTING

• one approach to designing optimum routing is by
  choosing the ?-variables such that the
  network-wide packet delay is minimized
• the following example may illustrate the
  fundamental concept

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An example

• consider the following simple network

• in the above network, the line speed of the two
  links are 20kbps, and average packet size is 1000
  bits

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• user A is sending data to user B at a rate of 10
  packets/sec, i.e. the exogamous traffic is
  r(1,2) 10 packets/sec
• according to the network topology, there are two
  possible paths to route traffic from A to B,
  namely (1-2)up and (1-2)low
• if the traffic is split over the two paths with
  relative proportion ?1 and ?2, as illustrated,
  where ?1 ?2 1, the average network-wide delay
  can be calculated as follows
• each link is modeled as an M/M/1 queue

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• for the upper link, packet arrival rate is 10?1
  pkt/sec, service rate is 20,000/1,000 20
  pkt/sec, the link delay is
• for the lower link, packet arrival rate is 10?2
  pkt/sec, service rate is 20,000/1,000 20
  pkt/sec, the link delay is

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• the average network-wide delay T is given by the
  weighted sum of Tup and Tlow, each weighted by
  the traffic volume
• the standard way to determine the minimum value
  of T is by solving
• after ?1 and ?2 have been determined, the routing
  problem of this case has been solved.

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• or this example, a plot of T against ?1, is shown
  below
• from the above plot, it can be seen that when
  ?10.5 (i.e. ?2 is also equal to 0.5), the
  average network-wide delay is minimum, which is
  equal 0.067 sec approximately

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• this example demonstrates that minimum
  network-wide delay routing can be achieved by
  distributing the traffic over the links within
  the network in an appropriate manner
• since the ?-variables are usually non-zero, the
  resultant routing algorithm usually employs an
  alternate routing approach, which is also called
  bifurcated routing
• Bifurcated routing in general
• consider a network consisting of M links and N
  nodes
• the network is so modeled that each link can be
  modeled as independent M/M/1 queue

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• suppose link i has a total traffic of ?i
  traveling over it, and that the average rate of
  transmitting the packets over link i is ?i, then
  the delay time in traversing link i is Ti given
  by
• and the the average number of packets
  waiting to be transmitted on link i is obtained
  by Little's theorem, as

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• suppose the average network-wide packet delay is
  denoted as E(T), and the average number of
  packets within the network is E(n), and the total
  traffic input to the network is ?, then according
  to Little's theorem the following can be
  established
• E(n) ? E(T)
• therefore
• E(T) E(n)/ ?
• if all the links are treated as independent M/M/1
  queues, E(n) can be calculated as the sum of
  individual link occupancy, i.e.

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• the average network-wide packet delay is
• once the external traffic are known, and the
  routing algorithm is known, all the ?is and ?is
  are known, and then E(T) can be calculated
• the minimum network-wide delay routing problem is
  to route the traffic so that E(T) is a minimum

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SHORTEST-PATH ROUTING

• since shortest-path routing aims at routing the
  data from a source node to a destination node
  over the shortest path
• the total path length is the summation of the
  individual link cost along the path, if the link
  costs represent delay time, this gives rise to
  minimum delay routing if the link costs
  represent transmission cost, this gives rise to
  least cost routing
• the shortest path between two nodes can be
  determined by algorithms that have been discussed
  in graph theory

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• two algorithms (or their variations) have been
  widely adopted for routing in data networks,
  namely
• Dijkstra algorithm (for positive link costs) that
  finds the shortest path from one source node to
  all other nodes (this is called Algorithm A in
  Schwartz's book)
• Bellman-Ford algorithm (Algorithm B in Schwartz's
  book) that finds the shortest path from all nodes
  to one destination node, this algorithm works for
  negative link costs

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• both Dijkstra and Bellman-Ford algorithms can be
  implemented in a centralized routing manner,
  where a central controller computes the shortest
  paths for all node pairs, and then distributes
  the routing tables to all nodes the shortest
  paths may be computed regularly or after some
  changes in user traffic or network state have
  taken place, resulting in a dynamic algorithm
• they may also be implemented in a distributed
  manner where every node participates in
  determining the shortest path, the nodes must be
  able to gather and exchange information about the
  network with the use of a routing protocol

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Distributed shortest path routing

• also known as distance-vector algorithm
• as an illustration, consider a node N that has
  neighboring nodes X, Y, and Z, as below

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• node N knows the direct distance from itself to
  its neighbors according to the above diagram
• node N keeps a routing table containing the
  shortest path length to each destination, and the
  outgoing link to route to this destination, as an
  example

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• regularly node N receives routing information
  from its neighboring nodes, in the form
• as an example, X announces that it can send data
  to node A as the destination over a path with
  length 21 then N will reason in this way "If I
  send a piece of data to destination A by giving
  it to X, my direct distance to X is 4, and X will
  use a path with length 21 to reach A, then the
  total path length is 42125"

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• similarly, if X routes data to A via Y, the total
  path length will be 52227 via Z, the total
  path length will be 62531
• so N will decide to send data to A via X, since
  this is the shortest path with length 25 N will
  compile a table like this
• the underlined entries are shortest paths

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• hence N will have an updated shortest path
  routing table like this

• and N will send the following distance table to
  its neighbors

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• in practice not the entire distance table needs
  to be sent out, only those entries that have
  changed need to be sent out, these are in the
  form of d, Dd(N), where "d" denotes the
  destination node, "Dd(N)" denotes the minimum
  distance from node N to destination node d
• all nodes in the network participate in the same
  manner, and convergence to the shortest path is
  guaranteed in most practical situations

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Link-state routing

• each node maintains a link-state database, which
  is identical to what other nodes have got
  throughout the network
• the link-sate database describe the complete map
  of the network
• based on this link-state database, a node can
  calculate the shortest paths to any other node by
  using, for example, Dijkstra algorithm
• the link-state database is formed by the
  cooperation of all nodes in the network
• a node will gather its local information and form
  a part of the link-state database, known as
  link-state advertisements (LSA)

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• an LSA consists of the following information
• the identity of the node itself (e.g. node
  address)
• a list of the node's outgoing links
• the identity of the node to which each outgoing
  link connects
• the cost of each outgoing link (e.g. packet
  transmission time) when used to forward data
• consider node N as follows

neighbour
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• the LSA gathered by node N will be
• the LSAs are distributed throughout the entire
  network by a routing method called flooding
• when a node receives a piece of data, it will
  copy this piece of data to all its output ports
• after all LSAs from all nodes are gathered, the
  entire map of the network can be constructed and
  then the shortest path to any destination node
  can be calculated

Flash movie Net map based on LSAs
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Distributed Bellman-Ford algorithm (distance
vector revisited)

• Each node maintains two tables a distance table
  and a routing table.
• The distance table for node v lists the cost to
  each destination via each outgoing link (or
  equivalent to each neighboring node).
• The cost to destination d via a node w, denoted
  as Cd(v,w), is listed in row d and column w.

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Distributed Bellman-Ford algorithm (cont.)

• The routing table lists the minimum cost and the
  next-node assignment in the distance table.
  Assume Dd(v) minw Cd(v,w) Cd(v,p). The
  routing table will have a p and Dd(v) in row d.
• Example distance and routing tables for node N

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Distributed Bellman-Ford algorithm routing table
example

• Example Routing table for node N

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The distributed Bellman-Ford algorithm

• The distributed distance vector algorithm for
  node v, the routing table contains pairs
  (n,Dd(v)) (next neighbor (node), distance to
  node d from v), the link cost from w to v is
  denoted as l(w,v) the cost to destination d via
  the neighboring node w is denoted as Cd(v,w).

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The distributed Bellman-Ford algorithm (part 1)

• Part 1 link (m,v) comes up.On recognizing this
  event node v
• Sets entry (m,m) (m_th row,m_th column) cost to
  m via m of the distance table to l(m,v).
• Computes minw Cm(v,w) Cm(v,p).
• If Cm(v,p) Dm(v), set Dm(v) Cm(v,p). The
  routing table is changed to (p, Dm(v)), and the
  control message m, Dm(v) is sent to all
  neighbors.
• The routing table is sent to m, each row of the
  routing table as one control message.

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The distributed Bellman-Ford algorithm (part 2)

• Part 2 cost of link (m,v) changes.On
  recognizing this event node v
• Makes the change in the column m (corresp. To
  node m) in all distance table.
• Computes minw Cm(v,w) Cm(v,p).
• If Cm(v,p) Dm(v), set Dm(v) Cm(v,p). The
  routing table is changed to (p, Dm(v)), and the
  control message m, Dm(v) is sent to all
  neighbors.

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The distributed Bellman-Ford algorithm (part 3)

• Part 3 A control message d,Dd(w) is received
  by node v.If dv (destination is v itself), v
  ignores it. Else, v does the following.
• Set Dd(v,w) Dd(w)l(w,v).
• Computes minw Cm(v,w) Cm(v,p).
• If Cm(v,p) Dm(v), set Dm(v) Cm(v,p). The
  routing table is changed to (p, Dm(v)), and the
  control message m, Dm(v) is sent to all
  neighbors.

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The distributed Bellman-Ford algorithm an example

• Node 1 comes up. All nodes operate in
  synchronism. Only row 1 (destination to node 1)
  is shown.

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The distributed Bellman-Ford algorithm an
example (cont.)
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Routing information protocol (RIP) for the
Internet

• A protocol for an autonomous system (a set of
  networks under the same organization).
• A dedicated device is responsible to direct data
  traffic for a network, known as router.
• Cost number of hops (number of intermediate
  routers traversed).

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Routing information protocol (RIP) (cont.)

• Routers advertise the table of distance vector
  regularly in 30 seconds interval.
• Count-to-infinity set to 16

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Routing information protocol (RIP) (cont.)

• Convergence all routers have agreed on the costs
  of routers. A router starts using the new update
  after waiting for three updates. Hold down 90
  secs.
• Speeding up convergence split horizon (A does
  not tell C that D is reachable though A) and
  poison reverse (A tells C that D is unreachable
  though A).
• Trigged updates whenever a router detects a
  change in router cost, it is required to send
  update message immediately.
• Age out the cost is increased by one if a
  router does not receive a route update. If no
  update is received for three minutes (6 update
  period), then the router is removed from the
  table.

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Link state routing for the Internet Open
shortest path first (OSPF)

• Also a protocol for an autonomous system.
• Features of OSPF
• open available in the open literature.
• supports various distance metrics, e.g.,
  physical distance, delay.
• Dynamic e.g., adapting to changes in the
  topology automatically and quickly.
• In OSFP and RIP version 2, authentication
  passwords are required in routing updating.