Topology Aggregation and Routing in Bandwidth-Delay Sensitive Networks

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Topology Aggregation and Routing in
Bandwidth-Delay Sensitive Networks

• King-Shan Lui, Klara Nahrstedt
• Department of Computer Science
• UIUC

2
Flow of the presentation

• Introduction
• Network Models
• QoS-Aware Topology Aggregation
• Line-Segment Routing Algorithm
• Simulation Results

3
Introduction

• As the network grows larger and larger, it is
  impossible to broadcast the whole topology to
  every node in the network to do routing because
  it takes an enormous amount of bandwidth, time
  and space.
• To deal with the scalability problem, topology
  aggregation is done.
• Nodes are grouped hierarchically into several
  clusters known as peer groups or domains.
• The internal topologies of these domains are
  aggregated before broadcasting.

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• All aggregation schemes suffer from different
  degrees of distortion.
• There are several ways to do aggregation with
  bounded distortion when there is only one metric
  under consideration.
• It is very difficult to do aggregation with
  bounded distortion when 2 or more parameters are
  under consideration.
• If there are several paths between source and
  target, how does one pick up the best QoS pair?
• This paper proposes an algorithm for topology
  aggregation that aggregates a peer group with 2
  metrics, delay and bandwidth with corresponding
  QoS routing protocol.

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Network Models

• The whole network is divided into disjoint peer
  groups.
• A peer group(PG) is a set of nodes connected by
  links.
• The network and the domains are represented by
  directed graphs and the links can be asymmetric.
• Nodes within a PG can see each other but nodes
  outside only have an aggregated view.
• Within a PG, some nodes connect to nodes outside
  the PG. These are the border nodes.

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• One representative topology is the star.
• Border nodes connect via virtual links called
  spokes to a virtual nucleus generating a
  symmetric star.
• Each link has associated set of QoS parameters.
• A limited no. of inter-border links called
  bypasses are allowed.
• Formally a PG is modeled as a tuple (V,B,E)
• V set of nodes
• B ( B is a subset of V) set of border nodes
• E set of directed (physical)links among nodes
  in
• V
• (D,W) QoS parameter of each physical link
• (D-delay, W-bandwidth)

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• Each pair (D,W) represents a single point on the
  delay-bandwidth plane.
• The delay of a path is the sum of all the delays
  of the physical links along that path.
• The bandwidth of a path is the minimum of the
  bandwidths among all the links.
• The parameter of a physical path is also a point
  on the delay-bandwidth plane.
• Hence if there are m physical paths between 2
  border nodes, there will be m points on the
  delay-bandwidth plane of the logical link between
  the 2 border nodes.

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• A network consists of PGs and links that connect
  them. Denoted as (G,L)
• Ggigi (Vi,Bi,Ei), 1lt i ltG
• L set of links between the PGs.

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QoS-Aware Topology Aggregation

• The basic principle is instead of using m points
  per logical link on the delay-bandwidth plane, a
  line segment to approximate the m points is used,
  thereby strongly decreasing the storage space for
  the QoS parameters.
• 2 phases in the algorithm
• 1. Find a line segment for each logical link in
  the mesh of the border nodes.
• 2. Find a star with bypasses aggregation from
  this mesh.

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• The parameter of a logical link is the best QoS
  parameter among all the physical links between
  the 2 nodes of the logical link.
• If we have 2 metrics per link, there exists no
  absolute order, however a partial order can be
  developed.
• Definition
• A point (x,y) is more representative than a
  point (x,y) if they are not the same and xltx
  and ygty. Given a set (S) of points in the
  delay-bandwidth plane, (x,y) ? S is a
  representative of S if there does not exist
  another point (x,y) ? S which is more
  representative than (x,y), which means that
  ?(x,y) ? S, x lt x or y gty.

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• Example 1
• Let S be a set of delay-bandwidth QoS pairs and
  S(4,5),(7,9),(10,8),(9,5),(2,3),(7,7). (2,3)
  is a representative of S since its delay is less
  than all other pts in S. Another representative
  is (7,9).
• We can plot all points on a delay-bandwidth
  plane.

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• Due to the storage limitation on routers, it is
  too expensive to store all the points for every
  logical link.
• Store only one point per logical link.
• However no matter which point we pick, much
  information is lost.
• To solve this, a line segment that approximates
  the staircase (all the points) is found by using
  the least square method.
• The shaded area defines the region of supported
  services, i.e. any request that falls inside this
  area can be supported by some physical path.
• After a line segment is found, all connections
  which fall under the line segment can be
  accepted.
• However not all these connections are supported.

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• For e.g. If L1 is chosen then un shaded areas
  below L1 represent connection requests that are
  accepted but not supported by any physical path
  i.e. crankback will occur.
• On the other hand, we may reject supported QoS by
  using a line segment. For e.g. If the connection
  request is in the shaded area above the line it
  will be rejected even though it can be served.
• Choice of line segment therefore depends on the
  desired quality of service.
• In the figure both L1 and L2 are possible line
  segments. L2 will reject more supported
  connection request than L1and L1 will have more
  crankbacks than L2.
• A line is represented as (a,b),(c,d). The
  endpoint with smaller bandwidth is lower endpoint
  and the other endpoint is the upper endpoint. So
  a line is represented as lower endpoint, upper
  endpoint.

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• A mesh that consists of b(b-1) logical links is
  still to expensive to be broadcasted.
• Aggregate this mesh into a star with bypasses.
• Let i and j be two border nodes and n be the
  nucleus of the star. If there is no bypass
  between i and j, the only path from i to j is
  i-gtn-gtj in the star.
• The goal of the aggregation is to find out the
  QoS parameters of the links i-gtn and n-gtj such
  that the delay and the bandwidth of i-gtn-gtj in
  the star is the same as the delay and bandwidth
  of i-gtj in the mesh.
• We have to split a single link i-gtj in the mesh
  into two links i-gtn and n-gtj in the star.

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• join operation () to find the QoS parameters of
  i-gtn-gtj given i-gtn and n-gtj is used.
• Definition
• (a,b),(c,d) (a,b),(c,d)
  (aa,min(b,b)), (cc,min(d,d))
• Now find spokes and bypasses 3 steps
• Find the spokes from border nodes to nucleus.
• Find the spokes from nucleus to border nodes .
• Find the bypasses between border nodes.
• Denotation lmij line segment from i to j in
  mesh.
• lsij - line segment from i to j in star.

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• Spokes incoming to the nucleus
• To find spokes we have to break line segments in
  the mesh.
• From the definition of join, it is clear that the
  endpoint delays of the spokes lsin and lsnj
  should be smaller than those in lmij while the
  endpoint bandwidths should not be smaller than
  those in lmij.
• Let l.lp and l.up denote the lower and upper
  endpoint of a line segment l.
• Let p.d and p.w denote the delay and bandwidth of
  a given point p.
• lsin (min_ld,max_lw),(min_ud,max_uw)
• where min_ldmin j ? B, i! jlmij,lp.d,min_ud
  min j ?B , i! jlmij,up.d, min_lwmin j ? B,
  i! jlmij,lp.w,min_uw minj ? B , i!
  jlmij,up.w.
• O(b) is time taken to find one spoke to the
  nucleus. There are b spokes incoming to n. Total
  time to find all spokes to n is O(b2).

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• Example 2
• Suppose the line segments from node 0 to nodes 1
  and 2 are (9,4) ,(19,6) and (3,7),(3,7)
  respectively.
• min_ldmin_ud3, and max_lwmax_uw7. Therefore
  the line segment from 0 to n is(3,7),(3,7).

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• Spokes outgoing from the nucleus
• Upto this point we know mesh (M) and spokes from
  borders to nucleus (Sb-gtn).
• That is, we know lmij and lsin. We have to find
  lsnj.
• We have lsin lsnj lmij
• So lmij lsin lsnj
• Definition
• (a,b),(c,d) - (a,b),(c,d)
  (a-a,min(b,b)), (c-c,min(d,d))
• Referring to the e.g. 2, lm01 (9,4),(19,6) and
  ls0n (3,7),(3,7) so we get lsn1 as
  (6,4),(16,6). However we can also get lsn1 from
  say lm21 . But in aggregation, we can have at
  most one lsn1. This problem is solved by taking
  the averages of all the delays and bandwidths of
  ideal lsn1s to be the real lsn1.

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• Finding Bypasses
• Due to aggregation, lsin lsnj may no longer be
  the same as lmij in the mesh.
• Some deviate only a bit while others might be
  quite different.
• In order to make the aggregation more precise,
  direct links between border pairs are introduced.

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Line-Segment Routing Algorithm

• LSRA is a QoS based source routing algorithm,
  integrating modified Dijkstras Algorithm(DA) and
  the centralized bandwidth-delay routing
  algorithm(CBDRA).
• DA is an optimal algorithm when finding the
  shortest-delay path when delay is the only
  metric.
• CBDRA works when there are 2 metrics, delay and
  bandwidth. It first prunes all the links that do
  not satisfy the bandwidth requirement, and then
  applies DA to find the min-delay path in the
  residue network.
• In LSRA this idea is augmented to deal with line
  segment representation.

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• LSRA requires that each node keeps the topology
  of its own PG and star aggregations of other PGs.
• There are 2 levels are routing inter-domain and
  intra-domain.
• An inter-domain routing path specifies the border
  nodes in different PGs to go through and
  intra-domain routing finds a path within a
  domain.
• LSRA accordingly has 2 phases
• Inter-Domain Routing
• After obtaining star aggregations from other PGs,
  each node can see border nodes of other PGs and
  can compute the line segment between any border
  pair in an outside PG.

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• The network that a node sees is called node-view
  network (NVN).
• A modified DA algorithm applying the technique of
  CBDRA is used to find the inter-domain path using
  NVN.
• Similar to DA, a path grows from the source to
  the target PG.
• The delay to each node in NVN is kept and each
  time a node is reached by the growing path, the
  delays of its neighbors are updates according to
  the links.
• There are 2 types of links in NVN
• -physical links which connect different PGs and
  nodes in the source PG.
• -logical links which are line segments
  connecting borders within the PG obtained from
  star aggregation.

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• Suppose the routing request is (reqd, reqw) and
  accumulated delay from source node to another
  node i in NVN is di. If there is a link, either
  physical or logical, from i to j, LSRA updates
  the delay of node j (dj) as follows
• Case I a physical link with (D,W). If Wltreqw
  means no feasible path can go through this link,
  so dj is unchanged. If Wgtreqw , dj
  mindj,di D as in DA.
• Case II a logical link l (dlp,wlp),(dup,wup).
  If wup lt reqw, dj is unchanged, otherwise dj
  min dj,di dreqw, where dreqw is the
  delay-coordinate of the line segment with
  bandwidth equal to reqw.
• The process stops when the path reaches one of
  the borders, say t, of the target PG. If
  dtltreqd, then request is accepted and LSRA
  goes ahead to do intra-domain routing. Else
  request is rejected.
• The running time complexity is the same as DA
  which is optimal.

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• Intra-Domain Routing
• In this phase LSRA finds the route in a
  distributed fashion.
• A message or a packet is sent from the source to
  travel along the inter-domain path found.
• When the border node t of PG g receives the
  message , and finds out the next hop in the
  inter-domain path is another border node t in g,
  it finds the path going from t to t using CBDRA.
• The message keeps accumulating delay along the
  path.
• If accumulated delay exceeds reqd, crankback
  occurs and the message is forwarded back to the
  source.
• If the message successfully reaches the target
  PG, a feasible path has been found.
• Complexity of CBDRA is same as DA.

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Simulation Results

• LSRA is compared to a SP algorithm (centralized
  modified Dijktras Algorithm).
• LSRA may suffer from crankback if it accepts a
  request after finding an inter-domain path but is
  unable to find a feasible intra-domain path.
• Also a feasible request may be rejected due to an
  inaccurate approximation of dreqw.
• Success ratio total no. of feasible paths found
• total no. of feasible requests
• A good algorithm should have a high success ratio
  but a small crankback ratio.

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• Simulated network topology consists of 10
  domains, each with 15-35 nodes, a total of 293
  nodes. With 3-4 border nodes per domain.
• LSRA achieves a very good success ratio and
  performs better than SP