QoS Routing Algorithms

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QoS Routing Algorithms

• Jian-Feng Xu
• EL938 Project
• Spring 2002

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Outline

• Big Picture
• QoS Routing
• QoS Routing Problems
• Multi-Path-constrained problem

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Big Picture

• QoS mechanisms
• Admission Control, Traffic Access Control, Packet
  Scheduling, Buffer Management, Flow Control, and
  QoS Routing
• Relationship between QoS Routing, Admission
  Control, and Resource Reservation

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1. Connection request
Admission Control
Routing
2. Src, dst, QoS parameters
5. result
3. feasible route
6. Connection response
4. Reservation result
Reservation
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QoS Routing

• Routing Objectives
• Tasks involved in Routing
• Classification of Routing

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QoS Routing Objectives

• Given a src, a dst, a set of constraints
  (bandwidth, buffer size, delay, jitter, loss
  rate,), find a feasible path from src to dst.
• Achieve overall network efficiency.

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Problem find a path from src to dst such that
bottleneck link bandwidth is at least 10, and
path delay is lt 30.
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Bw30,delay10
Bw35,delay10
dst
src
Bw1,delay100
Bw10,delay5
2
Bw10,delay5
Path 1 src-gt1-gtdst, bw30, delay20, feasible
and optimal Path 2 src-gt2-gtdst, bw10,
delay10, feasible and optimal Path 3 src-gtdst,
not feasible If path 1 is taken, what if next
connection asks for bw20? If path 2 is taken,
what if next connection asks for delay15?
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Tasks involved in Routing

• Each node maintain state information
• Broadcast state information
• Run algorithm to calculate optimal paths

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Classification of Routing

• Unicast/Multicast
• Source route/hop-by-hop/hierarchical

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QoS Routing Problems

• Link optimization
• Link constrained
• Path-optimization
• Path-constrained
• Combinations
• Multi-path-constrained

Figure 4. In ChenNahrstedt 1998 Overview..
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Bellman-Ford SP Algorithm
Bellman-Ford(G, W, scr) FOR each v in VG DO
dvlt- dslt-0 FOR i lt- 1 to VG
- 1 DO FOR each edge(u,v) in EG DO
RELAX(u,v,w)
dv is the length of the best path from src to v
found so far. is the predecessor of v in
this path.
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Bellman-Ford SP algorithm cont.
Relax(u, v, W) IF dv gt du W(u,v) THEN
dv lt- du Wu,v lt- u
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Properties of BFSP algorithm

• After the h iteration, algorithm has calculated
  the shortest paths from src to all nodes in less
  than or equal to h hops.
• The worst running complexity of the algorithm is
• O(V3), which is polynomial time.

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Example
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B
D
1
1
2
2
4
src
4
C
E
2
Calculate the shortest-path from src to all other
nodes
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Initially
B
D
0
src
C
E
After 1 iteration
1
B
D
1
0
src
4
4
C
E
17
1
9
8
After 2 iterations
B
D
1
src
1
4
C
E
2
2
1
After 3 iterations
8
B
D
1
4
src
1
C
E
4
2
2
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Multi-path-constraints problem

• Given G(N, E, src, dst, W, C), find a feasible
  path from src to dst.
• W(u,v)w1(u,v), w2(u,v),
• Weights are positive real numbers.
• A path p src-gtv1-gtv2-gtvn-gtdst.
• W(p) w1(p), w2(p),
• W1(p) w1(src-gtv1) w1(v1-gtv2)w1(vn-gtdst)
• C c1, c2,

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• A path p is feasible is w1(p)ltc1, w2(p)ltc2,
• A path p is optimal is there exists no other path
  q such that w(q)ltw(p)

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(20.0, 1.0)
(20.0, 1.0)
dst
src
(50.0, 4.0)
Fig. 1 from YuanLiu2001 Heuristic..
(1.0, 20.0)
2
(1.0, 20.0)
p1 src-gt1-gtdst is an optimal path, w(p1)(40.0,
2.0) P2 src-gt2-gtdst is an optimal path,
w(p2)(2.0, 40.0) P3 src-gtdst is not an optimal
path, w(p3)(50.0, 4.0)
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Extended BF to solve MPC
Fig. 3 from YuanLiu2001 Heuristic..
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Properties of EBFA

• Records all optimal paths (if any) from a src to
  all other nodes
• Guarantees to find a path that satisfies the
  constraints if such a path exists.
• The complexity the RELAX operation is run
  O(NE) times, the final complexity depends on
  the complexity of the RELAX operation.
• The complexity of EBFA can be exponential
  because the of paths that RELAX has to go
  through can be exponential

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The number of optimal paths can be exponential
Fig. 2 from YuanLiu2001 Heuristic..
The number of optimal paths from node 0 to node
3k is 2k.
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How to relax RELAX?

• How to reduce the number of optimal paths RELAX
  has to go through so that the resulting
  complexity is polynomial time?
• ChenNahrstedt, 1998, On Finding
• -if all metrics except one take bounded integer
  values, then MPC is solvable in polynomial time
• -proposed a heuristic scheme to solve a 2 path
  constraints problem.

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Example

• All these paths are optimal paths
• W(p1)(1.0, 10.0) W(p6)(2.5, 6.5)
• W(p2)(2.1, 9.9) W(p7)(2.6, 6.3)
• W(p3)(2.2, 9.8) W(p8)(2.7, 2.5)
• W(p4)(2.3, 8.7)
• W(p5)(2.4, 8.3)
• We can have infinite number of optimal paths,
  since metrics are real numbers.

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Example contd.

• Lets bound w2.
• Only allow w2 to be even integers from 0 to 10
  0, 2, 4, 6, 8, 10. If w2 is in between 2
  integers in the set, round it up.
• The set of paths becomes
• W(p1)(1.0, 10) W(p6)(2.5, 8)
• W(p2)(2.1, 10) W(p7)(2.6, 8)
• W(p3)(2.2, 10) W(p8)(2.7, 4)
• W(p4)(2.3, 10)
• W(p5)(2.4, 10)

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Example contd.

• New set of optimal paths
• W(p1)(1.0, 10)
• W(p6)(2.5, 8)
• W(p8)(2.7, 4)
• There can at most be X number of optimal paths, X
  is the number of integers in the set.
• How can we determine the bound and X, and how
  does it affect the performance of the heuristic.
• ChenNahrstedt, 1998, On Finding

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Yuan, 1999, On the

• For 2 path constraints
• Generalizes the limited granularity heuristic by
  not fixing a mapping scheme.
• Proves the uniform mapping scheme used by
  ChenNahrstedt can provide optimal worst case
  guarantee among all mapping schemes.
• Introduces the limited path heuristic
• Analytical and simulation studies on both schemes

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YuanLin, 2001, heuristic

• Generalized the 2 heuristics to solve k path
  constraints problems. Kgt2.
• Analytical and simulation studies on both schemes.

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The general limited path heuristic

• During the execution of EBFA, if PATH(v) already
  contains X optimal paths, do not add any more.
• Complexity O(NE(X2))
• How to choose the value of X such that the
  heuristic is efficient and effective?

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The General limited granularity heuristic

• Approximates k-1 metrics with k-1 bounded finite
  ranges
• Let w2wk be the k-1 metrics to be approximated
• W2 can only take values r1, r2, , rXc2, where
  X is the number of integers in the set, c2 is the
  QoS constraint on w2.
• When collecting optimal paths, we will ignore all
  paths with w2 gtc2. For those paths whose w2 lt
  c2, we will approximate them accordingly.
• Complexity of heuristic O(XNE), XX2X3.Xk

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Limited granularity algorithm based on EBFA
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Simulation

• Recommended mapping scheme
• r1c/X, r2 2c/X,

• Link wt Wi is randomly generated in the range of
  (0.0, 10.0 i), 1ltiltk
• Existence percentage total number of requests
  satisfied using EBFA /
• total number of requests

• Competitive ratio number of requests satisfied
  using a heuristic / number of requests
  satisfied using EBFA

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mesh

• Simulation done on 8x8 mesh
• K3 constraints
• 500 QoS route requests, all with same constraints
• Link weights are randomly generated for each
  request

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MCI backbone

• 1000 problems
• Each problem tries to find a path between
  randomly generated pairs, all with same QoS
  constraints

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Dependence on k

• Use MCI topology
• Fix number of entries in path table for both
  heuristics
• Limited granularity 4000 for 2 constraints
• 64x64 for 3 constraints
• 17x17x17 for 4 constraints
• 8x8x8x8 for 5 constraints
• 6x6x6x6x6 for 6 constraints

• Limited path table size 4.
• 1000 QoS problems

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References
1 S. Chen K. Nahrstedt, "An Overview of
Quality-of-Service Routing for the Next
Generation High-Speed Networks Problems and
Solutions", IEEE Network, Special Issue on
Transmission and Distribution of Digital
Video, Nov./Dec. 1998. -Gives a overall picture
of QoS Routing and proposed algorithms. 2 Z.
Wang J. Crowcroft, "Quality-of-Service Routing
for Supporting Multimedia Applications", IEEE
JSAC, Sept. 1996. -Proves that 2 or more
Constrained Path problems are NP-Complete. 3
S. Chen K. Nahrstedt, "On Finding
Multi-constrained Paths", International
Conference on Communications, June
1998. -Proposes a heuristic algorithm to
approximate the NP-Complete 2-constrained path
problem.
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References contd.
4 X. Yuan, "On the Extended Bellman-Ford
Algorithm to Solve Two-Constrained Quality of
Service Routing Problems", The Eighth Internationa
l Conference on Computer Communications and
Networks, October 1999. -Extends ref. 3 and
proposes another heuristic algorithm to
approximate 2-constrained path problems. 5 X.
Yuan X. Liu, "Heuristic Algorithms for
Multi-Constrained Quality of Service Routing",
Vol II p844-853, IEEE Infocom, 2001 -Extends
ref. 4 to cover k-constrained path
problems. 6 T. H. Cormen, C. E. Leiserson and
R. L. Rivest, Introduction to Algorithms.,
The MIT Press, 1990.