data structures for bandwidth reservations and quality of service on the internet andreas nilsson...
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Data structures for Bandwidth Reservations and Quality of
Service on the Internet
Andreas Nilsson
Division of Computer Science and Networking
Department of Computer Science and Electrical Engineering
Luleå University of Technology
Presentation outline• Paper presentation.• Background.• Queuing.• Bandwidth reservation problem (Two solutions):
– Static.
– Dynamic.
• Further Work
Introduction - papers
1. “Extended Expedited Forwarding: In-Time PHB group”.
2. “A Static Data Structure for Discrete Advance Bandwidth Reservations on the Internet”.
3. “Performance of QoS Agents for Provisioning Network Resources”.
4. “Data Structure for a Time-Based Bandwidth Reservations Problem”.
5. “Application of resource allocation problem to the analysis of spectra”.
Internet• Largest network of networks.
– 1977-111, 1987-10000, 2002 hosts.
• Packet switched network.– All packets are addressed.
• No guarantees.– Packets are delivered at best effort.
T O : C lien t 2F R O M : C lien t 1
8102
Real time on the Internet
• For video, TV, phone, process control etc.• Demands packets:
– At constant delay.
– In order.
– At a specified bandwidth.
• A “circuit switched Internet” is the “goal”.
Queuing
• Conforming traffic must be delivered In-Time and in order therefore a dedicated “lane” through the routers is needed.
• Excess traffic (additional traffic improving the
quality) belongs to a conforming flow, and must be delivered in order and in time, but may be tossed due to congestion.
• Best effort, the background traffic.• Space complexity: O(n) Time: O(1) per
packet
C o n fo rm in g
E x cess
B est E ffo rt
Reservations and Quality of Service
• Provide different levels of service on the Internet for different applications.– Thorax surgical robot controlled over the Internet.
– Live TV over the Internet.
– File transfer (web) over the Internet.
• Olov Schelén et.al. presented a QoS providing architecture, called Bandwidth Brokers.– Clients make bandwidth reservations for the traffic
through the Internet.
Bandwidth brokers• They manage the bandwidth reservations on
one link.
N etw o rk 1 N e tw o rk 2
B an d w id th b ro k e r
Interaction between bandwidth brokers
• Usually the route between two computers consists of several links.
• Entire route has to be reserved.
B an d w id th b ro k e r
N e tw o rk 4
B an d w id th b ro k e r
N e tw o rk 3
B an d w id th b ro k e r
N e tw o rk 1 N e tw o rk 2
B an d w id th b ro k e r
N e tw o rk 5
Bandwidth Reservation Problem• The problem of how to make the data structure needed
to handle the reservations in the Bandwidth Brokers efficient.
• Presents two solutions, in the comparison based model of computation:– Static (AST).– Dynamic (BinSeT).
• Both solutions implement the same set of operations:– Insert(Bandwidth, Interval)– Delete(Bandwidth, Interval)– MaxReserved(Interval)Bandwidth
Bandwidth Reservation ProblemAn example
Advanced Segment Tree (AST)
• Modified segment tree.• The tree is static, i.e.:
– The tree is only built once, and in advance, no nodes are added or deleted and therefore the tree is always perfectly balanced and covers a bounded universe M.
– The intervals available for reservations are determined upon construction
• All nodes on a level l:– have the same number of children.– represent a time interval.– cover intervals of the same size.– have intervals that mutually don't intersect.– have intervals, the union of which is M.– have an interval that is contained within one interval on level l’, where l’<l.
Tim e
n o d e v a lu e = 0m ax v a lu e = = 2 2 0m a x(0 + 3 0 ,2 0 + 2 0 0 )
n o d e v a lu e = 6 0m ax v a lu e = 9 0
9 00
00
00
00
00
3 00
2 0 00
n o d e v a lu e = 0m ax v a lu e = 3 0
n o d e v a lu e = 2 0m ax v a lu e = 2 0 0
n o d e v a lu e = 1 0m ax v a lu e = = 2 5 0m a x(5 0 + 2 0 0 ,0 + 2 2 0 )
n o d e v a lu e = 5 0m ax v a lu e = = 2 0 0m a x(6 0 + 9 0 ,1 2 0 + 8 0 )
n o d e v a lu e = 1 2 0m ax v a lu e = 8 0
8 00
AST - Nodes and their values
Binary Segment Tree (BinSeT)• Data structure that combines the properties of a binary search tree
and a segment tree.• The tree is dynamic, i.e.:
– The tree is continuously constructed, nodes are added upon insertions. Therefore the tree has to be balanced continuously.
– The intervals are chosen completely freely.– The tree covers an unbounded universe
• Consists of nodes (internal nodes) and leaves (nodes)– Nodes store
, max reserved bandwidth below the node , change during the interval , split time of the node
– Leaves store , max reserved bandwidth below the leaf , change at time t , start time that the leaf represents
A simple example BinSeT
1
1
B a n d w id th
T im e2
2
3 4-1
-2
0
1
1
B a n d w id th
T im e2
2
3 4-1
-2
0
1
1
B a n d w id th
T im e2
2
3 4-1
-2
0
Tim e
B an d w id th
3
4
1
2
1 2 3 40
Tim e
B an d w id th
3
4
1
2
1 2 3 40
Tim e
B an d w id th
3
4
1
2
1 2 3 40
23
+ 20
0
3
+ 10
-10
-20
-3
0
22
+ 2 -1 -100
0
1
0
-10
01
0+ 1
Further work
• Policing for the Bandwidth Brokers.• Generalisation of the data structures to more
dimensions.• A modified BinSeT to efficiently find unreserved
resources over time.• Other queries based on operations defining
monoids.• Time based data structures (similar way of reasoning as in
A. Brodnik, S. Carlsson, J. Karlsson, and J. I. Munro, “Worst Case Constant Time Priority Queue”, SODA 2001)
AST versus BinSeT
Data-structure
Comment Space Time
query
Time
updateAST static, wrap,
implicitO(M) O(log M) O(log M)
BinSeT Dynamic O(n) O(log n) O(log n)
M = size of universen = number of unique interval end points (event points)
max(1,1 )=3+2
max(1,1+1)=2
max( 1, )= 1 1 1
max( , -6)=4 4 4
max( ,1 2)=1 + 3
max(1,1-3)=1
max(-2,-2+1)=-1
max(1,1-2)=1
max(7,1 )=7+4
max(5,5 )=7+2
max(4,1+0)=4
max(3,3 )=5+2
max( 1, )=2 2 4+
max(3,3+1)=4
max(-1,-1+1)=0
+1
+2
+1
+1 -1
-1
+4
-6
+1
+2
+1
-3
-2
+1
+1 -2
Example 1 BinSeT
max(7,1 )=7+4
max(4,1+0)=4
max(3,3+1)=4
max(-1,-1+1)=0
AC
C
A
A
A
B
C
C
C
A
....
Example 2 BinSeT
Paper 1 A Static Data Structure for Discrete Advance
Bandwidth Reservations on the Internet
• Publications:– Technical report 2003.
– Conference records of SNCNW 2003.
• Authors:– Andrej Brodnik and Andreas Nilsson.
• Description:– Shows a static data structure for bandwidth
reservations.
Paper 2 Performance of QoS Agents for Provisioning Network Resources
• Publications:– Conference records of IWQoS’99.
• Authors:– Olov Schelén, Andreas Nilsson, Joakim Norrgård and
Stephen Pink.
• Description:– Shows that the hardware requirements of a QoS agent
are quite modest by in simulations compare two algorithms for making reservations.
Paper 3Extended Expedited Forwarding:
In-Time PHB group
• Publications:– Technical Report 2003.– Conference records of ISCC’2003, FTC’2001 and
CSEE’2001.
• Authors:– Ulf Bodin, Andrej Brodnik, Johan Karlsson, Andreas
Nilsson and Olov Schelén.
• Description:– Shows a proposal on how to handle excess traffic in
queues in relation to conforming traffic and best effort traffic.
Paper 4Data Structure for a Time-Based Bandwidth Reservations Problem
• Publications:– Technical Report 2003.
– Conference records of CSEE’2002.
• Authors:– Andrej Brodnik and Andreas Nilsson.
• Description:– Shows a dynamic solution to the bandwidth reservation
problem.
Paper 5Application of resource allocation problem to the analysis of spectra
• Publications:– In proceedings of MATH/CHEM/COMP/2002.
• Authors:– Andrej Brodnik, Ante Graovac, Andreas Nilsson,
Tomaz Pisanski.
• Description:– Only an abstract for a presentation in which it is shown
that the solution to the Bandwidth reservation problem also is applicable when analyzing spectra.
Roberto Grossi
• Personal Data– Associate Professor at the University of Pisa.
– Ph.D. and Laurea in Computer Science at the University of Pisa.
– Member of the Algorithms and Data Structures group at the Department of Computer Science.
– Formerly, Assistant Professor at the University of Florence.