1. An Equal-Opportunity-Loss MPLS-Based Network Design Model
Richard S. Barr
Richard V. Helgason
Maya Petkova
Southern Methodist University
Dallas, TX 75275
Saib Jarrar
MCI Data Network Engineering
Richardson, TX 75081
Paper Requests:

2. References
JARRAR, S. Formulation and evaluation of optimization models for MPLS traffic engineering with QoS requirements. D.Eng Praxis, Southern Methodist University, Dallas, TX, 2004.
KENNINGTON, J. L. EMIS Class Notes: Prospects for Operations Research in the Design and Analysis of Telecommunications Networks, (Summer 2002).
MATULA, D. W., and SHAHROKHI, F. The maximum concurrent flow problem. JACM 37 (1990),
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3. Outline Problem Background Basic Model
Objective: the maximal uniform traffic flow lower bound
Revenue Model
Parametric Study
Optimization Model
Computational Experiments
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4. Problem Background
Deficiencies of the traditional IP ( Internet Protocol) routing
imbalance of traffic load on different links
sub-optimal use of resources
does not take into account metrics related to QoS ( Quality of Service) and CoS (Class of Service)
MPLS (Multi-Protocol Label Switching) framework
introduced by IETF ( Internet Engineering Task Force)
integrates into IP networks
provides for efficient routing, forwarding, and switching of the traffic flows
Traffic Engineering over MPLS
enhances network performance
optimizes the resource utilization
controls traffic flows
data transmission occurs on LSPs (Label-Switched Paths),
(not necessarily the shortest paths)
(rouTopology only in its SP calc , does not consider QoS
Over-provisioning
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5. A Fundamental Traffic Engineering Problem for MPLS-Based IP Networks
Given:
Physical topology of an MPLS network
Link attributes
Capacity
Cost ( delay)
Traffic Matrix (aggregate traffic demand)
Resource Constraints
Link Capacities
Traffic Performance Constraints
Maximum Number of Hops
Maximum Delay
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6. A Fundamental Traffic Engineering Problem for MPLS-Based IP Networks (cont’d)
Objective:
Maximize revenues by admitting and routing via a single path as much traffic as possible while observing the resource and the traffic performance constraints
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7. A Fundamental Traffic Engineering Problem for MPLS-Based IP Networks (cont’d)
Logical path design problem
Previously studied design model
Builds the LSPs
Performs an admission control function
An Equal-Opportunity-Loss design model
Treats all demand pairs equally (fairly)
Guarantees equal level of % delivered traffic demand for all commodities by determination of the maximal concurrent traffic flow lower bound
Designs the paths by routing as much demand as possible so that each commodity’s delivered demand is at or above the guaranteed lower bound
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8. Basic Model (stage I) Notations
Topology of an MPLS network : undirected graph G = (N, E),
N set of nodes (routers); let n = |N|
E is the set of edges (links); let m = |E|.
Link (undirected) is an unordered pair of nodes l= (p, q). Each link is assigned a number from the set {1, 2, …,m}.
Directed arcs associated with link l: <p, q> and <q, p>.
The flow on arc <p, q> : referred to as the flow in the normal direction for link l.
The flow on arc <q, p> : referred to as the flow in the reverse direction for link l
Sets associated with a given node q
Capacity of a link : the bandwidth or the transmission speed of that link measured in units of bandwidth ( Mbps)
Cost of a a link : traffic performance metric, such as delay, and not a monetary cost
Commodity: distinct packet traffic to be routed from a source node to a destination node
Demand associated with a commodity: the data rate or bandwidth (measured in units of Mbps) consumed by that traffic.
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9. Basic Model Parameters
the set of nodes in the network, where n = |N|
the set of links in the network, where m = |E|
the set of links into node
the set of links out of node
the capacity in units of bandwidth on link
the administrative cost associated with link
the requirement for the commodity with origin node o at node n, where
supply node
demand node
transit node
h the maximum allowed number of hops that any commodity may traverse from
source to destination , h integer
 a unit of revenue generated from delivering a unit of demand of any commodity
a scaling factor or a weight used in the objective function
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10. Basic Model Parameters (cont’d)
a small deviation factor used in guaranteeing a single traffic delivery path
the guaranteed % delivered traffic demand (lower bound) for all commodities (used
in the second stage); optimal objective value from the first stage
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11. Basic Model Decision Variables
the flow of the commodity with origin node o and destination node d on link e in the
normal direction
reverse direction
the guaranteed % delivered traffic demand (uniform lower bound) for all
commodities (used in the first stage)
the % delivered (fulfillment) of the traffic requirement for the commodity with
origin node o at node n ( , if n is a transshipment node)
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12. Basic Model Derived Variables
the flow of all commodities with origin node c on link e in the normal direction
the flow of all commodities with origin node c on link e in the reverse direction
the total flow on link e in the normal direction
the total flow on link e in the reverse direction
the number of hops that a commodity will traverse form its origin node o to its
destination node d
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13. Mathematical Model Stage I
Maximize D
Subject to:
(1)
(2)
(3)
(4)
(5)
(6)
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14. Mathematical Model Stage I (cont’d)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
All variables are nonnegative
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15. Objective: The Maximal Uniform Traffic Flow Lower Bound
(Portion of The Model)
Maximize D
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16. Mathematical Model Stage II
Let is the optimal solution obtained in stage I
Maximize
Subject to:
Constraint sets (1) to (13) from stage I
(15)
All variables are nonnegative
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17. Parametric Study
The total requested packet traffic cannot be delivered
Construct set of congested links based on the flows from stage II
Congested link - at least 98% of its capacity has been used.
Individually double the capacities of each congested links
Determine the link (links), which contribute for the largest revenue increase
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18. Optimization Model Enhancement of the model
Determine by optimization the link (links), which contribute to the largest revenue increase
New parameter
New decision variable
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19. Optimization Model (cont’d)
Maximize
Subject to:
Constraint sets (1) to (10) , (13) , and (15)
(16)
(17)
(18)
(19)
All variables are nonnegative
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20. Computational Experiments: The Test Network
Realistic network
Typical topology of nationwide data communications network
20 nodes, 31 links
Average node degree ~3
Link capacities:
2488 Mbps (15 links) - OC48 transmission line
622 Mbps ( 16 links) - OC12 transmission line
Trunks connecting the nodes are bi-directional and full duplex 1 2 3 4 5 6 7 8 9
Example Network
2107
1445
1495
404
350
688
257 20
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21. Computational Experiments: Computing Environment
Tests performed on a Compaq AlphaServer DS20E with dual 667 MHz processors and 4096 MB RAM.
Machine configured as a Network Queuing System
Executes batch jobs
Each job has access to approximately 2 GB RAM
Models implemented using AMPL 8.0.
Integer programming solutions are generated using CPLEX Linear Optimizer 8.0.
Default setting for CPLEX used except for the MIP time limit set to 1500 seconds
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22. Computational Experiments: Data Sets
Traffic generator for multiple sets of commodities and traffic demands
OD pairs selected randomly and uniformly from the set of nodes
(no duplicates)
Demands associated with OD pairs selected randomly using uniform distribution over the range specified by the min and max demands
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23. Computational Experiments: Data Sets (cont’d)
OD Pairs
Demand Range
Mean Demand
Guaranteed % Delivered Demand
DS1 80
320
240
74.67
DS2
69.57
DS3
160
< 51.00
DS4
DS5
120
100.00
DS6
82.49
DS7
90.67
DS8
51.41
DS9 60
DS10
DS11
95.55
DS12
89.20
DS13
480
DS14
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24. Computational Experiments: The Results
Excel Data Sheets
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25. Future Work
Explore and test for significance factors that influence the performance of the Equal-Opportunity-Loss model
Compare the revenue and the network performance characteristics generated using our model with the previously studied MPLS Traffic Engineering Single Path model
Explore specialized model enhancements, which could result to reduced time to optimality
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