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: helgason@engr.smu.edu

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 8392 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), 318-334. 9/20/2018

Outline Problem Background Basic Model Objective: the maximal uniform traffic flow lower bound Revenue Model Parametric Study Optimization Model Computational Experiments 9/20/2018

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 9/20/2018

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 9/20/2018

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 9/20/2018

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 9/20/2018

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. 9/20/2018

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 9/20/2018

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 9/20/2018

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) 9/20/2018

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 9/20/2018

Mathematical Model Stage I Maximize D Subject to: (1) (2) (3) (4) (5) (6) 9/20/2018

Mathematical Model Stage I (cont’d) (7) (8) (9) (10) (11) (12) (13) (14) All variables are nonnegative 9/20/2018

Objective: The Maximal Uniform Traffic Flow Lower Bound (Portion of The Model) Maximize D 9/20/2018

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 9/20/2018

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 9/20/2018

Optimization Model Enhancement of the model Determine by optimization the link (links), which contribute to the largest revenue increase New parameter New decision variable 9/20/2018

Optimization Model (cont’d) Maximize Subject to: Constraint sets (1) to (10) , (13) , and (15) (16) (17) (18) (19) All variables are nonnegative 9/20/2018

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 9/20/2018

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 9/20/2018

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 9/20/2018

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 9/20/2018

Computational Experiments: The Results Excel Data Sheets 9/20/2018

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 9/20/2018