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  • 1.
    Broström, Peter
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Optimization in the Design of OSPF Telecommunication Networks2004Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis address optimization problems related to the design of lP (Internet Protocol) networks. One of the most commonly used IGP's (Interior Gateway Protocols) in telecommunication networks is the OSPF (Open Shortest Path First) protocol with ECM (Equal Cost Multipath) distribution. This link state based protocol uses link weights, which usually are set by an network operator, for providing routers necessary information regarding how traffic should be routed. By shortest path computations, router decide by themselves how to distribute the traffic.

    One problem considered in this thesis is the problem of designing networks which are capable of accommodating large parts of the traffic when network components fails. Link failures are the most common failures, and this is the kind of disturbance which is considered. A multiobjective optimization model is presented and we search for pareto-optimal solutions using a two-phased weight based search method. This method tries to minimize the design cost simultaneously as the level of network survivability is maximized. This method uses the fact that is is easy to compute how traffic is distributed when the OSPF metric is known.

    In contrary, it is a much more difficult task to determine if there are any OSPF weights that yield a desired flow distribution. This is a topic which also is studied in the thesis. Necessary conditions, which flow patterns must fulfill for being identical to the shortest paths obtained from OSPF weights, are reported. Sufficient conditions for a special type of flow patterns are also presented. The thesis also contains a polynomial method which can be used for detecting impossibilities in a set of flow patterns when this set do not correspond to the shortest paths of any OSPF weights.

    Flow patterns are the basis for a new model which is developed for designing lP networks where OSPF and ECM distribution is used . This model uses a set of in-graphs in order to represent weights implicitly. The model also uses a new set of constraints used for modeling ECM distribution. The usefulness of the model is verified by computational experiments.

    List of papers
    1. Multiobjective design of survivable IP networks
    Open this publication in new window or tab >>Multiobjective design of survivable IP networks
    2006 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 147, no 1, p. 235-253Article in journal (Refereed) Published
    Abstract [en]

    Modern communication networks often use Internet Protocol routing and the intra-domain protocol OSPF (Open Shortest Path First). The routers in such a network calculate the shortest path to each destination and send the traffic on these paths, using load balancing. The issue of survivability, i.e. the question of how much traffic the network will be able to accommodate if components fail, is increasingly important. We consider the problem of designing a survivable IP network, which also requires determining the routing of the traffic. This is done by choosing the weights used for the shortest path calculations.

    Keywords
    Internet protocol, Network design, OSPF, Survivability, Weight optimization
    National Category
    Engineering and Technology
    Identifiers
    urn:nbn:se:liu:diva-50114 (URN)10.1007/s10479-006-0067-y (DOI)
    Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12
    2. Determining the Non-Existence of a Compatible OSPF Metric
    Open this publication in new window or tab >>Determining the Non-Existence of a Compatible OSPF Metric
    2004 (English)Report (Other academic)
    Abstract [en]

    Many telecommunication networks use Internet Protocol for deciding the routing of traffic. The specifications OSPF (Open Shortest Path First) and ECM (Equal Cost Multipath) are very common, and state that each router sends the traffic on the shortest path to the destination. If there are several shortest path, the router splits the traffic evenly. In order to have some control over the traffic distribution, the operator can assign weights to the links in the network, and these weights are used by the routers when calculating the shortest paths. It has been shown that by optimizing over the values of the weights, the performance of a network can be much improved. A difficult question is whether or not for a set of desired traffic patterns there exists a compatible metric, i.e. weights making the routers give the specified traffic patterns. There is one known necessary condition for the existence of such a metric, but up to now no sufficient conditions. We investigate this problem, and find more general necessary conditions for the existence of compatible weights for a set of given desired "shortest path"-graphs. A polynomial algorithm that for most cases verifies the non-existence of a compatible metric is presented. The algorithm also indicates which parts of the traffic patterns that are in conflict. A few numer;cal examples are used to illustrate the procedure, and some computational tests are reported.

    Place, publisher, year, edition, pages
    Linköping: University of Linköping, Department of Mathematics, 2004. p. 42
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 6
    Keywords
    Internet protocol, OSPF, compatible metric, optimization
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-22362 (URN)1569 (Local ID)1569 (Archive number)1569 (OAI)
    Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-11-06
    3. Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric
    Open this publication in new window or tab >>Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric
    2004 (English)Report (Other academic)
    Abstract [en]

    A dominating standard for routing in telecommunication networks is Internet Protocol with OSPF (Open Shortest Path First) and ECM (Equal Cost Multipath). Each router sends the traffic on the shortest path to the destination. If there are several shortest path, the router splits the traffic evenly. The operator can assign weights to the links in the network, which are used by the routers when calculating the shortest paths. An important question is whether or not for a set of desired traffic patterns there exists a compatible metric, i.e. weights making the routers give the specified traffic patterns. We describe necessary conditions, stronger than those previously discovered, for the existence of compatible weights for a set of given desired shortest path-graphs.

    Place, publisher, year, edition, pages
    Linköping: Linköpings universitet, 2004. p. 24
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 8
    Keywords
    Internet protocol, OSPF, compatible metric, optimization
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-22361 (URN)1568 (Local ID)1568 (Archive number)1568 (OAI)
    Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-11-06
    4. Design of IP/OSPF Networks Using a Lagrangean Heuristic on an In-graph Based Model
    Open this publication in new window or tab >>Design of IP/OSPF Networks Using a Lagrangean Heuristic on an In-graph Based Model
    2005 (English)In: Proceedings of the International Network Optimization Conference, INOC 2005 / [ed] L. Gouveia and C. Mourao, Lisbon, Portugal: University of Lisbon , 2005, p. 702-Conference paper, Published paper (Refereed)
    Abstract [en]

    This paper address the problem of designing IP networks where traffic is distributed in accordance with the OSPF protocol. Routers use link weights for determining how traffic is distributed. All shortest paths between pairs of routers are used and the traffic is evenly divided when several paths are shortest. We formulate a new model for the design of IP networks with OSPF and ECM distribution where weights are implicitly included. Necessary constraints for representing the shortest paths obtained from link weights by in-graphs are described. A Lagrangean heuristic is developed for verifying the usefulness of the model. Numerical experiments on test problems shows that acceptable gaps are obtained in reasonable time.

    Place, publisher, year, edition, pages
    Lisbon, Portugal: University of Lisbon, 2005
    Keywords
    Internet Protocol, OSPF, network design, in-graph
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-30654 (URN)16250 (Local ID)16250 (Archive number)16250 (OAI)
    Conference
    INOC 2005: Lisbon, Portugal, March 20-23, 2005
    Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2013-11-06
  • 2.
    Broström, Peter
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Optimization Models and Methods for Telecommunication Networks using OSPF2006Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The routing in OSPF Telecommunication networks is determined by computing shortest paths with respect to link weights set by the network operator. All shortest paths to a destination are used by the routers when traffic is routed, and the routers split the traffic evenly when alternative shortest paths exist.

    This thesis includes models and methods for various problems related to OSPF networks and OSPF routing. Two different models for the design of OSPF networks are presented. One model ensures that the network is capable of accommodating large parts of the traffic even if a single link fails. The OSPF protocol is modeled using constraints based on weights, and a heuristical method uses the link weights for generating good feasible solutions. The second model is based on routing patterns and does not include the link weights. The OSPF protocol is modeled by ensuring that no pair of routing patterns contains different paths between the same pair of nodes, which is a necessary condition for the existence of weights. A Lagrangean heuristic is proposed as solution method.

    The thesis also includes models that can be used for determining if a set of desired routing patterns is obtainable in an OSPF network. The models are infeasible if no link weights yield shortest path graphs which are identical to the patterns, and this means that the patterns can not be used simultaneously in an OSPF network. Infeasible instances are characterized using LP-duality, and a certain structure called “valid cycle” is found in most infeasible instances. A valid cycle involves two routing patterns and indicates which parts of the patterns that are in conflict. This information can be used for finding weights that yields slightly modified patterns. Polynomial methods which can be used for finding valid cycles are presented. There are however also some infeasible instances where no valid cycle exists, so the absence of valid cycles is a necessary condition for the existence of weights. In this case, the conflict involves more than two routing patterns, and such conflicts are characterized by a structure called “3-valid set of cycles”. The absence of 3-valid sets of cycles is a stronger necessary condition for the existence of weights.

  • 3.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    A new derivation of valid cycles2005Report (Other academic)
  • 4.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Compatible Weights and Valid Cycles in Non-spanning OSPF Routing Patterns2007Report (Other academic)
  • 5.
    Broström, Peter
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Compatible Weights and Valid Cycles in Non-spanning OSPF Routing Patterns2009In: Algorithmic Operations Research, ISSN 1718-3235, Vol. 4, no 1, p. 19-35Article in journal (Refereed)
    Abstract [en]

    Many IP (Internet Protocol) networks use OSPF (Open Shortest Path First) for determining the routing of traffic. OSPF routers compute routing paths using link weights set by the network administrator, and the routers send traffic on all shortest paths to the destination. An interesting question is whether or not a set of prespecified routing patterns can be realized in an OSPF network. If not, we seek structural properties that explain why no such weights exist. Mathematical models for finding weights and for combining routing patterns are presented. We show that two possibly non-spanning routing patterns forming a ``valid cycle'' cannot simultaneously be obtained in an OSPF network. Two new methods for finding valid cycles are presented, illustrated by numerical examples, and shown to be faster that those previously known.

  • 6.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Design of OSPF Networks using Subpath Consistent Routing Patterns2007Report (Other academic)
  • 7.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Determining the Non-Existence of a Compatible OSPF Metric2004In: Nordic MPS 2004,2004, 2004Conference paper (Other academic)
  • 8.
    Broström, Peter
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Determining the Non-Existence of a Compatible OSPF Metric2004Report (Other academic)
    Abstract [en]

    Many telecommunication networks use Internet Protocol for deciding the routing of traffic. The specifications OSPF (Open Shortest Path First) and ECM (Equal Cost Multipath) are very common, and state that each router sends the traffic on the shortest path to the destination. If there are several shortest path, the router splits the traffic evenly. In order to have some control over the traffic distribution, the operator can assign weights to the links in the network, and these weights are used by the routers when calculating the shortest paths. It has been shown that by optimizing over the values of the weights, the performance of a network can be much improved. A difficult question is whether or not for a set of desired traffic patterns there exists a compatible metric, i.e. weights making the routers give the specified traffic patterns. There is one known necessary condition for the existence of such a metric, but up to now no sufficient conditions. We investigate this problem, and find more general necessary conditions for the existence of compatible weights for a set of given desired "shortest path"-graphs. A polynomial algorithm that for most cases verifies the non-existence of a compatible metric is presented. The algorithm also indicates which parts of the traffic patterns that are in conflict. A few numer;cal examples are used to illustrate the procedure, and some computational tests are reported.

  • 9.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Internet Protocol Network Design and Routing2003In: 18th International Symposium on Mathematical Programming,2003, 2003Conference paper (Other academic)
  • 10.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Multiobjective design of survivable IP networks2004Report (Other academic)
  • 11.
    Broström, Peter
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Multiobjective design of survivable IP networks2006In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 147, no 1, p. 235-253Article in journal (Refereed)
    Abstract [en]

    Modern communication networks often use Internet Protocol routing and the intra-domain protocol OSPF (Open Shortest Path First). The routers in such a network calculate the shortest path to each destination and send the traffic on these paths, using load balancing. The issue of survivability, i.e. the question of how much traffic the network will be able to accommodate if components fail, is increasingly important. We consider the problem of designing a survivable IP network, which also requires determining the routing of the traffic. This is done by choosing the weights used for the shortest path calculations.

  • 12.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    On the Extremal Structure of an OSPF Related Cone2007In: Vietnam journal of mathematics, ISSN 0866-7179, Vol. 35, p. 507-522Article in journal (Refereed)
  • 13.
    Broström, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Holmberg, Kaj
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    On the Extremal Structure of an OSPF Related Cone2006Report (Other academic)
  • 14.
    Broström, Peter
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric2004Report (Other academic)
    Abstract [en]

    A dominating standard for routing in telecommunication networks is Internet Protocol with OSPF (Open Shortest Path First) and ECM (Equal Cost Multipath). Each router sends the traffic on the shortest path to the destination. If there are several shortest path, the router splits the traffic evenly. The operator can assign weights to the links in the network, which are used by the routers when calculating the shortest paths. An important question is whether or not for a set of desired traffic patterns there exists a compatible metric, i.e. weights making the routers give the specified traffic patterns. We describe necessary conditions, stronger than those previously discovered, for the existence of compatible weights for a set of given desired shortest path-graphs.

  • 15.
    Broström, Peter
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Holmberg, Kaj
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Valid Cycles: A Source of Infeasibility in Open Shortest Path First Routing2008In: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 52, no 4, p. 206-215Article in journal (Refereed)
    Abstract [en]

    Many telecommunication networks use the open shortest path first (OSPF) protocol for the routing of traffic. In such networks, each router sends the traffic on the shortest paths to the destination, with respect to the link weights assigned. An interesting question is whether or not a set of desired routing patterns can be obtained in an OSPF network by assigning appropriate weights. If not, we wish to find the source of the infeasibility. We study these issues by formulating a mathematical model and investigating its feasibility. A certain structure, called valid cycle, is found to be present in most infeasible instances. This yields new necessary conditions, stronger than those previously known, for the existence of weights yielding a set of given desired shortest path graphs. A valid cycle indicates which parts of the routing patterns are in conflict and can be used for changing the routing patterns to make the problem feasible. A polynomial algorithm for finding valid cycles is presented, the method is illustrated by a numerical example, and computational tests are reported.

  • 16.
    Holmberg, Kaj
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Broström, Peter
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Design of IP/OSPF Networks Using a Lagrangean Heuristic on an In-graph Based Model2005In: Proceedings of the International Network Optimization Conference, INOC 2005 / [ed] L. Gouveia and C. Mourao, Lisbon, Portugal: University of Lisbon , 2005, p. 702-Conference paper (Refereed)
    Abstract [en]

    This paper address the problem of designing IP networks where traffic is distributed in accordance with the OSPF protocol. Routers use link weights for determining how traffic is distributed. All shortest paths between pairs of routers are used and the traffic is evenly divided when several paths are shortest. We formulate a new model for the design of IP networks with OSPF and ECM distribution where weights are implicitly included. Necessary constraints for representing the shortest paths obtained from link weights by in-graphs are described. A Lagrangean heuristic is developed for verifying the usefulness of the model. Numerical experiments on test problems shows that acceptable gaps are obtained in reasonable time.

  • 17.
    Holmberg, Kaj
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Broström, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Determining the Non-Existence of a Compatible OSPF Metric2005In: International Network Optimization Conference, INOC 2005,2005, Lisbon, Portugal: University of Lisbon, , 2005, p. 106-Conference paper (Refereed)
  • 18.
    Holmberg, Kaj
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Broström, Peter
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Stronger Necessary Conditions for the Existence of a Compatible OSPF Metric2004In: Nordic MPS 04,2004, 2004Conference paper (Other academic)
1 - 18 of 18
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