Mateusz Dzida

Warsaw University of Technology, Warsaw, Masovian Voivodeship, Poland

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Publications (20)1.03 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: In telecommunication networks based on the current Ethernet technology, routing of traffic demands is based on multiple spanning trees: the network operator configures different routing spanning trees and assigns each demand to be routed in one of the selected spanning trees. A major optimization issue in this solution is the combined determination of (i) aset of appropriate spanning trees, and (ii) assignment of demands to the trees, in order to achieve an optimal load balancing on the links of the network. In this paper we consider models and solving techniques for lexicographical optimization of two load balancing objective functions. The first objective is the min-max optimization of the n worst link loads (with n up to the total number of network links), and the second objective is the minimization of the average link load (when n is smaller than the total number of network links). Besides exact methods, a heuristic technique that can compute both feasible solutions and lower bounds for the addressed optimization problem is proposed. Finally, we discuss effectiveness of different solution using results of a numerical study of realistic case studies. KeywordsEthernet networks–Load balancing–Multiple spanning tree routing–Traffic engineering–Integer programming
    Telecommunication Systems 01/2010; 48(1):109-124. · 1.03 Impact Factor
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    ABSTRACT: This paper deals with optimal load balancing in telecommunication networks based on multiple spanning tree routing. This is the case in switched Ethernet networks where the operator configures different routing spanning trees and assigns each demand VLAN to one of the spanning trees. We consider modeling and solving three load balancing objectives: (i) minimization of the average link load with a guaranteed optimal worst case link load, (ii) minimization of the worst case link load with a guaranteed optimal average link load and (iii) the min-max optimization of link loads. We also propose heuristic techniques to compute both feasible solutions and lower bounds for the addressed optimization problems. Finally, we assess both the efficiency and the efficacy of the different solution techniques and compare the quality of each problem solution taking into account the optimization criteria of the other problems.
    Next Generation Internet Networks, 2009. NGI '09; 08/2009
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    ABSTRACT: This paper deals with optimal load balancing in telecommunication networks based on multiple spanning tree routing. This is the case in switched Ethernet networks where the operator configures different routing spanning trees and assigns each demand VLAN to one of the spanning trees. We consider modeling and solving three load balancing objectives: (i) minimization of the average link load with a guaranteed optimal worst case link load, (ii) minimization of the worst case link load with a guaranteed optimal average link load and (iii) the min-max optimization of link loads. We also propose heuristic techniques to compute both feasible solutions and lower bounds for the addressed optimization problems. Finally, we assess both the efficiency and the efficacy of the different solution techniques and compare the quality of each problem solution taking into account the optimization criteria of the other problems.
    Next Generation Internet Networks, 2009. NGI '09, Aviero, Portugal, July 1-3, 2009; 01/2009
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    ABSTRACT: The paper addresses an optimization problem re-lated to dimensioning links in a resilient two-layer network. A particular version of the problem which assumes that links of the upper layer are supported by unique paths in the lower layer is considered. Two mixed-integer programming formu-lations of this problem are presented and discussed. Direct re-solving of these formulations requires pre-selection of "good" candidate paths in the upper layer of the network. Thus, the paper presents an alternative approach which is based on decomposing the resolution process into two phases, resolved iteratively. The first phase subproblem is related to design-ing lower layer path flows that provide the capacities for the logical links of the upper layer. The second phase is related to designing the flow patterns in the upper layer with protec-tion assured through diversity of paths. In this phase we take into account the failures of the logical links that result from the failures of the lower layer links (so called shared risk link groups). Keywords— link dimensioning, path diversity, resilient routing, two-layer network optimization.
    01/2009;
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    ABSTRACT: Intra-domain routing in IP networks is based on the shortest path principle by assigning administrative weights (costs) to links. The resulting least-cost paths determine routes between pairs of routers. If several such equal-cost paths exist between a pair of routers, it may not be clear which of them is actually used to route traffic. This makes it difficult to predict the network traffic flow distribution. Therefore, the selected link costs should assure uniqueness of the shortest paths. On top of that, the link costs can be optimized with respect to some traffic objective. The resulting optimization problem, referred to as SSPP, turns out to be NP-hard. SSPP can be formulated as a mixed-integer programming problem and, as such, solved with branch-and- bound (B&B). In this paper, we consider three methods for SSPP. Two of them are exact methods based on B&B, namely branch- and-cut and constraint programming. Since the exact solutions of SSPP may require excessive computation time and may not always be effective when applied to practical networks, we also study a fast heuristic method. Finally, in a numerical study, we compare the effectiveness of the three approaches.
    Next Generation Internet Networks, 2008. NGI 2008; 05/2008
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    ABSTRACT: In this paper we address link dimensioning and routing problems related to the area of resilient network design. We present two network design problems that assume different flow restoration schemes used to cope with network failures. In both cases we allow bifurcation of traffic flows in the normal (failure-less) network state. In the case of a failure, we assume that affected primary flows (i.e., flows applied in the normal state) are restored using assigned protection paths and that the primary flows are restored (also in a bifurcated manner) in a separate pool of (protection) capacity, distinct from the basic capacity used in the normal network operation state. The two presented models differ in the way protection paths are used to protect primary flows against different failure states. The first model, called state-independent flow restoration, assumes that once the backup path is assigned it must be used in every state in which the protected primary path fails. The second model allows different protection paths to be used in different network failure states and is called state-dependent flow restoration. The considered problems are formulated as linear programming (LP) problems using link-path (L-P) notation of multi-commodity flow network optimization. As the L-P notation is useful only when an effective column generation scheme is known, we discuss the applicability of this method on the basis of the theory of duality of LP. The paper presents and compares three different approaches and evaluates their usefulness for solving problem instances of practical size.
    Next Generation Internet Networks, 2008. NGI 2008; 05/2008
  • M. Zagozdzon, M. Dzida, M. Pioro
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    ABSTRACT: In this paper we address intra-domain routing optimization issues in Internet networks related to a combination of open shortest path first (OSPF) and multi protocol label switching (MPLS) routing protocols. Since MPLS can be combined with any routing protocol there has appeared an idea of coupling IP streams routed via the OSPF protocol and MPLS label switched paths (LSPs) in the same network. Such combined routing is potentially more flexible and efficient than OSPF itself from the traffic engineering (TE) viewpoint. In the paper we present the exact approach to the considered hybrid routing design using a strict mathematical formulation of the underlying optimization problem, and also a heuristic approach decomposing the problem into two subproblems solved with evolutionary algorithm and simulated allocation. The effectiveness of both approaches is illustrated by means of a numerical study.
    Advanced Computing and Communications, 2007. ADCOM 2007. International Conference on; 01/2008
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    ABSTRACT: A powerpoint presentation is given. The paper discusses flow optimization in IP networks with fast proactive recovery. IP fast rerouting includes equal-cost multiple paths, loop free alternate and multihop repair path. The main purpose of the optimization model is to exhibit the efficiency of the IPFR , to develop an efficient resolution method based on iterative heuristic partitioning method by numerical experiments, and to be able to eliminate almost all( disadvantageous) MHRP paths.
    Telecommunications Network Strategy and Planning Symposium, 2008. Networks 2008. The 13th International; 01/2008
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    Computational Science and Its Applications - ICCSA 2008, International Conference, Perugia, Italy, June 30 - July 3, 2008, Proceedings, Part II; 01/2008
  • M. Dzida, M. Zagozdzon, M. Pioro
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    ABSTRACT: In the paper we address traffic engineering problems related to optimization of routing in IP networks applying destination-based shortest path routing (SPR) of the OSPF type. An SPR routing pattern is determined by a system of (administrative) weights defined over the set of IP links: the routes for IP forwarding are determined as the shortest paths computed locally at the nodes using the current link weights. When the shortest path from a certain node (node v, say) to a particular destination (destination t, say) is not unique, the traffic routed from node v to destination t is split equally among all links outgoing from v that belong to the shortest paths to destination t, i.e., according to the Equal Cost Multiple-Paths (ECMP) rule. The basic problem considered in this paper consists in finding a resilient link weight system generating a routing scheme that satisfies given traffic demands and does not lead to link overloads both in the normal network state of operation and in all considered failure states when certain IP links are failed. We assume that if a failure occurs then the weight system is modified by assigning infinite weights to the failed links, and not altering the weights of the remaining, operating links. We consider the traffic engineering goal related to minimization, over all failure states, of the maximal link overload. We formulate the considered problem as a mixed integer programme (MIP) and propose a heuristic algorithm based on the tabu search metaheuristic. The efficiency of the proposed weight optimization method is illustrated by means of a numerical study.
    Design and Reliable Communication Networks, 2007. DRCN 2007. 6th International Workshop on; 11/2007
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    ABSTRACT: We present a mathematical model for a distributed process of routing optimization that could be run in the control plane of the Internet using existing EGP routing protocols. A more detailed description of the results presented in this paper is given in [1].
    NETWORKING 2007. Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet, 6th International IFIP-TC6 Networking Conference, Atlanta, GA, USA, May 14-18, 2007, Proceedings; 01/2007
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    M. Dzida, M. Mycek, M. Zago
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    ABSTRACT: In autonomous systems of the Internet packets are routed on shortest paths to their destinations, for example according to the ECMP principle. The problem of finding a feasible traffic routing configuration realized on paths which can be generated by a system of weights assigned to IP links is NP-hard. This problem can be formulated as a mixed-integer program and attempted with a branch-and-cut algorithm if effective cuts (valid inequalities) can be derived. In this paper we present exact and approximate LP- and MIP- based methods for generating valid inequalities that separate fractional solutions of the basic problem. Besides, a family of complementary valid inequalities, generated with a shortest-path algorithm, related to combinatorial properties of feasible traffic routes is introduced to speed up the cut generation process. Results of a numerical study illustrating computational issues are discussed.
    01/2007;
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    ABSTRACT: The paper considers a problem of routing, protection and load balancing in the IP/MPLS network. A network design problem combining all these aspects is presented. Proportionally fair distribution of residual bandwidths on links is used for load balancing, and protection is achieved with failure–dependent backup paths. The efficiency of the proposed approach is tested by combining optimization and simulation tools. Numerical experiments show that using the proposed load balancing and protection mechanisms decreases the number of disrupted LSPs in case of failures, as compared to other recovery options considered.
    Managing Traffic Performance in Converged Networks, 20th International Teletraffic Congress, ITC20 2007, Ottawa, Canada, June 17-21, 2007, Proceedings; 01/2007
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    ABSTRACT: In this paper we address the problem of routing optimization in IP networks. We assume that traffic is routed along the shortest paths computed with respect to administrative link metrics. Metrics are distributed in a network by open shortest path first (OSPF) or a similar routing protocol. If it happens that the shortest path is not unique then equal-cost multi-path (ECMP) load balancing principle is applied. It means that the demand traffic destined to specific node is split among all the shortest paths to that node. The problem considered here is to determine the shortest-path routing pattern satisfying traffic demands, and to find appropriate link metrics while link capacities are not exceeded. Besides that many traffic engineering criterias can be used as objective function of the problem, we assume that the residual capacity volume is maximized. In this paper we formulate the problem as a mixed integer programme (MIP) and propose some combinatorial separation cuts for the problem and give an effective method for deriving such cuts
    Transparent Optical Networks, 2006 International Conference on; 07/2006
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    ABSTRACT: We address some Internet core network optimization issues related to a combination of Open Shortest Path First (OSPF) and Multi Protocol Label Switching (MPLS) routing protocols. Since MPLS can be combined with any routing protocol there has appeared an idea of coupling IP streams routed via the OSPF protocol and MPLS Label Switched Paths (LSPs) in the same network. One expected advantage behind such a combined routing is to adjust the design stage by allowing some flows to be routed via OSPF while others to be transmitted via MPLS LSPs. In the paper we discuss two routing optimization problems. In the first case, OSPF routing protocol works over logical network with generalized IP links. These links are either standard IP links or IP links established as MPLS LSPs. In the second case, we distinguish two types of demands depending on whether OSPF routing is used or packets are switched by MPLS Label Switch Routers (LSR). We present both problem formulations and discuss the question on how to effectively solve these problems.
    Systems Science 01/2006; 32(3).
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    ABSTRACT: The paper deals with traffic recovery in IP/MPLS network carrying traffic of different priority classes. Two off-line network design problems are presented employing two different recovery mechanisms – single backup path and failure-dependent backup path protection Also, two routing strategies are studied in this paper. A network design problem with failure-dependent path protection mechanism combined with the routing strategy implying both load balancing and path length minimization is proposed in this paper. The efficiency of the approach proposed is tested by combining optimization and simulation tools. Numerical experiments show that using the proposed protection mechanism allows more traffic to be accommodated in the network and decreases the number of disrupted LSPs in case of failure, as compared to other recovery options considered.
    Systems Science 01/2006; 32(3).
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    ABSTRACT: The rapid growth of traffic induced by Internet services makes the simple over-provisioning of resources not economical and hence imposes new requirements on the dimensioning methods. Therefore, the problem of network design with the objective of minimizing the cost and at the same time solving the tradeoff between maximizing the service data flows and providing fair treatment of all demands becomes more and more important. In this context, the so-called max-min fair (MMF) principle is widely considered to help finding reasonable bandwidth allocation schemes for competing demands. Roughly speaking, MMF assumes that the worst service performance is maximized, and then is the second worst performance, the third one, and so on, leading to a lexicographically maximized vector of sorted demand bandwidth allocations. It turns out that the MMF optimal solution cannot be approached in a standard way (i.e., as a mathematical programming problem) due to the necessity of lexicographic maximization of ordered quantities (bandwidth allocated to demands). Still, for convex models, it is possible to formulate effective sequential procedures for such lexicographic optimization. The purpose of the presented paper is three-fold. First, it discusses resolution algorithms for a generic MMF problem related to telecommunications network design. Second, it gives a survey of network design instances of the generic formulation, and illustrates the efficiency of the general algorithms in these particular cases. Finally, the paper discusses extensions of the formulated problems into more practical (unfortunately non-convex) cases, where the general for convex MMF problems approach fails.
    Next Generation Internet Networks, 2005; 05/2005
  • MMB & PGTS 2004, 12th GI/ITG Conference on Measuring and Evaluation of Computer and Communication Systems (MMB) together with 3rd Polish-German Teletraffic Symposium (PGTS), September 12-15, 2004, Dresden, Germany; 01/2004
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    ABSTRACT: Link dimensioning and routing problems in resilient network design are considered. Reliable network operation is ensured by means of flow restoration which is performed on preselected protection (backup) paths that can absorb traffic overflows from failed primary paths. Backup and primary flows use separated link capacities, and can be split among many paths. In the paper, two restoration models are considered. The first model assumes that once the backup path is assigned it must be used in every state in which the protected primary path fails while the second model allows different protection paths to be used in different network failure states. The problems are formulated as multiple commodity linear programming (LP) models using the link-path (L-P) notation and solved by the column generation technique. Consequent pricing models and algorithms are introduced. Computational efficiency of the presented approaches is analyzed.
    01/1970: pages 820-835;
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    ABSTRACT: The goal of the report is to present a mathematical model for opti-mizing traffic routing in a multi-domain Internet-type network. In such an envi-ronment each domain is operated autonomously and has access to very limited information about the rest of the network. Our model attempts to reflect this situation through an appropriate problem decomposition with respect to indi-vidual domains. The decomposition aims at supporting a distributed process of routing optimization that could be run in the control plane of the network using existing EGP routing protocols. The usefulness of the Lagrangean and Dantzig-Wolfe decompositions is investigated and illustrated with numerical examples. The model is formulated in the context of multiple traffic classes.