Michal Zagozdzon

Path Generation for a Class of Survivable Network Design Problems

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.

Optimization of The Shortest-Path Routing with Equal-Cost Multi-Path Load Balancing

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

Flow optimization in IP networks with fast proactive recovery

The post-failure convergence of the shortest path routing (SPR) protocols used in IP networks can be too slow to meet the restrictive requirements (i.e., maximum allowable delay, jitter, etc.) of the multimedia services and therefore new restoration mechanisms combined with IP routing are of interest. The paper addresses optimization of three potential rerouting mechanisms based on the IP fast reroute mechanism proposed by Shand and Bryant [1]. The first mechanism takes advantage of equal-cost multiple (shortest) paths (ECMP) where two or more ECMP paths outgoing from one router can be used to protect one another in the IP fast reroute mechanism. Due to a limited number of the ECMP paths, the ECMP protection cannot be used as a stand-alone rerouting mechanism which assures protection against all link failures. Therefore, two other mechanisms, called loop-free alternate (LFA) and multi-hop repair path (MHRP) are considered. The LFA protection consists in determining an alternative next-hop address used in the case of a link failure. MHRP is a generalization of LFA which uses multi-hop tunnels to redirect packets from the failing link to a router that is able to send them to the destination based on a shortest path based forwarding. For each of the mechanisms we formulate an appropriate optimization problem as a mixed integer program (MIP). Moreover, we consider a combined approach where protection is assured through ECMP paths, LFA next-hop addresses, or MHRP paths. Thanks to the variety of protection mechanisms, the IP fast reroute technique is able to provide protection for any single link failure. The associated optimization problem (consisting in a simultaneous optimization of a weight system, LFA alternative next-hop addresses and MHRP paths) is difficult and is thus approached with a heuristic method. In our numerical experiments we evaluate effectiveness of this method.

Path Generation Issues for Survivable Network Design

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.

A subgradient optimization approach to inter-domain routing in IP/MPLS networks

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].

Optimization of resilient IP networks with shortest path routing

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 meta-heuristic. The efficiency of the proposed weight optimization method is illustrated by means of a numerical study. (Less)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.

Three Methods for Optimizing Single-Shortest Path Routing

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.

Optimization of resilient weight systems for shortest-path routing in IP networks

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 meta-heuristic. The efficiency of the proposed weight optimization method is illustrated by means of a numerical study. (Less)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.

Traffic Flow Optimization in Networks with Combined OSPF/MPLS Routing

Developing object-oriented database for web applications may not remain constant and may vary to a large extent due to a variety of reasons like correcting mistakes, adding new features or any changes in the structure of the real world artifacts modeled in the database. Class versioning is one of the evolution strategy employed that addressing the above issues. The existing strategy for instance adaptation introduces the adaptation code directly into the class versions upon evolution. Consequently, if the behavior of a routine needs to be changed and maintenance has to be performed on all the class versions it was introduced. A new approach for instance adaptation is achieved by encapsulating the instance adaptation code through aspects - abstractions introduced by aspect-oriented programming that localize cross-cutting concerns. A web-based student database system was developed with different versions and the versioning problem was solved using update/backdate aspects with selective lazy conversion. The update/backdate aspects are invoked whenever version incompatibility arises and selective lazy conversion aspect is invoked when the condition for converting objects into new version is satisfied and this converts only a subset of the old version objects into new version.

Traffic flow optimization in networks with combined OSPF/MPLS routing

Developing object-oriented database for web applications may not remain constant and may vary to a large extent due to a variety of reasons like correcting mistakes, adding new features or any changes in the structure of the real world artifacts modeled in the database. Class versioning is one of the evolution strategy employed that addressing the above issues. The existing strategy for instance adaptation introduces the adaptation code directly into the class versions upon evolution. Consequently, if the behavior of a routine needs to be changed and maintenance has to be performed on all the class versions it was introduced. A new approach for instance adaptation is achieved by encapsulating the instance adaptation code through aspects - abstractions introduced by aspect-oriented programming that localize cross-cutting concerns. A web-based student database system was developed with different versions and the versioning problem was solved using update/backdate aspects with selective lazy conversion. The update/backdate aspects are invoked whenever version incompatibility arises and selective lazy conversion aspect is invoked when the condition for converting objects into new version is satisfied and this converts only a subset of the old version objects into new version.