Browsing by Subject "Flow Formulation"

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Open Access
Failure independent path protection against single-SRLG failures in Elastic Optical Networks
(2018-02) Uysal, Hasan Gökhan
In Elastic Optical Networks, exi-grid spectrum allocation is used where the the spectrum is assigned to optical connections according to their bandwidth requirements so that the capacity is used more e ciently. Ensuring network survivability is one of the main problem in elastic optical networks. In this thesis, we study network survivability against failure of a single link or a single Shared Risk Link Group (SRLG), which is a group of links sharing a common risk of failure. We formulate the network survivability problem where the objective is to minimize the required capacity resources and maximize their e cient usage such that the elastic optical network can recover against all single-SRLG failures. We developed two formulations towards this end using ow and path formulation approaches, respectively. In both approaches, the aim is to use two paths called the active and backup paths for all connection demands. In the normal operations, the active path is used. It is switched to the backup path in case of a failure of the active path. The active and backup paths are chosen SRLG-disjoint so that the network can recover from the failure without knowing the location of the failure, which is called failure independent protection. For the spectrum allocation, an Adaptive Coding and Modulation (AMC) scheme, which assigns the appropriate AMC pro le based on the path length, is used. The backup paths can be shared among active paths because concurrent failure of multiple SRLGs is neglected. In the Flow Formulation, an Integer Linear Programming (ILP) is used to calculate SRLG-disjoint active and backup paths according to a given network topology, the set of connection demands and the AMC pro le. In the Path Formulation, an ILP is used to select active and backup paths from a pre-computed set of SRLG-disjoint path pairs. In both approaches, the aim is to minimize the resource usage. The formulations are tested for the 14-node NSFNET and the 24-node USANET topologies. Although the performance of the Flow Formulation is better than the Path Formulation, the Path Formulation has smaller execution times due to its simplicity. The Path Formulation nds a solution for all possible connection demands of the 14-node NSFNET and the 24-node USANET, but the Flow Formulation was not able to nd a solution for the NSFNET topology when the number of demands is large and for the USANET topology even for low number of demands. Both formulations are tested for 10 randomly selected demand sets each with 50 connection requests for 14- node NSFNET and the performance of the Flow Formulation is 5% better than the Path Formulation on the average. In some cases, the Path Formulation gives a better solution than the Flow Formulation when the runtime is limited because of the quality of the pre-computed set of path pairs. The Path Formulation is tested by limiting the number of pre-computed path pairs for all possible demands in 24-node USANET. It is found that the optimal solution rst decreases rapidly as the number of path pair increases, but then it saturates when the number of path pairs per connection exceeds 30.
Open Access
Min-degree constrained minimum spanning tree problem: New formulation via Miller-Tucker-Zemlin constraints
(Elsevier, 2010-01) Akgun, I.; Tansel, B.
Given an undirected network with positive edge costs and a positive integer d > 2, the minimum-degree constrained minimum spanning tree problem is the problem of finding a spanning tree with minimum total cost such that each non-leaf node in the tree has a degree of at least d. This problem is new to the literature while the related problem with upper bound constraints on degrees is well studied. Mixed-integer programs proposed for either type of problem is composed, in general, of a tree-defining part and a degree-enforcing part. In our formulation of the minimum-degree constrained minimum spanning tree problem, the tree-defining part is based on the Miller-Tucker-Zemlin constraints while the only earlier paper available in the literature on this problem uses single and multi-commodity flow-based formulations that are well studied for the case of upper degree constraints. We propose a new set of constraints for the degree-enforcing part that lead to significantly better solution times than earlier approaches when used in conjunction with Miller-Tucker-Zemlin constraints. © 2009 Elsevier Ltd. All rights reserved