Ankara : The Department of Industrial Engineering and The Institute of Engineering and Science of Bilkent Univ., 2007.Thesis (Ph.D.) -- Bilkent University, 2007.Includes bibliographical references leaves 160-166.In this thesis, we study the design of networks robust to changes in demand
estimates. We consider the case where the set of feasible demands is defined by
an arbitrary polyhedron. Our motivation is to determine link capacity or routing
configurations, which remain feasible for any realization in the corresponding
demand polyhedron. We consider three well-known problems under polyhedral
demand uncertainty all of which are posed as semi-infinite mixed integer programming
problems. We develop explicit, compact formulations for all three problems
as well as alternative formulations and exact solution methods.
The first problem arises in the Virtual Private Network (VPN) design field.
We present compact linear mixed-integer programming formulations for the problem
with the classical hose traffic model and for a new, less conservative, robust
variant relying on accessible traffic statistics. Although we can solve these formulations
for medium-to-large instances in reasonable times using off-the-shelf MIP
solvers, we develop a combined branch-and-price and cutting plane algorithm to
handle larger instances. We also provide an extensive discussion of our numerical
results.
Next, we study the Open Shortest Path First (OSPF) routing enhanced with
traffic engineering tools under general demand uncertainty with the motivation to
discuss if OSPF could be made comparable to the general unconstrained routing
(MPLS) when it is provided with a less restrictive operating environment. To
the best of our knowledge, these two routing mechanisms are compared for the
first time under such a general setting. We provide compact formulations for
both routing types and show that MPLS routing for polyhedral demands can
be computed in polynomial time. Moreover, we present a specialized branchand-price
algorithm strengthened with the inclusion of cuts as an exact solution tool. Subsequently, we compare the new and more flexible OSPF routing with
MPLS as well as the traditional OSPF on several network instances. We observe
that the management tools we use in OSPF make it significantly better than the
generic OSPF. Moreover, we show that OSPF performance can get closer to that
of MPLS in some cases.
Finally, we consider the Network Loading Problem (NLP) under a polyhedral
uncertainty description of traffic demands. After giving a compact multicommodity
formulation of the problem, we prove an unexpected decomposition
property obtained from projecting out the flow variables, considerably simplifying
the resulting polyhedral analysis and computations by doing away with metric inequalities,
an attendant feature of most successful algorithms on NLP. Under the
hose model of feasible demands, we study the polyhedral aspects of NLP, used as
the basis of an efficient branch-and-cut algorithm supported by a simple heuristic
for generating upper bounds. We provide the results of extensive computational
experiments on well-known network design instances.Altın, AyşegülPh.D
