198 research outputs found
Designing Network Protocols for Good Equilibria
Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs
Optimization of Free Space Optical Wireless Network for Cellular Backhauling
With densification of nodes in cellular networks, free space optic (FSO)
connections are becoming an appealing low cost and high rate alternative to
copper and fiber as the backhaul solution for wireless communication systems.
To ensure a reliable cellular backhaul, provisions for redundant, disjoint
paths between the nodes must be made in the design phase. This paper aims at
finding a cost-effective solution to upgrade the cellular backhaul with
pre-deployed optical fibers using FSO links and mirror components. Since the
quality of the FSO links depends on several factors, such as transmission
distance, power, and weather conditions, we adopt an elaborate formulation to
calculate link reliability. We present a novel integer linear programming model
to approach optimal FSO backhaul design, guaranteeing -disjoint paths
connecting each node pair. Next, we derive a column generation method to a
path-oriented mathematical formulation. Applying the method in a sequential
manner enables high computational scalability. We use realistic scenarios to
demonstrate our approaches efficiently provide optimal or near-optimal
solutions, and thereby allow for accurately dealing with the trade-off between
cost and reliability
Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity
International audienceFlow thinning (FT) is a concept of a traffic routing and protection strategy applicable to communication networks withvariable capacity of links. In such networks, the links do not attain their nominal (maximum) capacity simultaneously, so in atypical network state only some links are fully available whereas on each of the remaining links only a fraction of itsmaximum capacity is usable. Every end-to-end traffic demand is assigned a set of logical tunnels whose total capacity isdedicated to carry the demand’s traffic. The nominal (i.e., maximum) capacity of the tunnels, supported by the nominal(maximum) link capacity, is subject to state-dependent thinning to account for variable capacity of the links fluctuating belowthe maximum. Accordingly, the capacity available on the tunnels is also fluctuating below their nominal levels and hence theinstantaneous traffic sent between the demand’s end nodes must accommodate to the current total capacity available onits dedicated tunnels. The related multi-commodity flow optimization problem is NP-hard and its noncompact linearprogramming formulation requires path generation. For that, we formulate an integer programming pricing problem, atthe same time showing the cases when the pricing is polynomial. We also consider an important variant of FT, affinethinning, that may lead to practical FT implementations. We present a numerical study illustrating traffic efficiency of FT andcomputational efficiency of its optimization models. Our considerations are relevant, among others, for wireless meshnetworks utilizing multiprotocol label switching tunnels
Optimization in Telecommunication Networks
Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Menger’s disjoint paths theorem, and Ford-Fulkerson’s max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;
Randomized rounding algorithms for large scale unsplittable flow problems
Unsplittable flow problems cover a wide range of telecommunication and
transportation problems and their efficient resolution is key to a number of
applications. In this work, we study algorithms that can scale up to large
graphs and important numbers of commodities. We present and analyze in detail a
heuristic based on the linear relaxation of the problem and randomized
rounding. We provide empirical evidence that this approach is competitive with
state-of-the-art resolution methods either by its scaling performance or by the
quality of its solutions. We provide a variation of the heuristic which has the
same approximation factor as the state-of-the-art approximation algorithm. We
also derive a tighter analysis for the approximation factor of both the
variation and the state-of-the-art algorithm. We introduce a new objective
function for the unsplittable flow problem and discuss its differences with the
classical congestion objective function. Finally, we discuss the gap in
practical performance and theoretical guarantees between all the aforementioned
algorithms
Dynamic unsplittable flows with path-change penalties: new formulations and solution schemes for large instances
In this work, we consider the dynamic unsplittable flow problem. This
variation of the unsplittable flow problem has received little attention so
far. The unsplittable flow problem is an NP-hard extension of the
multi-commodity flow problem where each commodity sends its flow on only one
path. In its dynamic version, this problem features several time steps and a
penalty is paid when a commodity changes its path from one time step to the
next. We present several mixed-integer linear programming formulations for this
problem and compare the strength of their linear relaxation. These formulations
are embedded in several solvers which are extensively compared on small to
large instances. One of these formulations must be solved through a column
generation process whose pricing problem is more difficult than those used in
classical flow problems. We present limitations of the pricing schemes proposed
in earlier works and describe two new schemes with a better worst-case
complexity. Overall, this work lays a strong algorithmic baseline for the
resolution of the dynamic unsplittable flow problem, proposes original
formulations, and discusses the compared advantages of each, thus hopefully
contributing a step towards a better understanding of this problem for both OR
researchers and practical applications
Algorithms for Inverse Optimization Problems
We study inverse optimization problems, wherein the goal is to map given solutions to an underlying optimization problem to a cost vector for which the given solutions are the (unique) optimal solutions. Inverse optimization problems find diverse applications and have been widely studied. A prominent problem in this field is the inverse shortest path (ISP) problem [D. Burton and Ph.L. Toint, 1992; W. Ben-Ameur and E. Gourdin, 2004; A. Bley, 2007], which finds applications in shortest-path routing protocols used in telecommunications. Here we seek a cost vector that is positive, integral, induces a set of given paths as the unique shortest paths, and has minimum l_infty norm. Despite being extensively studied, very few algorithmic results are known for inverse optimization problems involving integrality constraints on the desired cost vector whose norm has to be minimized.
Motivated by ISP, we initiate a systematic study of such integral inverse optimization problems from the perspective of designing polynomial time approximation algorithms. For ISP, our main result is an additive 1-approximation algorithm for multicommodity ISP with node-disjoint commodities, which we show is tight assuming P!=NP. We then consider the integral-cost inverse versions of various other fundamental combinatorial optimization problems, including min-cost flow, max/min-cost bipartite matching, and max/min-cost basis in a matroid, and obtain tight or nearly-tight approximation guarantees for these. Our guarantees for the first two problems are based on results for a broad generalization, namely integral inverse polyhedral optimization, for which we also give approximation guarantees. Our techniques also give similar results for variants, including l_p-norm minimization of the integral cost vector, and distance-minimization from an initial cost vector
Exact approaches for designing multifacility buy-at-bulk networks
We study a problem that integrates buy-at-bulk network design into the classical facility location problem. We consider a generalization of the facility location problem where multiple clients may share a capacitated network to connect to open facilities instead of requiring direct links. In this problem, we wish to open facilities, build a routing network by installing access cables of different costs and capacities, and route every client demand to an open facility. We provide a path based formulation and we compare it with the natural compact formulation for this problem. We then design an exact branch-price-and-cut algorithm for solving the path based formulation. We study the effect of two families of valid inequalities. In addition to this, we present three different types of primal heuristics and employ a hybrid approach to effectively combine these heuristics in order to improve the primal bounds. We finally report the results of our approach that were tested on a set of real world instances as well as two sets of benchmark instances and evaluate the effects of our valid inequalities and primal heuristics
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