Survivable Logical Topology Mapping under Multiple Constraints in IP-over-WDM Networks

The survivable logical topology mapping problem in an IP-over-WDM network deals with the cascading effect of link failures from the bottom (physical) layer to the upper (logical) layer. Multiple logical links may get disconnected due to a single physical link failure, which may cause the disconnection of the logical network. Here we study survivability issues in IP-over-WDM networks with respect to various criteria.We first give an overview of the two major lines of pioneering works for the survivable design problem. Though theoretically elegant, the first approach which uses Integer Linear Programming (ILP) formulations suffers from the drawback of scalability. The second approach, the structural approach, utilizes the concept of duality between circuits and cutsets in a graph and is based on an algorithmic framework called Survivable Mapping Algorithm by Ring Trimming (SMART). Several SMART-based algorithms have been proposed in the literature.In order to generate the survivable routing, the SMART-based algorithms require the existence of disjoint lightpaths for certain groups of logical links in the physical topology, which might not always exist. Therefore, we propose in Chapter 4 an approach to augment the logical topology with new logical links to guarantee survivability. We first identify a logical topology that admits a survivable mapping against one physical link failure. We then generalize these results to achieve augmentation of a given logical topology to survive multiple physical link failures.We propose in Chapter 5 a generalized version of SMART-based algorithms and introduce the concept of robustness of an algorithm which captures the ability of the algorithm to provide survivability against multiple physical link failures. We demonstrate that even when a SMART-based algorithm cannot be guaranteed to provide survivability against multiple physical link failures, its robustness could be very high.Most previous works on the survivable logical topology design problem in IP-over-WDM networks did not consider physical capacities and logical demands. In Chapter 6, we study this problem taking into account logical link demands and physical link capacities. We define weak survivability and strong survivability in capacitated IP-over-WDM networks. Two-stage Mixed-Integer Linear Programming (MILP) formulations and heuristics to solve the survivable design problems are proposed. Based on the 2-stage MILP framework, we also propose several extensions to the weakly survivable design problem, considering several performance criteria. Noting that for some logical networks a survivable mapping may not exist, which prohibits us from applying the 2-stage MILP approach, our first extension is to augment the logical network using an MILP formulation to guarantee the existence of a survivable routing. We then propose approaches to balance the logical demands satisfying absolute or ratio-weighted fairness. Finally we show how to formulate the survivable logical topology design problem as an MILP for the multiple failure case.We conclude with an outline of two promising new directions of research

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

Fairness in Communication and Computer Network Design

In communication networks, fair sharing of resources is an important issue for one main reason. The growth of network capacity is in general not matching the rapid growth of traffic. Consequently, the resources consumed by each user have to be limited. This implies that users cannot always be assigned the end-to-end bandwidth they ask for. Instead, the limited network resources should be distributed to users in a way that assures fair end-to-end bandwidth assignment among them. Obtaining fairness between network users and at the same time assuring efficient network utilization, is a source of non-trivial network optimization problems. Complicating factors are that each user has limited access to the (limited) network resources and that different users require and consume different amounts and types of resources. In this thesis different types of optimization problems associated with fair resource sharing in communication networks are studied. Initially, the notions of max-min fairness, proportional fairness, alpha-fairness etc., are put in a formal framework of fair rational preference relations. A clear, unified definition of fairness is presented. The theory is first applied to different types of allocation problems. Focus is put on convex and non-convex max-min fair traffic allocation problems, and a difference in difficulty between the two groups of problems is demonstrated. The studies are continued by an investigation of proportionally fair dimensioning. Two different cases are studied -- a simpler, when no resilience to failures is required, and a more complicated, assuming the possibility of link failures. In the context of fair sharing of the resources of a communication network, this thesis presents several original theoretical findings as well as solution algorithms for the studied problems. The results are accompanied by numerical results, illustrating algorithm efficiency for virtually all of the studied problems

Approximation Algorithms for Resource Allocation

This thesis is devoted to designing new techniques and algorithms for combinatorial optimization problems arising in various applications of resource allocation. Resource allocation refers to a class of problems where scarce resources must be distributed among competing agents maintaining certain optimization criteria. Examples include scheduling jobs on one/multiple machines maintaining system performance; assigning advertisements to bidders, or items to people maximizing profit/social fairness; allocating servers or channels satisfying networking requirements etc. Altogether they comprise a wide variety of combinatorial optimization problems. However, a majority of these problems are NP-hard in nature and therefore, the goal herein is to develop approximation algorithms that approximate the optimal solution as best as possible in polynomial time. The thesis addresses two main directions. First, we develop several new techniques, predominantly, a new linear programming rounding methodology and a constructive aspect of a well-known probabilistic method, the Lov\'{a}sz Local Lemma (LLL). Second, we employ these techniques to applications of resource allocation obtaining substantial improvements over known results. Our research also spurs new direction of study; we introduce new models for achieving energy efficiency in scheduling and a novel framework for assigning advertisements in cellular networks. Both of these lead to a variety of interesting questions. Our linear programming rounding methodology is a significant generalization of two major rounding approaches in the theory of approximation algorithms, namely the dependent rounding and the iterative relaxation procedure. Our constructive version of LLL leads to first algorithmic results for many combinatorial problems. In addition, it settles a major open question of obtaining a constant factor approximation algorithm for the Santa Claus problem. The Santa Claus problem is a $NP$-hard resource allocation problem that received much attention in the last several years. Through out this thesis, we study a number of applications related to scheduling jobs on unrelated parallel machines, such as provisionally shutting down machines to save energy, selectively dropping outliers to improve system performance, handling machines with hard capacity bounds on the number of jobs they can process etc. Hard capacity constraints arise naturally in many other applications and often render a hitherto simple combinatorial optimization problem difficult. In this thesis, we encounter many such instances of hard capacity constraints, namely in budgeted allocation of advertisements for cellular networks, overlay network design, and in classical problems like vertex cover, set cover and k-median

A resource allocation framework for network slicing

International audienceTelecommunication networks are converging to a massively distributed cloud infrastructure interconnected with software defined networks. In the envisioned architecture, services will be deployed flexibly and quickly as network slices. Our paper addresses a major bottleneck in this context, namely the challenge of computing the best resource provisioning for network slices in a robust and efficient manner. With tractability in mind, we propose a novel optimization framework which allows fine-grained resource allocation for slices both in terms of network bandwidth and cloud processing. The slices can be further provisioned and auto-scaled optimally based on a large class of utility functions in real-time. Furthermore, by tuning a slice-specific parameter, system designers can trade off traffic-fairness with computing-fairness to provide a mixed fairness strategy. We also propose an iterative algorithm based on the alternating direction method of multipliers (ADMM) that provably converges to the optimal resource allocation and we demonstrate the method’s fast convergence in a wide range of quasi-stationary and dynamic settings

Fair Resource Allocation in Macroscopic Evacuation Planning Using Mathematical Programming: Modeling and Optimization

Evacuation is essential in the case of natural and manmade disasters such as hurricanes, nuclear disasters, fire accidents, and terrorism epidemics. Random evacuation plans can increase risks and incur more losses. Hence, numerous simulation and mathematical programming models have been developed over the past few decades to help transportation planners make decisions to reduce costs and protect lives. However, the dynamic transportation process is inherently complex. Thus, modeling this process can be challenging and computationally demanding. The objective of this dissertation is to build a balanced model that reflects the realism of the dynamic transportation process and still be computationally tractable to be implemented in reality by the decision-makers. On the other hand, the users of the transportation network require reasonable travel time within the network to reach their destinations. This dissertation introduces a novel framework in the fields of fairness in network optimization and evacuation to provide better insight into the evacuation process and assist with decision making. The user of the transportation network is a critical element in this research. Thus, fairness and efficiency are the two primary objectives addressed in the work by considering the limited capacity of roads of the transportation network. Specifically, an approximation approach to the max-min fairness (MMF) problem is presented that provides lower computational time and high-quality output compared to the original algorithm. In addition, a new algorithm is developed to find the MMF resource allocation output in nonconvex structure problems. MMF is the fairness policy used in this research since it considers fairness and efficiency and gives priority to fairness. In addition, a new dynamic evacuation modeling approach is introduced that is capable of reporting more information about the evacuees compared to the conventional evacuation models such as their travel time, evacuation time, and departure time. Thus, the contribution of this dissertation is in the two areas of fairness and evacuation. The first part of the contribution of this dissertation is in the field of fairness. The objective in MMF is to allocate resources fairly among multiple demands given limited resources while utilizing the resources for higher efficiency. Fairness and efficiency are contradicting objectives, so they are translated into a bi-objective mathematical programming model and solved using the ϵ-constraint method, introduced by Vira and Haimes (1983). Although the solution is an approximation to the MMF, the model produces quality solutions, when ϵ is properly selected, in less computational time compared to the progressive-filling algorithm (PFA). In addition, a new algorithm is developed in this research called the θ progressive-filling algorithm that finds the MMF in resource allocation for general problems and works on problems with the nonconvex structure problems. The second part of the contribution is in evacuation modeling. The common dynamic evacuation models lack a piece of essential information for achieving fairness, which is the time each evacuee or group of evacuees spend in the network. Most evacuation models compute the total time for all evacuees to move from the endangered zone to the safe destination. Lack of information about the users of the transportation network is the motivation to develop a new optimization model that reports more information about the users of the network. The model finds the travel time, evacuation time, departure time, and the route selected for each group of evacuees. Given that the travel time function is a non-linear convex function of the traffic volume, the function is linearized through a piecewise linear approximation. The developed model is a mixed-integer linear programming (MILP) model with high complexity. Hence, the model is not capable of solving large scale problems. The complexity of the model was reduced by introducing a linear programming (LP) version of the full model. The complexity is significantly reduced while maintaining the exact output. In addition, the new θ-progressive-filling algorithm was implemented on the evacuation model to find a fair and efficient evacuation plan. The algorithm is also used to identify the optimal routes in the transportation network. Moreover, the robustness of the evacuation model was tested against demand uncertainty to observe the model behavior when the demand is uncertain. Finally, the robustness of the model is tested when the traffic flow is uncontrolled. In this case, the model's only decision is to distribute the evacuees on routes and has no control over the departure time

Dagstuhl News January - December 2007

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

Robust network design under polyhedral traffic uncertainty

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