Abstract — Disruption Tolerant Networks (DTNs) are designed to overcome limitations in connectivity due to conditions such as mobility, poor infrastructure, and short range radios. DTNs rely on the inherent mobility in the network to deliver packets around frequent and extended network partitions using a store-carry-andforward paradigm. However, missed contact opportunities decrease throughput and increase delay in the network. We propose the use of throwboxes in mobile DTNs to create a greater number of contact opportunities, consequently improving the performance of the network. Throwboxes are wireless nodes that act as relays, creating additional contact opportunities in the DTN. We propose algorithms to deploy stationary throwboxes in the network that simultaneously consider routing as well as placement. We also present placement algorithms that use more limited knowledge about the network structure. We perform an extensive evaluation of our algorithms by varying both the underlying routing and mobility models. Our results suggest several findings to guide the design and operation of throwbox-augmented DTNs. I.

Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers in both the logistics and stochastic/robust optimization communities. Indeed, a large number of the approaches that have been proposed for optimization under uncertainty have been applied to facility location problems. This paper reviews the literature...

The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current state-of-the-art. In particular, continuous location models, network location models, mixed-integer programming models, and applications are summarized.

We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the "continuous k-median (Weber) problem" where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed as an integral over the relevant region, versus the usual discrete sum of distances. The resulting facility location problems are inherently geometric, requiring analysis techniques of computational geometry. We provide polynomial-time algorithms for various versions of the L1 1-median (Weber) problem. We also consider the multiple-center version of the L1 k-median problem, which we prove is NP-hard for large k.

Many objectives have been proposed for optimization under uncertainty. The typical stochastic programming objective of minimizing expected cost may yield solutions that are inexpensive in the long run but perform poorly under certain realizations of the random data. On the other hand, the typical robust optimization objective of minimizing maximum cost or regret tends to be overly conservative, planning against a disastrous but unlikely scenario. In this paper, we present facility location models that combine the two objectives by minimizing the expected cost while bounding the relative regret in each scenario. In particular, the models seek the minimum-expected-cost solution that is p-robust; i.e., whose relative regret is no more than 100p% in each scenario.

The p-median problem, like most location problems, is classified as NP-hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.

Consider a network facility location problem where congestion arises at facilities, and is represented by delay functions that approximate the queueing process. We strive to minimize the sum of customers' transportation and waiting times, and facilities' fixed and variable costs. The problem is solved using a column generation technique within a Branch-and-Bound scheme. Numerical results are reported and a bilevel (user-optimized) formulation considered, among other extensions. Keywords. Facility location. Column generation. Branch-and-Bound. Nonlinear programming. Integer programming. 1 Research supported by NSERC grant URF0037812 and by FCAR grants NC0301 and EQ4144F 2 Research conducted while on sabbatical leave from CMR Saint-Jean at Universit'e Blaise Pascal, Clermont-Ferrand (France), and supported by NSERC grant A5789 The Congested Facility Location Problem Martin Desrochers 1 GERAD and ' Ecole Polytechnique Patrice Marcotte 2 CRT (Universit'e de Montr'eal) Mihnea Stan ...

. In the operation of communication and computer networks, it may become desirable or necessary to add a new function to the network through the placement of the corresponding electronic device within certain existing user locations. This will involve deciding which user locations will have devices placed at them as well as deciding an assignment of users to device locations. The objective when adding the new function is to choose these locations and assignments such that the combined cost of placing the devices and routing users to their assigned device locations is minimized. This problem, which we call the device placement problem, is closely related to the simple plant location problem and the p-median problem. Like these problems, the device placement problem is NP-hard, and thus it is highly unlikely that efficient methods for solving this problem to optimality exist. We discuss and test several heuristic methods for the device placement problem, as well as a very efficient meth...

I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii A distributed virtual environment (DVE) is a shared virtual environment where multiple users at their workstations interact with each other. Some of these systems may support a large number of users, e.g., massive multi-player online games, and these users may be geographically distributed. An important performance measure in a DVE system is the delay for an update of a user’s state (e.g., his position in the virtual environment) to arrive at the workstations of those users who are affected by the update. This update delay often has a stringent requirement (e.g., less than 100 ms) in order to ensure interactivity among users. In designing a DVE system, an important issue is how well the system scales as the number of users increases. In terms of scalability, a promising system archi-

this paper we consider a restricted version of the problem of locating "access facilities", or concentration points, to permit economical connection of users to resources. This problem has been already studied [16]. Actually, we consider only one resource that does not have a important place in the optimization problem. This assumption leads to a strong relation with the problem of finding a minimum r-rooted 2-height spanning tree, giving as result conceptually easy heuristics, that are easilly implemented as well. In the next section we describe in details the restricted concentrator location problem, and some related problems often found in the literature. In section