Telecommunication carrier selection under volume discounts: a case study.

During 2001 many of the European mobile phone markets have reached saturation, and hence mobile phone operators have shifted their attention from growth and market share to cutting costs. One way of doing so is to reduce spending on international calls which are routed via network operating companies (carriers). These carriers charge per call-minute for each destination and may use a joint business volume discount to price their services. We developed a software system that supports the decision of allocating destinations to carriers. The core of this system is a min-cost flow routine that is embedded in a branch-and-bound framework. Our system not only solves the operational problem to optimality, it is also capable of performing what-if analyses and sensitivity analysis. It has been implemented at a major telecommunication services provider. The main benefits realized are twofold: the business process of allocating carriers to destinations has been structured and the costs arising from routing international calls have significantly decreased.Selection; Case studies; Studies; Markets; Market; Costs; International; Companies; Software; Decision; Framework; Sensitivity; Processes;

Pricing bridges to cross a river.

We consider a Stackelberg pricing problem in directed, uncapacitated networks. Tariffs have to be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs are assumed to be given. There are n clients, the followers, that route their demand independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by problems in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + lnD)–approximation. Here, D is upper bounded by the total demand of all clients. We furthermore discuss some polynomially solvable special cases, and present a short computational study with instances from France Télécom. In addition, we consider the problem under the additional restriction that the operator must serve all clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless NP = ZPP, and we prove the existence of an n–approximation algorithm.Pricing; Networks; Tariffs; Costs; Cost; Demand; Problems; Order; Yield; Studies; Approximation; Algorithms; Performance;

Dynamical Friction in Gravitational Atoms

Due to superradiant instabilities, clouds of ultralight bosons can spontaneously grow around rotating black holes, creating so-called "gravitational atoms". In this work, we study their dynamical effects on binary systems. We first focus on open orbits, showing that the presence of a cloud can increase the cross section for the dynamical capture of a compact object by more than an order of magnitude. We then consider closed orbits and demonstrate that the backreaction of the cloud's ionization on the orbital motion should be identified as dynamical friction. Finally, we study for the first time eccentric and inclined orbits. We find that, while ionization quickly circularizes the binary, it barely affects the inclination angle. These results enable a more realistic description of the dynamics of gravitational atoms in binaries and pave the way for dedicated searches with future gravitational wave detectors.Comment: 36 pages, 13 figure

Superradiance: Axionic Couplings and Plasma Effects

Spinning black holes can transfer a significant fraction of their energy to ultralight bosonic fields via superradiance, condensing them in a co-rotating structure or "cloud". This mechanism turns black holes into powerful particle detectors for bosons with extremely feeble interactions. To explore its full potential, the couplings between such particles and the Maxwell field in the presence of plasma need to be understood. In this work, we study these couplings using numerical relativity. We first focus on the coupled axion-Maxwell system evolving on a black hole background. By taking into account the axionic coupling concurrently with the growth of the cloud, we observe for the first time that a new stage emerges: that of a stationary state where a constant flux of electromagnetic waves is fed by superradiance, for which we find accurate analytical estimates. Moreover, we show that the existence of electromagnetic instabilities in the presence of plasma is entirely controlled by the axionic coupling; even for dense plasmas, an instability is triggered for high enough couplings.Comment: 32 pages, 23 figure

Cache as ca$h can

In this contribution several caching strategies for the World Wide Weba re studied. Special attention is paid to the so-called proxy placement, i.e. placing of caches on carefully selected nodes in the network near to the end users

Random multi-index matching problems

The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.Comment: 22 pages, 16 figure