An Improved Upper Bound for the Ring Loading Problem

The Ring Loading Problem emerged in the 1990s to model an important special case of telecommunication networks (SONET rings) which gained attention from practitioners and theorists alike. Given an undirected cycle on $n$ nodes together with non-negative demands between any pair of nodes, the Ring Loading Problem asks for an unsplittable routing of the demands such that the maximum cumulated demand on any edge is minimized. Let $L$ be the value of such a solution. In the relaxed version of the problem, each demand can be split into two parts where the first part is routed clockwise while the second part is routed counter-clockwise. Denote with $L^*$ the maximum load of a minimum split routing solution. In a landmark paper, Schrijver, Seymour and Winkler [SSW98] showed that $L \leq L^* + 1.5D$, where $D$ is the maximum demand value. They also found (implicitly) an instance of the Ring Loading Problem with $L = L^* + 1.01D$. Recently, Skutella [Sku16] improved these bounds by showing that $L \leq L^* + \frac{19}{14}D$, and there exists an instance with $L = L^* + 1.1D$. We contribute to this line of research by showing that $L \leq L^* + 1.3D$. We also take a first step towards lower and upper bounds for small instances

Stability vs. optimality in selfish ring routing

We study the asymmetric atomic selfish routing in ring networks, which has diverse practical applications in network design and analysis. We are concerned with minimizing the maximum latency of source-destination node-pairs over links with linear latencies. We obtain the first constant upper bound on the price of anarchy and significantly improve the existing upper bounds on the price of stability. Moreover, we show that any optimal solution is a good approximate Nash equilibrium. Finally, we present better performance analysis and fast implementation of pseudo-polynomial algorithms for computing approximate Nash equilibria

On-board B-ISDN fast packet switching architectures. Phase 2: Development. Proof-of-concept architecture definition report

For the next-generation packet switched communications satellite system with onboard processing and spot-beam operation, a reliable onboard fast packet switch is essential to route packets from different uplink beams to different downlink beams. The rapid emergence of point-to-point services such as video distribution, and the large demand for video conference, distributed data processing, and network management makes the multicast function essential to a fast packet switch (FPS). The satellite's inherent broadcast features gives the satellite network an advantage over the terrestrial network in providing multicast services. This report evaluates alternate multicast FPS architectures for onboard baseband switching applications and selects a candidate for subsequent breadboard development. Architecture evaluation and selection will be based on the study performed in phase 1, 'Onboard B-ISDN Fast Packet Switching Architectures', and other switch architectures which have become commercially available as large scale integration (LSI) devices

The development of a mathematical programming technique as a design tool for traffic management

In urban areas, competition for road space at junctions is one of the major causes of congestion and accidents. Routes chosen to avoid conflict at junctions have a mutually beneficial effect which should improve circulation and reduce accidents. A prototype design tool has been developed to provide for traffic management based on such routes. The mathematical model behind the design tool works with a given road network and a given O-D demand matrix to produce feasible routes for all drivers in such a way that the weighted sum of potential conflicts is minimised. The result is a route selection in which all journeys from origin i to destination j follow the same route. The method which works best splits the problem into single commodity problems and solves these repeatedly by the Out-of-Kilter algorithm. Good locally optimal solutions can be produced by this method, even though global optimality cannot be guaranteed. Software for a microcomputer presented here as part of the design tool is capable of solving problems on realistic networks in a reasonable time. This method is embedded in a suite of computer programs which makes the input and output straightforward. Used as a design tool in the early stages of network design it gives a network-wide view of the possibilities for reducing conflict and indicates a coherent set of traffic management measures. The ideal measure would be automatic route guidance, such as the pilot scheme currently being developed for London. Other measures include a set of one-way streets and banned turns. The resulting turning flows could be used as input to the signal optimiser TRANSYT to determine signal settings favouring the routeing pattern. The project was funded by the S. E. R. C. and carried out at Middlesex Polytechnic in collaboration with MVA Systematica

Gemischt-autonome Flotten in der urbanen Logistik

We consider a city logistics application in which a service provider seeks a repeatable plan to transport commodities from distribution centers to satellites. The service provider uses a mixed autonomous fleet that is composed of autonomous vehicles and manually operated vehicles. The autonomous vehicles are only able to travel independently on feasible streets of the heterogeneous infrastructure but elsewhere need to be pulled by manually operated vehicles in platoons. We introduce the service network design problem with mixed autonomous fleets to determine a tactical plan that minimizes the total costs over a medium-term time horizon. The tactical plan determines the size and mix of the fleet, schedules transportation services, and decides on the routing or outsourcing of commodities. We model this problem as an integer program on a time-expanded network and study the impact of different problem characteristics on the solutions. To precisely depict the synchronization requirements of the problem, the time-expanded networks need to consider narrow time intervals. Thus, we develop an exact solution approach based on the dynamic discretization discovery scheme that refines partially time-expanded networks containing only a fraction of the nodes and arcs of the fully time-expanded network. Further methodological contributions of this work include the introduction of valid inequalities, two enhancements that exploit linear relaxations, and a heuristic search space restriction. Computational experiments show that all evaluated variants of the solution approach outperform a commercial solver. For transferring a tactical plan to an operational solution that minimizes the transshipment effort on a given day, we present a post-processing technique that specifically assigns commodities to vehicles and vehicles to platoons. Finally, we solve a case study on a real-world based network resembling the city of Braunschweig, Germany. Analyzing the tactical and operational solutions, we assess the value of using a mixed autonomous fleet and derive practical implications.Wir betrachten eine Anwendung der urbanen Logistik, bei der ein Dienstleister einen wiederholbaren Plan für den Gütertransport von Distributionszentren zu Satelliten anstrebt. Dafür setzt der Dienstleister eine gemischt-autonome Flotte ein, die sich aus autonomen Fahrzeugen und manuell gesteuerten Fahrzeugen zusammensetzt. Die autonomen Fahrzeuge können nur auf bestimmten Straßen der heterogenen Infrastruktur selbstständig fahren, außerhalb dieser müssen sie von manuell gesteuerten Fahrzeugen mittels Platooning gezogen werden. Wir führen das „service network design problem with mixed autonomous fleets“ ein, um einen taktischen Plan zu ermitteln, der die Gesamtkosten über einen mittelfristigen Zeithorizont minimiert. Der taktische Plan bestimmt die Größe und Zusammensetzung der Flotte, legt die Transportdienste fest und entscheidet über das Routing oder das Outsourcing von Gütern. Wir modellieren dieses Problem als ganzzahliges Programm auf einem zeiterweiterten Netzwerk und untersuchen die Auswirkungen verschiedener Problemeigenschaften auf die Lösungen. Um die Synchronisationsanforderungen des Problems präzise darzustellen, müssen die zeiterweiterten Netzwerke kleine Zeitintervalle berücksichtigen. Daher entwickeln wir einen exakten Lösungsansatz, der auf dem Schema des „dynamic discretization discovery“ basiert und partiell zeiterweiterte Netzwerke entwickelt, die nur einen Teil der Knoten und Kanten des vollständig zeiterweiterten Netzwerks enthalten. Weitere methodische Beiträge dieser Dissertation umfassen die Einführung von Valid Inequalities, zweier Erweiterungen, die lineare Relaxationen verwenden, und einer heuristischen Suchraumbegrenzung. Experimente zeigen, dass alle evaluierten Varianten des Lösungsansatzes einen kommerziellen Solver übertreffen. Um einen taktischen Plan in eine operative Lösung zu überführen, die die Umladevorgänge an einem bestimmten Tag minimiert, stellen wir eine Post-Processing-Methode vor, mit der Güter zu Fahrzeugen und Fahrzeuge zu Platoons eindeutig zugeordnet werden. Schließlich lösen wir eine Fallstudie auf einem realitätsnahen Netzwerk, das der Stadt Braunschweig nachempfunden ist. Anhand der taktischen und operativen Lösungen bewerten wir den Nutzen einer gemischt-autonomen Flotte und leiten Implikationen für die Praxis ab