Assigning a single server to inhomogeneous queues with switching costs

AbstractIn this paper we study the preemptive assignment of a single server to two queues. Customers arrive at both queues according to Poisson processes, and all service times are exponential, but with rates depending on the queues. The costs to be minimized consist of both holding costs and switching costs. The limiting behavior of the switching curve is studied, resulting in a good threshold policy. Numerical results are included to illustrate the complexity of the optimal policy and to compare the optimal policy with the threshold policy

Towards a unifying theory on branching-type polling systems in heavy traffic

For a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

Towards a unifying theory on branching-type polling models in heavy traffic

htmlabstractFor a broad class of polling models the evolution of the system at specific embedded polling instants is known to constitute a multi-type branching process (MTBP) with immigration. In this paper we derive heavy-traffic limits for general MTBP-type of polling models. The results generalize and unify many known results on the waiting times in polling systems in heavy traffic, and moreover, lead to new exact results for classical polling models that have not been observed before. To demonstrate the usefulness of the results, we derive closed-form expressions for the LST of the waiting-time distributions for models with cyclic globally-gated polling regimes, and for cyclic polling models with general branching-type service policies. As a by-product, our results lead to a number of asymptotic insensitivity properties, providing new fundamental insights in the behavior of polling models

Actualización de semaforización en Santa Marta Magdalena

En el presente informe estará desarrollado bajo la modalidad de auxiliar de investigación el cual consta del proyecto de investigación. ACTIALIZACION DE LOS SISTEMAS DE SEMAFORIZACION DE LA CIUDAD DE SANTA MARTA EMPLEANDO NUEVAS TECNOLOGIAS. llevado a cabo por el semillero de investigación de la universidad cooperativa de Colombia seccional Santa Marta, donde presentaremos los análisis y estudios necesarios para cumplir con el objetivo general que se ha planteado dentro de este, el cual consta de la caracterización de sistemas tecnológicos implementados en redes de semaforización en países seleccionados a nivel mundial. Con fin de estudiar y analizar cada una de las opciones escogidas y poder implementarlas en la actualización de las redes de semaforización de la ciudad de Santa Marta en pro a mejorar la fluidez y garantizar una seguridad optima en el tráfico principalmente enhoras picos. Este proyecto está compuesto por la introducción donde se establecerá la importancia de este tipo de investigaciones y los beneficios que han tenido en forma general. Tendremos un planteamiento del problema donde se identifica el problema y se delimita el espacio geográfico, así como su espacio temporal a través de la investigación del problema para una posterior formulación de este. Lo que nos lleva a plantar un objetivo general descrito anteriormente y unos objetivos específicos que nos brindan la posibilidad de llegar a una solución óptima. Dentro del informe se establecerá los métodos de investigación utilizados, marco conceptual, métodos de análisis de literatura. Registro de dichos análisis, análisis de resultados, conclusiones.This report will be developed under the modality of research assistant which consists of the research project. UPDATE OF THE SEMPHORIZATION SYSTEMS OF THE CITY OF SANTA MARTA USING NEW TECHNOLOGIES. carried out by the research seedbed of the Santa Marta sectional cooperative university of Colombia, where we will present the analyzes and studies necessary to fulfill the general objective that has been proposed within this, which consists of the characterization of technological systems implemented in traffic light networks in selected countries worldwide. In order to study and analyze each of the chosen options and to be able to implement them in updating the traffic light networks of the city of Santa Marta in order to improve fluidity and guarantee optimal traffic safety, mainly during peak hours. This project consists of the introduction where the importance of this type of research and the benefits they have had in general will be established. We will have an approach to the problem where the problem is identified and the geographical space is delimited, as well as its temporal space through the investigation of the problem for a later formulation of it. Which leads us to plant a general objective described above and specificobjectives that give us the possibility of reaching an optimal solution. The report will establish the research methods used, the conceptual framework, and the literature analysis methods. Record of said analyzes, analysis of results, conclusions.Resumen. -- Abstract. -- Introduccion. -- Planteamiento del problema. -- Formulación del problema. -- Objetivos. -- Objetivo general. -- Objetivos específicos. -- Justificación. -- Marco conceptual. -- De-limitación de la investigación. -- Linea de investigación. -- Delimitaciòn espacial. -- Delimitaciòn temporal. -- Metodología. -- Tipo de investigación. -- Diseño de la investigación. -- Técnica para la recolección de información. -- Análisis de literatura. -- Resultados. -- Conclusiones. -- Recomendaciones. -- Bibliográfica. -

Heavy traffic analysis of roving server networks

This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves the system or is routed to another queue. This type of customer routing in queueing networks arises very naturally in many application areas (in production systems, computer- and communication networks, maintenance, etc.). In these networks, the single most important characteristic of the system performance is oftentimes the path time, i.e. the total time spent in the system by an arbitrary customer traversing a specific path. The current paper presents the first HT asymptotic for the path-time distribution in queueing networks with a roving server under general renewal arrivals. In particular, we provide a strong conjecture for the system's behaviour under HT extending the conjecture of Coffman et al. [E.G. Coffman Jr., A.A. Puhalskii, M.I. Reiman 1995 and 1998] to the roving server setting of the current paper. By combining this result with novel light-traffic asymptotics we derive an approximation of the mean path-time for arbitrary values of the load and renewal arrivals. This approximation is not only highly accurate for a wide range of parameter settings, but is also exact in various limiting cases

Self-Control of Traffic Lights and Vehicle Flows in Urban Road Networks

Based on fluid-dynamic and many-particle (car-following) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of self-organized oscillations of pedestrian flows at bottlenecks [D. Helbing and P. Moln\'ar, Phys. Eev. E 51 (1995) 4282--4286], we propose a self-organization approach to traffic light control. The problem can be treated as multi-agent problem with interactions between vehicles and traffic lights. Specifically, our approach assumes a priority-based control of traffic lights by the vehicle flows themselves, taking into account short-sighted anticipation of vehicle flows and platoons. The considered local interactions lead to emergent coordination patterns such as ``green waves'' and achieve an efficient, decentralized traffic light control. While the proposed self-control adapts flexibly to local flow conditions and often leads to non-cyclical switching patterns with changing service sequences of different traffic flows, an almost periodic service may evolve under certain conditions and suggests the existence of a spontaneous synchronization of traffic lights despite the varying delays due to variable vehicle queues and travel times. The self-organized traffic light control is based on an optimization and a stabilization rule, each of which performs poorly at high utilizations of the road network, while their proper combination reaches a superior performance. The result is a considerable reduction not only in the average travel times, but also of their variation. Similar control approaches could be applied to the coordination of logistic and production processes

A mathematical programming approach to stochastic and dynamic optimization problems

Includes bibliographical references (p. 46-50).Supported by a Presidential Young Investigator Award. DDM-9158118 Supported by matching funds from Draper Laboratory.Dimitris Bertsimas