Rate control of a queue with quality-of-service constraint under bounded and unbounded action spaces

We consider a simple Markovian queue with Poisson arrivals and exponential service times for jobs. The controller can choose service rates from a specified action space depending on number of jobs in the queue. The queue has a finite buffer and when full, new jobs get rejected. The controller’s objective is to choose optimal (state-dependent) service rates that minimize a suitable long-run average cost, subject to an upper bound on the job rejection-rate (quality-of-service constraint). We solve this problem of finding and computing the optimal control under two cases: When the action space is unbounded (i.e. [0, ∞)) and when it is bounded (i.e. [0, μ ̄], for some μ ̄ \u3e 0). We also numerically compute and compare the solutions for different specific choices of the cost function

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Closed queueing networks under congestion: non-bottleneck independence and bottleneck convergence

We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.Comment: 22 page

Performance controls for distributed telecommunication services

As the Internet and Telecommunications domains merge, open telecommunication service architectures such as TINA, PARLAY and PINT are becoming prevalent. Distributed Computing is a common engineering component in these technologies and promises to bring improvements to the scalability, reliability and flexibility of telecommunications service delivery systems. This distributed approach to service delivery introduces new performance concerns. As service logic is decomposed into software components and distnbuted across network resources, significant additional resource loading is incurred due to inter-node communications. This fact makes the choice of distribution of components in the network and the distribution of load between these components critical design and operational issues which must be resolved to guarantee a high level of service for the customer and a profitable network for the service operator. Previous research in the computer science domain has addressed optimal placement of components from the perspectives of minimising run time, minimising communications costs or balancing of load between network resources. This thesis proposes a more extensive optimisation model, which we argue, is more useful for addressing concerns pertinent to the telecommunications domain. The model focuses on providing optimal throughput and profitability of network resources and on overload protection whilst allowing flexibility in terms of the cost of installation of component copies and differentiation in the treatment of service types, in terms of fairness to the customer and profitability to the operator. Both static (design-time) component distribution and dynamic (run-time) load distribution algorithms are developed using Linear and Mixed Integer Programming techniques. An efficient, but sub-optimal, run-time solution, employing Market-based control, is also proposed. The performance of these algorithms is investigated using a simulation model of a distributed service platform, which is based on TINA service components interacting with the Intelligent Network through gateways. Simulation results are verified using Layered Queuing Network analytic modelling Results show significant performance gains over simpler methods of performance control and demonstrate how trade-offs in network profitability, fairness and network cost are possible

Optimal Topological Arrangement of Queues in Closed Finite Queueing Networks

Closed queueing networks are widely used in many different kinds of scientific and business applications. Since the demands of saving energy and reducing costs are becoming more and more significant with developing technologies, finding a systematic methodology for getting the best arrangement is very important. In this thesis, design rules are proposed for tandem and various other topologies, to help the designer find the best arrangements which maximize the throughput. Our topological arrangements problem (TAP) can be established as: the system has m-service stations in a network and each one may have different design parameters. To relax the queueing system, the original finite buffer queue is decomposed into a buffer and an infinite buffer server system. Mean Value Analysis (MVA) is used to measure the performance of each topology arrangement. Finally, mixed-integer sequential quadratic programming (MISQP) is used to solve the optimization problem and it is compared with enumeration and a simulation model of Arena (a discrete-event model)

A Bibliometric Analysis of Operations Research and Management Science

Bibliometric analysis is the quantitative study of bibliographic material. It provides a general picture of a research field that can be classified by papers, authors and journals. This paper presents a bibliometric overview of research published in operations research and management science in recent decades. The main objective of this study is to identify some of the most relevant research in this field and some of the newest trends according to the information found in the Web of Science database. Several classifications are made, including an analysis of the most influential journals, the two hundred most cited papers of all time and the most productive and influential authors. The results obtained are in accordance with the common wisdom, although some variations are found.European Commission PIEF-GA-2011-300062 Chilean Government 116028

A Stochastic Resource-Sharing Network for Electric Vehicle Charging

We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.Comment: 13 pages, 8 figure

Applications of stochastic modeling in air traffic management : Methods, challenges and opportunities for solving air traffic problems under uncertainty

In this paper we provide a wide-ranging review of the literature on stochastic modeling applications within aviation, with a particular focus on problems involving demand and capacity management and the mitigation of air traffic congestion. From an operations research perspective, the main techniques of interest include analytical queueing theory, stochastic optimal control, robust optimization and stochastic integer programming. Applications of these techniques include the prediction of operational delays at airports, pre-tactical control of aircraft departure times, dynamic control and allocation of scarce airport resources and various others. We provide a critical review of recent developments in the literature and identify promising research opportunities for stochastic modelers within air traffic management