EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Стационарные характеристики ненадежной системы массового обслуживания с групповым марковским потоком

Unreliable queuing systems are of considerable interest both in mathematical terms and for applications. Systems with stationary Poisson flows of customers and breakdowns and exponentially distributed service and repair times are mainly considered. This circumstance greatly simplifies the mathematical analysis of the corresponding models but rarely occurs in real systems, especially in telecommunications networks. The purpose of this study is to analyze the stationary behavior of a multi-server unreliable queueing system with a batch Markovian arrival process, which takes into account the correlation and bursty nature of real traffic. The service and repair processes are described by phase type distributions which makes it possible to take into account not only the average service and repair times but also the variance of these times. As a result of the research, the operation of the system is described by a multi-dimensional Markov chain. The condition of ergodicity of this chain is presented in a simple algorithmic form. An algorithm for calculating the stationary distribution is proposed. Formulas for the key performance characteristics of the system are obtained in terms of the stationary distribution of the Markov chain describing the system dynamics. The results can be used to make expert decisions in analyzing the performance and design of various telecommunication networks. Ненадежные системы массового обслуживания представляют значительный интерес как в математическом плане, так и для приложений. В основном рассматриваются системы со стационарными пуассоновскими потоками заявок и поломок и экспоненциально распределенными временами обслуживания и ремонтов. Это обстоятельство значительно упрощает математический анализ соответствующих моделей, но редко выполняется в реальных системах, особенно в телекоммуникационных сетях. Целью исследования является анализ стационарного поведения многолинейной ненадежной системы массового обслуживания с групповым марковским потоком заявок, который учитывает корреляцию и взрывной характер реального трафика. Процессы обслуживания и ремонтов описываются фазовыми распределениями, что позволяет учесть не только средние времена обслуживания и ремонтов, но и дисперсию этих времен. В результате процесс функционирования системы представляется многомерной цепью Маркова. Условие эргодичности этой цепи задается в простом алгоритмическом виде. Предлагается алгоритм вычисления стационарного распределения. Получены формулы для ключевых характеристик производительности системы в терминах стационарного распределения цепи Маркова, описывающей динамику системы. Приведенные результаты могут использоваться для принятия экспертных решений при анализе производительности и проектировании телекоммуникационных сетей различного назначения

Call Center Experience Optimization: A Case for a Virtual Predictive Queue

The evolution of the call center into contact centers and the growth of their use in providing customer-facing service by many companies has brought considerable capabilities in maintaining customer relationships but it also has brought challenges in providing quality service when call volumes are high. Limited in their ability to provide service at all times to all customers, companies are forced to balance the costs associated with hiring more customer service representatives and the quality of service provided by a fewer number. A primary challenge when there are not enough customer service representatives to engage the volume of callers in a timely manner is the significant wait times that can be experienced by many customers. Normally, callers are handled in accordance with a first-come, first-served policy with exceptions being skill-based routing to those customer service representatives with specialized skills. A proposed call center infrastructure framework called a Virtual Predictive Queue (VPQ) can allow some customers to benefit from a shorter call queue wait time. This proposed system can be implemented within a call center’s Automatic Call Distribution (ACD) device associated with computer telephony integration (CTI) and theoretically will not violate a first-come, first served policy

MAP/PH/1 systems with group service: performance analysis under different admission strategies

2015 - 2016Recent advances in wireless communication networks led to possibility of multi-rate transmission of information. The queueing theory represents a valid tool to study how the performances of such communication systems can be improved, and to give proper solutions. Modeling a multi-rate transmission system, in terms of queueing theory, means that a particular discipline has to be considered: a group of requests from users can be processed simultaneously in parallel and processing of the whole group is supposed finished if processing of all individual requests belonging to this group is over. In order to model this typology of telecommunication systems, some particular assumption can be made on arrivals, which occur by a Markovian arrival process, and on service time and length of admission period, which are regulated by phase type distributions. Thus, in this thesis MAP/PH/1 queueing systems have been considered, with and without retrial to take into account all possible behaviours of the customers. The main goal of the research activity presented in this work is to introduce novel admission strategies for the described systems, in order to give a major contribute to the current performance analysys, in particular as regard the choice of the optimal length of admission period and optimal size of the groups. Dynamics of such systems are described by multidimensional Markov chains. Ergodicity condition for these Markov chains have been derived, stationary probability distribution of the states have been computed, formulas for the main performance measures of the system have been attained. Essential advantages of the proposed customer’s service disciplines have been numerically illustrated. [edited by author]I recenti progressi ottenuti per le reti di comunicazione wireless, permettono la trasmissione multi-frequenza delle informazioni. La teoria delle code rappresenta un valido strumento per studiare come le performance di tali sistemi di comunicazione possano essere migliorate, e individuare opportune soluzioni. In termini di teoria delle code, modellare un sistema di trasmissione multi-frequenza significa considerare una determinata disciplina: un gruppo di richieste da parte di utenti possono essere processate simultaneamente in parallelo, e il processo dell’intero gruppo risulta completato se tutte le richieste appartenenti a tale gruppo sono espletate. Al fine di modellare tale tipologia di sistemi di telecomunicazione, si possono definire particolari assunzioni sugli arrivi, determinati da processi di arrivo Markoviani, e sul tempo di servizio e lunghezza del periodo di ammissione, regolati da distribuzioni di tipo a fasi. Pertanto, in tale lavoro di tesi sono stati considerati sistemi a coda di tipo MAP/PH/1, con e senza retrial per considerare tutti i possibili comportamenti degli utenti. Il principale obiettivo dell’attivita` di ricerca presentata in tale lavoro `e introdurre nuove strategie di ammissione per i sistemi descritti, al fine di fornire un maggior contributo alle attuali analisi sulle performance, in particolare relativamente alla scelta della lunghezza ottimale del periodo di ammissione e la dimensione ottimale dei gruppi. Le dinamiche di tali sistemi sono descritte da catene di Markov multidimensionali. `E stata ricavata la condizione di ergodicit`a per tali catene di Markov, `e stata calcolata la distribuzione delle probabilita` stazionarie degli stati, e sono state ottenute le formule per le misure dei principali parametri prestazionali del sistema. I principali vantaggi delle discipline di servizio proposte sono state illustrate numericamente. [a cura dell'autore]XXIX n.s

The application of Approximate Dynamic Programming techniques

Koole, G.M. [Promotor]Bhulai, S. [Copromotor

Queues: Flows, Systems, Networks

В сборнике излагаются новые результаты научных исследований в области разработки и оптимизации моделей процессов передачи информации в телекоммуникационных сетях с использованием аппарата теории систем и сетей массового обслуживания. Предназначен специалистам в области вероятностного анализа, случайных процессов, математического моделирования, и математической статистики, а также специалистам в области проектирования и эксплуатации сетей связи и компьютерных сетей

Performability modelling of homogenous and heterogeneous multiserver systems with breakdowns and repairs

This thesis presents analytical modelling of homogeneous multi-server systems with reconfiguration and rebooting delays, heterogeneous multi-server systems with one main and several identical servers, and farm paradigm multi-server systems. This thesis also includes a number of other research works such as, fast performability evaluation models of open networks of nodes with repairs and finite queuing capacities, multi-server systems with deferred repairs, and two stage tandem networks with failures, repairs and multiple servers at the second stage. Applications of these for the popular Beowulf cluster systems and memory servers are also accomplished. Existing techniques used in performance evaluation of multi-server systems are investigated and analysed in detail. Pure performance modelling techniques, pure availability models, and performability models are also considered. First, the existing approaches for pure performance modelling are critically analysed with the discussions on merits and demerits. Then relevant terminology is defined and explained. Since the pure performance models tend to be too optimistic and pure availability models are too conservative, performability models are used for the evaluation of multi-server systems. Fault-tolerant multi-server systems can continue service in case of certain failures. If failure does not occur at a critical point (such as breakdown of the head processor of a farm paradigm system) the system continues serving in a degraded mode of operation. In such systems, reconfiguration and/or rebooting delays are expected while a processor is being mapped out from the system. These delay stages are also taken into account in addition to failures and repairs, in the exact performability models that are developed. Two dimensional Markov state space representations of the systems are used for performability modelling. Following the critical analysis of the existing solution techniques, the Spectral Expansion method is chosen for the solution of the models developed. In this work, open queuing networks are also considered. To evaluate their performability, existing modelling approaches are expanded and validated by simulations, for performability analysis of multistage open networks with finite queuing capacities. The performances of two extended modelling approaches are compared in terms of accuracy for open networks with various queuing capacities. Deferred repair strategies are becoming popular because of the cost reductions they can provide. Effects of using deferred repairs are analysed and performability models are provided for homogeneous multi-server systems and highly available farm paradigm multi-server systems. Since one of the random variables is used to represent the number of jobs in one of the queues, analytical models for performance evaluation of two stage tandem networks suffer because of numerical cumbersomeness. Existing approaches for modelling these systems are actually pure performance models since breakdowns and repairs cannot be considered. One way of modelling these systems can be to divide one of the random variables to present both the operative and non-operative states of the server in one dimension. However, this will give rise to state explosion problem severely limiting the maximum queue capacity that can be handled. In order to overcome this problem a new approach is presented for modelling two stage tandem networks in three dimensions. An approximate solution is presented to solve such a system. This approach manifests itself as a novel contribution for alleviating the state space explosion problem for large and/or complex systems. When two state tandem networks with feedback are modelled using this approach, the operative states can be handled independently and this makes it possible to consider multiple operative states at the second stage. The analytical models presented can be used with various parameters and they are extendible to consider systems with similar architectures. The developed three dimensional approach is capable to handle two stage tandem networks with various characteristics for performability measures. All the approaches presented give accurate results. Numerical solutions are presented for all models developed. In case the solution presented is not exact, simulations are performed to validate the accuracy of the results obtained

Optical flow switched networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 253-279).In the four decades since optical fiber was introduced as a communications medium, optical networking has revolutionized the telecommunications landscape. It has enabled the Internet as we know it today, and is central to the realization of Network-Centric Warfare in the defense world. Sustained exponential growth in communications bandwidth demand, however, is requiring that the nexus of innovation in optical networking continue, in order to ensure cost-effective communications in the future. In this thesis, we present Optical Flow Switching (OFS) as a key enabler of scalable future optical networks. The general idea behind OFS-agile, end-to-end, all-optical connections-is decades old, if not as old as the field of optical networking itself. However, owing to the absence of an application for it, OFS remained an underdeveloped idea-bereft of how it could be implemented, how well it would perform, and how much it would cost relative to other architectures. The contributions of this thesis are in providing partial answers to these three broad questions. With respect to implementation, we address the physical layer design of OFS in the metro-area and access, and develop sensible scheduling algorithms for OFS communication. Our performance study comprises a comparative capacity analysis for the wide-area, as well as an analytical approximation of the throughput-delay tradeoff offered by OFS for inter-MAN communication. Lastly, with regard to the economics of OFS, we employ an approximate capital expenditure model, which enables a throughput-cost comparison of OFS with other prominent candidate architectures. Our conclusions point to the fact that OFS offers significant advantage over other architectures in economic scalability.(cont.) In particular, for sufficiently heavy traffic, OFS handles large transactions at far lower cost than other optical network architectures. In light of the increasing importance of large transactions in both commercial and defense networks, we conclude that OFS may be crucial to the future viability of optical networking.by Guy E. Weichenberg.Ph.D