Analysis of queueing models with batch service

This dissertation is the result of my research work at the SMACS research group (Department of Telecommunications and Information Processing, Ghent University) and it concerns the analysis of queueing models with batch service. A queueing model basically is a mathematical abstraction of a situation where customers arrive and queue up until they receive some kind of service. These phenomena are omnipresent in real life: people waiting at a counter of a post office or bank, people in the waiting room of a doctor, airplanes waiting to take off, people waiting until they get connected with the call center, data packets which are temporarily stored into a buffer until the transmisssion channel is available, et cetera. The analysis of queueing models constitutes the subject of the applied mathematical discipline called queueing theory and amounts to answering questions such as “How many customers are waiting on average?”, “How long do customers have to wait?”, “Is there a large variation on the waiting time?”, “What is the probability that data packets are lost due to a full buffer?”, “What is the probability that a customer suffers a lengthy delay?”, et cetera. In queueing theory, the number of customers and their waiting time are often denominated by respectively buffer content and customer delay. In addition, the probability that a quantity, such as the buffer content or customer delay, is very large or lengthy, is generally called a tail probability. The models we investigate throughout this dissertation have in common that customers can be served in batches, meaning that several customers can be served simultaneously. An elevator can be viewed as a classic example, as several people can be transported simultaneously to another floor. Also, in a variety of production or transport processes several goods can be processed together. Furthermore, in quality control, classification of items as good or bad can often be achieved more economically by examining the items in groups rather than individually. If the result of a group test is good, all items within it can then be classified as good, whereas one or more items are bad in the opposite case, where the items can then be retested by considering smaller groups. Group testing is especially of importance when the percentage of bad items is small. In addition, in telecommunications networks, packets with the same destination and quality of service (QoS) requirements are often aggregated into so-called bursts and these bursts are transmitted over the network. This is mainly done for efficiency reasons, since only one header per aggregated burst has to be constructed, instead of one header per single information unit, thus leading to an increased throughput. Technologies using packet aggregation include for instance Optical burst switched (OBS) networks and IEEE 802.11n wireless local area networks (WLANs). An inherent aspect of batch service is that newly arriving customers cannot join the ongoing service, even if there is free capacity (we denominate the maximum number of customers that can be served simultaneously by server capacity). For instance, an arriving person cannot enter an elevator that has just left, even if space is available. This person has to wait until the elevator has transported its occupants to their requested floors and has returned, which might take a long time in high buildings. In view of this, it is of importance to take a well-considered decision when the server becomes available and finds less customers than it can serve in theory. This decision is called the service policy. A whole spectrum of service policies exist. The server could, for instance, start serving the already present customers immediately. Although the present customers benefit from this approach, capacity is wasted: customers that arrive later cannot join the ongoing service. An alternative for this so-called immediate-batch service policy is the full-batch service policy. In this case, the available server postpones service until the number of present customers reaches or exceeds the server capacity, which, in turn, has a negative effect on the delay of the customers waiting to form a full batch (postponing delay). The threshold-based policy is a kind of compromise between immediate-batch service policy and full-batch service policy. When the number of present customers is below some service threshold, service is postponed, whereas service is initiated when the number of present customers reaches or exceeds this threshold. It is important to realize that even with this compromise, long postponing delays are possible. Therefore, in this dissertation, we combine a thresholdbased policy with a timer mechanism that avoids excessive postponing delays. The purpose of this dissertation is to calculate a large spectrum of performance measures, which enable to evaluate a broad set of situations with batch service and aid in selecting an efficient service policy. The studied performance measures are moments, such as the mean value and variance, and tail probabilities of the buffer content and the customer delay. This dissertation is structured as follows. In chapter 1, we motivate our work and we introduce crucial concepts such as probability generating functions (PGFs), whose useful properties are frequently relied upon throughout the analysis. Then we deduce moments and tail probabilities of the buffer content in chapter 2. The resulting formulas still contain unknown probabilities that have to be calculated numerically. As this might become unfeasible in some cases, we compute in chapter 3 approximations for the buffer content. Next, moments and tail probabilities of the customer delay are covered in respectively chapters 4 and 5. In order to analyze the moments, we conceive the customer delay as the sum of two non-overlapping parts, whereas for the tail probabilities, it turns out to be more convenient to interpret the delay as the maximum of two time periods. Further, in real life the customer arrival process often exhibits some kind of dependency. For instance, if a large amount of customers have recently arrived, it is likely that many customers arrive in the near future, as it might be an indication of a peak moment. Therefore, we investigate in chapter 6 the influence of dependency in the arrival process on the behaviour of batch-service phenomena and on the selection of an efficient service policy. Finally, the main contributions are summarized in chapter 7

Dynamic power allocation and routing for satellite and wireless networks with time varying channels

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2004.Includes bibliographical references (p. 283-295).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Satellite and wireless networks operate over time varying channels that depend on attenuation conditions, power allocation decisions, and inter-channel interference. In order to reliably integrate these systems into a high speed data network and meet the increasing demand for high throughput and low delay, it is necessary to develop efficient network layer strategies that fully utilize the physical layer capabilities of each network element. In this thesis, we develop the notion of network layer capacity and describe capacity achieving power allocation and routing algorithms for general networks with wireless links and adaptive transmission rates. Fundamental issues of delay, throughput optimality, fairness, implementation complexity, and robustness to time varying channel conditions and changing user demands are discussed. Analysis is performed at the packet level and fully considers the queueing dynamics in systems with arbitrary, potentially bursty, arrival processes. Applications of this research are examined for the specific cases of satellite networks and ad-hoc wireless networks. Indeed, in Chapter 3 we consider a multi-beam satellite downlink and develop a dynamic power allocation algorithm that allocates power to each link in reaction to queue backlog and current channel conditions. The algorithm operates without knowledge of the arriving traffic or channel statistics, and is shown to achieve maximum throughput while maintaining average delay guarantees. At the end of Chapter 4, a crosslinked collection of such satellites is considered and a satellite separation principle is developed, demonstrating that joint optimal control can be implemented with separate algorithms for the downlinks and crosslinks.(cont.) Ad-hoc wireless networks are given special attention in Chapter 6. A simple cell- partitioned model for a mobile ad-hoc network with N users is constructed, and exact expressions for capacity and delay are derived. End-to-end delay is shown to be O(N), and hence grows large as the size of the network is increased. To reduce delay, a transmission protocol which sends redundant packet information over multiple paths is developed and shown to provide O(vN) delay at the cost of reducing throughput. A fundamental rate- delay tradeoff curve is established, and the given protocols for achieving O(N) and O(vN) delay are shown to operate on distinct boundary points of this curve. In Chapters 4 and 5 we consider optimal control for a general time-varying network. A cross-layer strategy is developed that stabilizes the network whenever possible, and makes fair decisions about which data to serve when inputs exceed capacity. The strategy is decoupled into separate algorithms for dynamic flow control, power allocation, and routing, and allows for each user to make greedy decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimally fair operating point that is achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an end-to-end delay increase for data that is served by the network.by Michael J. Neely.Ph.D

Enlace de retorno satelital DVB-RCS2 : modelagem de fila e otimização de alocação de recursos baseada em teoria dos jogos

Tese (doutorado) — Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2022.É esperado que satélites tenham um papel fundamental no futuro dos sistemas de comunicação, integrando-se às infraestruturas terrestres. Esta dissertação de mestrado propõe três contribuições principais: primeiramente, se apresenta um arcabouço de simulação capaz de prover detalhes da performance de redes de comunicação satelital em cenários realistas. Este arcabouço aplica uma metodologia orientada a eventos, modelando a rede de comunicação como um sistema baseado em eventos discretos (DES), focando no enlace de retorno do protocolo DVB-RCS2. Três diferentes cenários simulados demonstram os possíveis usos das saídas do simulador para entender o comportamento dinâmico da rede e alcançar um ponto ótimo de operação do sistema. Cada cenário explora uma característica diferente do simulador, enquanto cobre um grande território de usuários, que em nosso caso estudo o país de escolha foi o Brasil. Em um segundo tópico, este trabalho introduz um novo algoritmo modificado do método de alocação de timeslots baseado em teoria dos jogos, aplicando-se no protocolo DVB-RCS2. Este procedimento considera a eficiência espectral do terminal como um parâmetro de peso para o problema de otimização convexa resultante da solução da barganha de Nash. Este novo método garante o cumprimento dos requisitos de Qualidade de Serviço (QoS) enquanto provê uma medida de justiça maior; os resultados mostram uma melhoria de 5% na medida de justiça, com uma diminuição de 75% no desvio padrão de justiça entre os quadros, também alcançando um aumento de 12% na satisfação individual média pela alocação de capacidade aos terminais. Por final, apresentamos uma modelagem alternativa para o enlace de retorno do DVB-RCS2 usando cadeias de Markov, predizendo parâmetros tradicionais de fila como a intensidade de tráfego, tempo médio de espera, dentre outros. Utilizamos dados coletados de uma série de simulações usando o arcabouço orientado a eventos para validar o modelo de filas como uma aproximação numérica útil para o cenário real de aplicação. Nós apresentamos o algoritmo de alocação de controle do parâmetro alfa (GTAC) que consegue controlar o tempo médio de espera de um RCST na fila, respeitando um limiar de tempo enquanto otimiza a taxa média média de transmissão de dados dos terminais.Satellite networks are expected to play a vital role in future communication systems, with complex features and seamless integration with ground-based infrastructure. This dissertation proposes three main contributions: firstly, it presents a novel simulation framework capable of providing a detailed assessment of a satellite communication’s network performance in realistic scenarios, employing an event-driven methodology and modeling the communications network as a DES (discrete event system). This work focuses on the return link of the Digital Video Broadcast Return Channel via Satellite (DVB-RCS2) standard. Three different scenarios demonstrate possible uses of the simulator’s output to understand the network’s dynamic behavior and achievable optimal system operation. Each scenario explores a different feature of the simulator. The simulated range covers a large territory with thousands of users, which in our case study was the country of Brazil. In the second theme, this work introduces a novel algorithm modification for the conventional game theory-based time slot assignment method, applying it to the DVB-RCS system. This procedure considers the spectral efficiency as a weighting parameter. We use it as an input for the resulting convex optimization problem of the Nash Bargaining Solution. This approach guarantees the fulfillment of Quality of Service (QoS) constraints while maintaining a higher fairness measure; results show a 5% improvement in fairness, with a 73% decrease in the standard deviation of fairness between frames, while also managing to reach a 12.5% increase in average normalized terminal BTU allocation satisfaction. Lastly, we present an alternative queuing model analysis for the DVB-RCS2 return link using Markov chains, developed to predict traditional queue parameters such as traffic intensity, average queue size, average waiting time, among others. We used data gathered from a series of simulations using the DES framework to validate this queuing model as a useful numerical approximation to the real application scenario, and, by the end of the scope, we present the alpha allocation algorithm (GTAC) that can maintain the average waiting time of a terminal in the queue to a threshold while optimizing the average terminal throughput