Queueing-Theoretic End-to-End Latency Modeling of Future Wireless Networks

The fifth generation (5G) of mobile communication networks is envisioned to enable a variety of novel applications. These applications demand requirements from the network, which are diverse and challenging. Consequently, the mobile network has to be not only capable to meet the demands of one of these applications, but also be flexible enough that it can be tailored to different needs of various services. Among these new applications, there are use cases that require low latency as well as an ultra-high reliability, e.g., to ensure unobstructed production in factory automation or road safety for (autonomous) transportation. In these domains, the requirements are crucial, since violating them may lead to financial or even human damage. Hence, an ultra-low probability of failure is necessary. Based on this, two major questions arise that are the motivation for this thesis. First, how can ultra-low failure probabilities be evaluated, since experiments or simulations would require a tremendous number of runs and, thus, turn out to be infeasible. Second, given a network that can be configured differently for different applications through the concept of network slicing, which performance can be expected by different parameters and what is their optimal choice, particularly in the presence of other applications. In this thesis, both questions shall be answered by appropriate mathematical modeling of the radio interface and the radio access network. Thereby the aim is to find the distribution of the (end-to-end) latency, allowing to extract stochastic measures such as the mean, the variance, but also ultra-high percentiles at the distribution tail. The percentile analysis eventually leads to the desired evaluation of worst-case scenarios at ultra-low probabilities. Therefore, the mathematical tool of queuing theory is utilized to study video streaming performance and one or multiple (low-latency) applications. One of the key contributions is the development of a numeric algorithm to obtain the latency of general queuing systems for homogeneous as well as for prioritized heterogeneous traffic. This provides the foundation for analyzing and improving end-to-end latency for applications with known traffic distributions in arbitrary network topologies and consisting of one or multiple network slices.Es wird erwartet, dass die fünfte Mobilfunkgeneration (5G) eine Reihe neuartiger Anwendungen ermöglichen wird. Allerdings stellen diese Anwendungen sowohl sehr unterschiedliche als auch überaus herausfordernde Anforderungen an das Netzwerk. Folglich muss das mobile Netz nicht nur die Voraussetzungen einer einzelnen Anwendungen erfüllen, sondern auch flexibel genug sein, um an die Vorgaben unterschiedlicher Dienste angepasst werden zu können. Ein Teil der neuen Anwendungen erfordert hochzuverlässige Kommunikation mit niedriger Latenz, um beispielsweise unterbrechungsfreie Produktion in der Fabrikautomatisierung oder Sicherheit im (autonomen) Straßenverkehr zu gewährleisten. In diesen Bereichen ist die Erfüllung der gestellten Anforderungen besonders kritisch, da eine Verletzung finanzielle oder sogar personelle Schäden nach sich ziehen könnte. Eine extrem niedrige Ausfallwahrscheinlichkeit ist daher von größter Wichtigkeit. Daraus ergeben sich zwei wesentliche Fragestellungen, welche diese Arbeit motivieren. Erstens, wie können extrem niedrige Ausfallwahrscheinlichkeiten evaluiert werden. Ihr Nachweis durch Experimente oder Simulationen würde eine extrem große Anzahl an Durchläufen benötigen und sich daher als nicht realisierbar herausstellen. Zweitens, welche Performanz ist für ein gegebenes Netzwerk durch unterschiedliche Konfigurationen zu erwarten und wie kann die optimale Konfiguration gewählt werden. Diese Frage ist insbesondere dann interessant, wenn mehrere Anwendungen gleichzeitig bedient werden und durch sogenanntes Slicing für jeden Dienst unterschiedliche Konfigurationen möglich sind. In dieser Arbeit werden beide Fragen durch geeignete mathematische Modellierung der Funkschnittstelle sowie des Funkzugangsnetzes (Radio Access Network) adressiert. Mithilfe der Warteschlangentheorie soll die stochastische Verteilung der (Ende-zu-Ende-) Latenz bestimmt werden. Dies liefert unterschiedliche stochastische Metriken, wie den Erwartungswert, die Varianz und insbesondere extrem hohe Perzentile am oberen Rand der Verteilung. Letztere geben schließlich Aufschluss über die gesuchten schlimmsten Fälle, die mit sehr geringer Wahrscheinlichkeit eintreten können. In der Arbeit werden Videostreaming und ein oder mehrere niedriglatente Anwendungen untersucht. Zu den wichtigsten Beiträgen zählt dabei die Entwicklung einer numerischen Methode, um die Latenz in allgemeinen Warteschlangensystemen für homogenen sowie für priorisierten heterogenen Datenverkehr zu bestimmen. Dies legt die Grundlage für die Analyse und Verbesserung von Ende-zu-Ende-Latenz für Anwendungen mit bekannten Verkehrsverteilungen in beliebigen Netzwerktopologien mit ein oder mehreren Slices

On a general mixed priority queue with server discretion

This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastic Models on June, 24, 2016, available online: http://dx.doi.org/10.1080/15326349.2016.1193753.We consider a single-server queueing system which attends to N priority classes that are classified into two distinct types: (i) urgent: classes which have preemptive resume priority over at least one lower priority class, and (ii) non-urgent: classes which only have non-preemptive priority among lower priority classes. While urgent customers have preemptive priority, the ultimate decision on whether to interrupt a current service is based on certain discretionary rules. An accumulating prioritization is also incorporated. The marginal waiting time distributions are obtained and numerical examples comparing the new model to other similar priority queueing systems are provided.This research was supported by the Natural Sciences and Engineering Research Council of Canada. In particular, Steve Drekic acknowledges the financial support provided via the agency's Discovery Grants program (#238675-2010-RGPIN)

A Generalization of M/G/1 Priority Models via Accumulating Priority

Priority queueing systems are oftentimes set up so that arriving customers are placed into one of $N$ distinct priority classes. Moreover, to determine the order of service, each customer (upon arriving to the system) is assigned a priority level that is unique to the class to which it belongs. In static priority queues, the priority level of a class-$k$ ($k=1,2,\ldots,N$) customer is assumed to be constant with respect to time. This simple prioritization structure is easy to implement in practice, and as such, various types of static priority queues have been analyzed and subsequently applied to real-life queueing systems. However, the assumption of constant priority levels for the customers may not always be appropriate. Furthermore, static priority queues can often display poor system performance as their design does not provide systems managers the means to balance the classical trade-off inherent in all priority queues, that is: reducing wait times of higher priority customers consequently increases the wait times for those of lower priority. An alternative to static priority queues are accumulating priority queues, where the priority level of a class-$k$ customer is assumed to accumulate linearly at rate $b_k>0$ throughout the class-$k$ customer's time in the system. The main benefit of accumulating priority queues is the ability, through the specification of the accumulating priority rates $\{b_k\}_{k=1}^N$, to control the waiting times of each class. In the past, due to the complex nature of the accumulating prioritization structure, the control of waiting times in accumulating priority queues was limited --- being administered only through their first moments. Nowadays, with the advent of a very useful tool called the maximal priority process, it is possible to characterize the waiting time distributions of several types of accumulating priority queues. In this thesis, we incorporate the concept of accumulating priority to several previously analyzed static priority queues, and use the maximal priority process to establish the corresponding steady-state waiting time distributions. In addition, since static priority queues may be captured from accumulating priority queues, useful comparisons between the considered accumulating priority queues and their static priority counterparts are made throughout this thesis. Thus, in the end, this thesis results in a set of extensive analyses on these highly flexible accumulating priority queueing models that provide a better understanding of their overall behaviour, as well as exemplify their many advantages over their static priority equivalents

Random trees in queueing systems with deadlines

AbstractWe survey our research on scheduling aperiodic tasks in real-time systems in order to illustrate the benefits of modelling queueing systems by means of random trees. Relying on a discrete-time single-server queueing system, we investigated deadline meeting properties of several scheduling algorithms employed for servicing probabilistically arriving tasks, characterized by arbitrary arrival and execution time distributions and a constant service time deadline T. Taking a non-queueing theory approach (i.e., without stable-stable assumptions) we found that the probability distribution of the random time sT where such a system operates without violating any task's deadline is approximately exponential with parameter λT = 1μT, with the expectation E[sT] = μT growing exponentially in T. The value μT depends on the particular scheduling algorithm, and its derivation is based on the combinatorial and asymptotic analysis of certain random trees. This paper demonstrates that random trees provide an efficient common framework to deal with different scheduling disciplines and gives an overview of the various combinatorial and asymptotic methods used in the appropriate analysis

Scheduling for today’s computer systems: bridging theory and practice

Scheduling is a fundamental technique for improving performance in computer systems. From web servers to routers to operating systems, how the bottleneck device is scheduled has an enormous impact on the performance of the system as a whole. Given the immense literature studying scheduling, it is easy to think that we already understand enough about scheduling. But, modern computer system designs have highlighted a number of disconnects between traditional analytic results and the needs of system designers. In particular, the idealized policies, metrics, and models used by analytic researchers do not match the policies, metrics, and scenarios that appear in real systems. The goal of this thesis is to take a step towards modernizing the theory of scheduling in order to provide results that apply to today’s computer systems, and thus ease the burden on system designers. To accomplish this goal, we provide new results that help to bridge each of the disconnects mentioned above. We will move beyond the study of idealized policies by introducing a new analytic framework where the focus is on scheduling heuristics and techniques rather than individual policies. By moving beyond the study of individual policies, our results apply to the complex hybrid policies that are often used in practice. For example, our results enable designers to understand how the policies that favor small job sizes are affected by the fact that real systems only have estimates of job sizes. In addition, we move beyond the study of mean response time and provide results characterizing the distribution of response time and the fairness of scheduling policies. These results allow us to understand how scheduling affects QoS guarantees and whether favoring small job sizes results in large job sizes being treated unfairly. Finally, we move beyond the simplified models traditionally used in scheduling research and provide results characterizing the effectiveness of scheduling in multiserver systems and when users are interactive. These results allow us to answer questions about the how to design multiserver systems and how to choose a workload generator when evaluating new scheduling designs

Inferring Queueing Network Models from High-precision Location Tracking Data

Stochastic performance models are widely used to analyse the performance and reliability of systems that involve the flow and processing of customers. However, traditional methods of constructing a performance model are typically manual, time-consuming, intrusive and labour-intensive. The limited amount and low quality of manually-collected data often lead to an inaccurate picture of customer flows and poor estimates of model parameters. Driven by advances in wireless sensor technologies, recent real-time location systems (RTLSs) enable the automatic, continuous and unintrusive collection of high-precision location tracking data, in both indoor and outdoor environment. This high-quality data provides an ideal basis for the construction of high-fidelity performance models. This thesis presents a four-stage data processing pipeline which takes as input high-precision location tracking data and automatically constructs a queueing network performance model approximating the underlying system. The first two stages transform raw location traces into high-level “event logs” recording when and for how long a customer entity requests service from a server entity. The third stage infers the customer flow structure and extracts samples of time delays involved in the system; including service time, customer interarrival time and customer travelling time. The fourth stage parameterises the service process and customer arrival process of the final output queueing network model. To collect large-enough location traces for the purpose of inference by conducting physical experiments is expensive, labour-intensive and time-consuming. We thus developed LocTrack- JINQS, an open-source simulation library for constructing simulations with location awareness and generating synthetic location tracking data. Finally we examine the effectiveness of the data processing pipeline through four case studies based on both synthetic and real location tracking data. The results show that the methodology performs with moderate success in inferring multi-class queueing networks composed of single-server queues with FIFO, LIFO and priority-based service disciplines; it is also capable of inferring different routing policies, including simple probabilistic routing, class-based routing and shortest-queue routing

A 2-class maintenance model with dynamic server behavior

This is a post-peer-review, pre-copyedit version of an article published in TOP. The final authenticated version is available online at: https://doi.org/10.1007/s11750-019-00509-1We analyze a 2-class maintenance system within a single-server polling model framework. There are C+f machines in the system, where C is the cap on the number of machines that can be turned on simultaneously (and hence, be at risk of failure), and the excess f machines comprise a maintenance float which can be used to replace machines that are taken down for repair. The server’s behavior is dynamic, capable of switching queues upon a machine failure or service completion depending on both queue lengths. This generalized server behavior permits the analysis of several classic service policies, including preemptive resume priority, non-preemptive priority, and exhaustive. More complicated polices can also be considered, such as threshold-based ones and a version of the Bernoulli service rule. The system is modeled as a level-dependent quasi-birth-and-death process and matrix analytic methods are used to find the steady-state joint queue length distribution, as well as the distribution for the sojourn time of a broken machine. An upper bound on the expected number of working machines as a function of C is derived, and Little’s Law is used to find the relationship between the expected number of working machines and the expected sojourn time of a failed machine when f=0 or f≥1. Several numerical examples are presented, including how one might optimize an objective function depending on the mean number of working machines, with penalty costs attributed to increasing C or f.Steve Drekic and Kevin Granville acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada through its Discovery Grants program (RGPIN-2016-03685) and Postgraduate Scholarship-Doctoral program, respectively

Performance of Computer Systems; Proceedings of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna, Austria, February 6-8, 1979

These proceedings are a collection of contributions to computer system performance, selected by the usual refereeing process from papers submitted to the symposium, as well as a few invited papers representing significant novel contributions made during the last year. They represent the thrust and vitality of the subject as well as its capacity to identify important basic problems and major application areas. The main methodological problems appear in the underlying queueing theoretic aspects, in the deterministic analysis of waiting time phenomena, in workload characterization and representation, in the algorithmic aspects of model processing, and in the analysis of measurement data. Major areas for applications are computer architectures, data bases, computer networks, and capacity planning. The international importance of the area of computer system performance was well reflected at the symposium by participants from 19 countries. The mixture of participants was also evident in the institutions which they represented: 35% from universities, 25% from governmental research organizations, but also 30% from industry and 10% from non-research government bodies. This proves that the area is reaching a stage of maturity where it can contribute directly to progress in practical problems

An Application of Matrix Analytic Methods to Queueing Models with Polling

We review what it means to model a queueing system, and highlight several components of interest which govern the behaviour of customers, as well as the server(s) who tend to them. Our primary focus is on polling systems, which involve one or more servers who must serve multiple queues of customers according to their service policy, which is made up of an overall polling order, and a service discipline defined at each queue. The most common polling orders and service disciplines are discussed, and some examples are given to demonstrate their use. Classic matrix analytic method theory is built up and illustrated on models of increasing complexity, to provide context for the analyses of later chapters. The original research contained within this thesis is divided into two halves, finite population maintenance models and infinite population cyclic polling models. In the first half, we investigate a 2-class maintenance system with a single server, expressed as a polling model. In Chapter 2, the model we study considers a total of C machines which are at risk of failing when working. Depending on the failure that a machine experiences, it is sorted into either the class-1 or class-2 queue where it awaits service among other machines suffering from similar failures. The possible service policies that are considered include exhaustive, non-preemptive priority, and preemptive resume priority. In Chapter 3, this model is generalized to allow for a maintenance float of f spare machines that can be turned on to replace a failed machine. Additionally, the possible server behaviours are greatly generalized. In both chapters, among other topics, we discuss the optimization of server behaviour as well as the limiting number of working machines as we let C go to infinity. As these are systems with a finite population (for a given C and f), their steady-state distributions can be solved for using the algorithm for level-dependent quasi-birth-and-death processes without loss of accuracy. When a class of customers are impatient, the algorithms covered in this thesis require their queue length to be truncated in order for us to approximate the steady-state distribution for all but the simplest model. In Chapter 4, we model a 2-queue polling system with impatient customers and k_i-limited service disciplines. Finite buffers are assumed for both queues, such that if a customer arrives to find their queue full then they are blocked and lost forever. Finite buffers are a way to interpret a necessary truncation level, since we can simply assume that it is impossible to observe the removed states. However, if we are interested in approximating an infinite buffer system, this inconsistency will bias the steady-state probabilities if blocking probabilities are not negligible. In Chapter 5, we introduce the Unobserved Waiting Customer approximation as a way to reduce this natural biasing that is incurred when approximating an infinite buffer system. Among the queues considered within this chapter is a N-queue system with exhaustive service and customers who may or may not be impatient. In Chapter 6, we extend this approximation to allow for reneging rates that depend on a customer's place in their queue. This is applied to a N-queue polling system which generalizes the model of Chapter 4

Performance modelling of replication protocols

PhD ThesisThis thesis is concerned with the performance modelling of data replication protocols. Data replication is used to provide fault tolerance and to improve the performance of a distributed system. Replication not only needs extra storage but also has an extra cost associated with it when performing an update. It is not always clear which algorithm will give best performance in a given scenario, how many copies should be maintained or where these copies should be located to yield the best performance. The consistency requirements also change with application. One has to choose these parameters to maximize reliability and speed and minimize cost. A study showing the effect of change in different parameters on the performance of these protocols would be helpful in making these decisions. With the use of data replication techniques in wide-area systems where hundreds or even thousands of sites may be involved, it has become important to evaluate the performance of the schemes maintaining copies of data. This thesis evaluates the performance of replication protocols that provide differ- ent levels of data consistency ranging from strong to weak consistency. The protocols that try to integrate strong and weak consistency are also examined. Queueing theory techniques are used to evaluate the performance of these protocols. The performance measures of interest are the response times of read and write jobs. These times are evaluated both when replicas are reliable and when they are subject to random breakdowns and repairs.Commonwealth Scholarshi