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

A Mathematical Modelling Approach for Systems Where the Servers Are Almost Always Busy

The design and implementation of new configurations of mental health services to meet local needs is a challenging problem. In the UK, services for common mental health disorders such as anxiety and depression are an example of a system running near or at capacity, in that it is extremely rare for the queue size for any given mode of treatment to fall to zero. In this paper we describe a mathematical model that can be applied in such circumstances. The model provides a simple way of estimating the mean and variance of the number of patients that would be treated within a given period of time given a particular configuration of services as defined by the number of appointments allocated to different modes of treatment and the referral patterns to and between different modes of treatment. The model has been used by service planners to explore the impact of different options on throughput, clinical outcomes, queue sizes, and waiting times. We also discuss the potential for using the model in conjunction with optimisation techniques to inform service design and its applicability to other contexts

Modeling the Emergency Care Delivery System Using a Queueing Approach

This thesis considers a regional emergency care delivery system that has a common emergency medical service (EMS) provider and two hospitals, each with a single emergency department (ED) and an inpatient department (ID). Patients arrive at one of the hospital EDs either by ambulance or self-transportation, and we assume that an ambulance patient has preemptive priority over a walk-in patient. Both types of patients can potentially be admitted into the ID or discharged directly from the ED. An admitted patient who cannot access the ID due to the lack of available inpatient beds becomes a boarding patient and blocks an ED server. An ED goes on diversion, e.g., requests the EMS provider to divert incoming ambulances to the neighboring facility, if the total number of its ambulance patients and boarding patients exceeds its capacity (the total number of its servers). The EMS provider will accept the diversion request if the neighboring ED is not on diversion. Both EDs choose its capacity as its diversion threshold and never change the threshold value strategically, and hence they never game. Although the network could be an idealized model of an actual operation, it can be thought of as the simplest network model that is rich enough to reproduce the variety of interactions among different system components. In particular, we aim to highlight the bottleneck effect of inpatient units on ED overcrowding and the network effects resulting from ED diversions. A continuous time Markov chain is introduced for the network model. We show that the chain is irreversible and hence its stationary distribution is difficult to characterize analytically. We identify an alternative solution that builds on queueing decomposition and matrix-analytic methods. We demonstrate through discrete-event simulations the effectiveness of this solution on deriving various performance measures of the original network model. Moreover, by conducting extensive numerical experiments, we provide potential explanations for the overcrowding and delays in a network of hospitals. We suggest remedies from a queueing perspective for the operational challenges facing emergency care delivery systems

Analysis of Bandwidth and Latency Constraints on a Packetized Cloud Radio Access Network Fronthaul

Cloud radio access network (C-RAN) is a promising architecture for the next-generation RAN to meet the diverse and stringent requirements envisioned by fifth generation mobile communication systems (5G) and future generation mobile networks. C-RAN offers several advantages, such as reduced capital expenditure (CAPEX) and operational expenditure (OPEX), increased spectral efficiency (SE), higher capacity and improved cell-edge performance, and efficient hardware utilization through resource sharing and network function virtualization (NFV). However, these centralization gains come with the need for a fronthaul, which is the transport link connecting remote radio units (RRUs) to the base band unit (BBU) pool. In conventional C-RAN, legacy common public radio interface (CPRI) protocol is used on the fronthaul network to transport the raw, unprocessed baseband in-phase/quadrature-phase (I/Q) samples between the BBU and the RRUs, and it demands a huge fronthaul bandwidth, a strict low-latency, in the order of a few hundred microseconds, and a very high reliability. Hence, in order to relax the excessive fronthaul bandwidth and stringent low-latency requirements, as well as to enhance the flexibility of the fronthaul, it is utmost important to redesign the fronthaul, while still profiting from the acclaimed centralization benefits. Therefore, a flexibly centralized C-RAN with different functional splits has been introduced. In addition, 5G mobile fronthaul (often also termed as an evolved fronthaul ) is envisioned to be packet-based, utilizing the Ethernet as a transport technology. In this thesis, to circumvent the fronthaul bandwidth constraint, a packetized fronthaul considering an appropriate functional split such that the fronthaul data rate is coupled with actual user data rate, unlike the classical C-RAN where fronthaul data rate is always static and independent of the traffic load, is justifiably chosen. We adapt queuing and spatial traffic models to derive the mathematical expressions for statistical multiplexing gains that can be obtained from the randomness in the user traffic. Through this, we show that the required fronthaul bandwidth can be reduced significantly, depending on the overall traffic demand, correlation distance and outage probability. Furthermore, an iterative optimization algorithm is developed, showing the impacts of number of pilots on a bandwidth-constrained fronthaul. This algorithm achieves additional reduction in the required fronthaul bandwidth. Next, knowing the multiplexing gains and possible fronthaul bandwidth reduction, it is beneficial for the mobile network operators (MNOs) to deploy the optical transceiver (TRX) modules in C-RAN cost efficiently. For this, using the same framework, a cost model for fronthaul TRX cost optimization is presented. This is essential in C-RAN, because in a wavelength division multiplexing-passive optical network (WDM-PON) system, TRXs are generally deployed to serve at a peak load. But, because of variations in the traffic demands, owing to tidal effect, the fronthaul can be dimensioned requiring a lower capacity allowing a reasonable outage, thus giving rise to cost saving by deploying fewer TRXs, and energy saving by putting the unused TRXs in sleep mode. The second focus of the thesis is the fronthaul latency analysis, which is a critical performance metric, especially for ultra-reliable and low latency communication (URLLC). An analytical framework to calculate the latency in the uplink (UL) of C-RAN massive multiple-input multiple-output (MIMO) system is presented. For this, a continuous-time queuing model for the Ethernet switch in the fronthaul network, which aggregates the UL traffic from several massive MIMO-aided RRUs, is considered. The closed-form solutions for the moment generating function (MGF) of sojourn time, waiting time and queue length distributions are derived using Pollaczek–Khinchine formula for our M/HE/1 queuing model, and evaluated via numerical solutions. In addition, the packet loss rate – due to the inability of the packets to reach the destination in a certain time – is derived. Due to the slotted nature of the UL transmissions, the model is extended to a discrete-time queuing model. The impact of the packet arrival rate, average packet size, SE of users, and fronthaul capacity on the sojourn time, waiting time and queue length distributions are analyzed. While offloading more signal processing functionalities to the RRU reduces the required fronthaul bandwidth considerably, this increases the complexity at the RRU. Hence, considering the 5G New Radio (NR) flexible numerology and XRAN functional split with a detailed radio frequency (RF) chain at the RRU, the total RRU complexity is computed first, and later, a tradeoff between the required fronthaul bandwidth and RRU complexity is analyzed. We conclude that despite the numerous C-RAN benefits, the stringent fronthaul bandwidth and latency constraints must be carefully evaluated, and an optimal functional split is essential to meet diverse set of requirements imposed by new radio access technologies (RATs).Ein cloud-basiertes Mobilfunkzugangsnetz (cloud radio access network, C-RAN) stellt eine vielversprechende Architektur für das RAN der nächsten Generation dar, um die vielfältigen und strengen Anforderungen der fünften (5G) und zukünftigen Generationen von Mobilfunknetzen zu erfüllen. C-RAN bietet mehrere Vorteile, wie z.B. reduzierte Investitions- (CAPEX) und Betriebskosten (OPEX), erhöhte spektrale Effizienz (SE), höhere Kapazität und verbesserte Leistung am Zellrand sowie effiziente Hardwareauslastung durch Ressourcenteilung und Virtualisierung von Netzwerkfunktionen (network function virtualization, NFV). Diese Zentralisierungsvorteile erfordern jedoch eine Transportverbindung (Fronthaul), die die Antenneneinheiten (remote radio units, RRUs) mit dem Pool an Basisbandeinheiten (basisband unit, BBU) verbindet. Im konventionellen C-RAN wird das bestehende CPRI-Protokoll (common public radio interface) für das Fronthaul-Netzwerk verwendet, um die rohen, unverarbeitet n Abtastwerte der In-Phaseund Quadraturkomponente (I/Q) des Basisbands zwischen der BBU und den RRUs zu transportieren. Dies erfordert eine enorme Fronthaul-Bandbreite, eine strenge niedrige Latenz in der Größenordnung von einigen hundert Mikrosekunden und eine sehr hohe Zuverlässigkeit. Um die extrem große Fronthaul-Bandbreite und die strengen Anforderungen an die geringe Latenz zu lockern und die Flexibilität des Fronthauls zu erhöhen, ist es daher äußerst wichtig, das Fronthaul neu zu gestalten und dabei trotzdem von den erwarteten Vorteilen der Zentralisierung zu profitieren. Daher wurde ein flexibel zentralisiertes CRAN mit unterschiedlichen Funktionsaufteilungen eingeführt. Außerdem ist das mobile 5G-Fronthaul (oft auch als evolved Fronthaul bezeichnet) als paketbasiert konzipiert und nutzt Ethernet als Transporttechnologie. Um die Bandbreitenbeschränkung zu erfüllen, wird in dieser Arbeit ein paketbasiertes Fronthaul unter Berücksichtigung einer geeigneten funktionalen Aufteilung so gewählt, dass die Fronthaul-Datenrate mit der tatsächlichen Nutzdatenrate gekoppelt wird, im Gegensatz zum klassischen C-RAN, bei dem die Fronthaul-Datenrate immer statisch und unabhängig von der Verkehrsbelastung ist. Wir passen Warteschlangen- und räumliche Verkehrsmodelle an, um mathematische Ausdrücke für statistische Multiplexing- Gewinne herzuleiten, die aus der Zufälligkeit im Benutzerverkehr gewonnen werden können. Hierdurch zeigen wir, dass die erforderliche Fronthaul-Bandbreite abhängig von der Gesamtverkehrsnachfrage, der Korrelationsdistanz und der Ausfallwahrscheinlichkeit deutlich reduziert werden kann. Darüber hinaus wird ein iterativer Optimierungsalgorithmus entwickelt, der die Auswirkungen der Anzahl der Piloten auf das bandbreitenbeschränkte Fronthaul zeigt. Dieser Algorithmus erreicht eine zusätzliche Reduktion der benötigte Fronthaul-Bandbreite. Mit dem Wissen über die Multiplexing-Gewinne und die mögliche Reduktion der Fronthaul-Bandbreite ist es für die Mobilfunkbetreiber (mobile network operators, MNOs) von Vorteil, die Module des optischen Sendeempfängers (transceiver, TRX) kostengünstig im C-RAN einzusetzen. Dazu wird unter Verwendung des gleichen Rahmenwerks ein Kostenmodell zur Fronthaul-TRX-Kostenoptimierung vorgestellt. Dies ist im C-RAN unerlässlich, da in einem WDM-PON-System (wavelength division multiplexing-passive optical network) die TRX im Allgemeinen bei Spitzenlast eingesetzt werden. Aufgrund der Schwankungen in den Verkehrsanforderungen (Gezeiteneffekt) kann das Fronthaul jedoch mit einer geringeren Kapazität dimensioniert werden, die einen vertretbaren Ausfall in Kauf nimmt, was zu Kosteneinsparungen durch den Einsatz von weniger TRXn und Energieeinsparungen durch den Einsatz der ungenutzten TRX im Schlafmodus führt. Der zweite Schwerpunkt der Arbeit ist die Fronthaul-Latenzanalyse, die eine kritische Leistungskennzahl liefert, insbesondere für die hochzuverlässige und niedriglatente Kommunikation (ultra-reliable low latency communications, URLLC). Ein analytisches Modell zur Berechnung der Latenz im Uplink (UL) des C-RAN mit massivem MIMO (multiple input multiple output) wird vorgestellt. Dazu wird ein Warteschlangen-Modell mit kontinuierlicher Zeit für den Ethernet-Switch im Fronthaul-Netzwerk betrachtet, das den UL-Verkehr von mehreren RRUs mit massivem MIMO aggregiert. Die geschlossenen Lösungen für die momenterzeugende Funktion (moment generating function, MGF) von Verweildauer-, Wartezeit- und Warteschlangenlängenverteilungen werden mit Hilfe der Pollaczek-Khinchin-Formel für unser M/HE/1-Warteschlangenmodell hergeleitet und mittels numerischer Verfahren ausgewertet. Darüber hinaus wird die Paketverlustrate derjenigen Pakete, die das Ziel nicht in einer bestimmten Zeit erreichen, hergeleitet. Aufgrund der Organisation der UL-Übertragungen in Zeitschlitzen wird das Modell zu einem Warteschlangenmodell mit diskreter Zeit erweitert. Der Einfluss der Paketankunftsrate, der durchschnittlichen Paketgröße, der SE der Benutzer und der Fronthaul-Kapazität auf die Verweildauer-, dieWartezeit- und dieWarteschlangenlängenverteilung wird analysiert. Während das Verlagern weiterer Signalverarbeitungsfunktionalitäten an die RRU die erforderliche Fronthaul-Bandbreite erheblich reduziert, erhöht sich dadurch im Gegenzug die Komplexität der RRU. Daher wird unter Berücksichtigung der flexiblen Numerologie von 5G New Radio (NR) und der XRAN-Funktionenaufteilung mit einer detaillierten RF-Kette (radio frequency) am RRU zunächst die gesamte RRU-Komplexität berechnet und später ein Kompromiss zwischen der erforderlichen Fronthaul-Bandbreite und der RRU-Komplexität untersucht. Wir kommen zu dem Schluss, dass trotz der zahlreichen Vorteile von C-RAN die strengen Bandbreiten- und Latenzbedingungen an das Fronthaul sorgfältig geprüft werden müssen und eine optimale funktionale Aufteilung unerlässlich ist, um die vielfältigen Anforderungen der neuen Funkzugangstechnologien (radio access technologies, RATs) zu erfüllen