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"

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

Unreliable Retrial Queues in a Random Environment

This dissertation investigates stability conditions and approximate steady-state performance measures for unreliable, single-server retrial queues operating in a randomly evolving environment. In such systems, arriving customers that find the server busy or failed join a retrial queue from which they attempt to regain access to the server at random intervals. Such models are useful for the performance evaluation of communications and computer networks which are characterized by time-varying arrival, service and failure rates. To model this time-varying behavior, we study systems whose parameters are modulated by a finite Markov process. Two distinct cases are analyzed. The first considers systems with Markov-modulated arrival, service, retrial, failure and repair rates assuming all interevent and service times are exponentially distributed. The joint process of the orbit size, environment state, and server status is shown to be a tri-layered, level-dependent quasi-birth-and-death (LDQBD) process, and we provide a necessary and sufficient condition for the positive recurrence of LDQBDs using classical techniques. Moreover, we apply efficient numerical algorithms, designed to exploit the matrix-geometric structure of the model, to compute the approximate steady-state orbit size distribution and mean congestion and delay measures. The second case assumes that customers bring generally distributed service requirements while all other processes are identical to the first case. We show that the joint process of orbit size, environment state and server status is a level-dependent, M/G/1-type stochastic process. By employing regenerative theory, and exploiting the M/G/1-type structure, we derive a necessary and sufficient condition for stability of the system. Finally, for the exponential model, we illustrate how the main results may be used to simultaneously select mean time customers spend in orbit, subject to bound and stability constraints

(R1971) Analysis of Feedback Queueing Model with Differentiated Vacations under Classical Retrial Policy

This paper analyzes an M/M/1 retrial queue under differentiated vacations and Bernoulli feedback policy. On receiving the service, if the customer is not satisfied, then he may join the retrial group again with some probability and demand for service or may leave the system with the complementary probability. Using the probability generating functions technique, the steady-state solutions of the system are obtained. Furthermore, we have obtained some of the important performance measures such as expected orbit length, expected length of the system, sojourn times and probability of server being in different states. Using MATLAB software, we have represented the graphical interpretation of the results obtained. Finally, the cost is optimized using the parabolic method

Shot-noise queueing models

We provide a survey of so-called shot-noise queues: queueing models with the special feature that the server speed is proportional to the amount of work it faces. Several results are derived for the workload in an M/G/1 shot-noise queue and some of its variants. Furthermore, we give some attention to queues with general workload-dependent service speed. We also discuss linear stochastic fluid networks, and queues in which the input process is a shot-noise process

Solution methods for controlled queueing networks

In this dissertation we look at a controlled queueing network where a controller routes the incoming arrivals to parallel queues using state-dependent rules. Besides this general arrival there are dedicated arrivals to each queue. The dedicated arrivals can only be served by their designated server, hence there is no routing decision involved. The goal of the controller is to find a stationary policy that will minimize the average number of customers in the system;The problem is modeled as a semi-Markov decision process and solved using techniques from the theory of Markov decision processes. We develop an efficient policy iteration based methodology which performs better than the value iteration method which is widely thought of as the best method to use for large-scale problems. The novelty in our approach is to use iterative methods in solving the system of linear equations, and also take advantage of the sparsity of matrices. The methodology could be used for other problems that are similar in nature. Using this methodology we solve much larger problems than reported in the literature. We also look at how several heuristic methods perform on our problem. No heuristic method is suitable to use for all instances. In general, however, these heuristic methods offer quick and reasonable solutions to very large problems