Fitting simulation input models for correlated traffic data

The adequate representation of input models is an important step in building valid simulation models. Modeling independent and identically distributed data is well established in simulation, but for some application areas like computer and communication networks it is known, that the assumption of independent and identically distributed data is violated in practice and that for example interarrival times or packet sizes exhibit autocorrelation over a large number of lags. Moreover, it is known that negligence of these correlations can result in a serious loss of validity of the simulation model. Although different stochastic processes, which can model these autocorrelations, like e.g. Autoregressive-To-Anything (ARTA) processes and Markovian Arrival Processes (MAPs), have been proposed in the past and more recently fitting algorithms to set the parameters of these processes such that they resemble the behavior of observations from a real system have been developed, the integration of correlated processes into simulation models is still a challenge. In this work ARTA processes are extended in several ways to account for the requirements when simulating models of computer and communication systems. In a first step ARTA processes are extended to use an Autoregressive Moving Average (ARMA) process instead of a pure Autoregressive (AR) base process to be able to capture a large number of autocorrelation lags, while keeping the model size small. In a second step they are enabled to use the flexible class of acyclic Phase-type distributions as marginal distribution. To support the usage of these novel processes in simulation models a fitting algorithm is presented, software for fitting and simulating these processes is developed and the tools are integrated into the toolkit ProFiDo, which provides a complete framework for fitting and analyzing different stochastic processes. By means of synthetically generated and real network traces it is shown that the presented stochastic processes are able to provide a good approximation of the marginal distribution as well as the correlation structure of the different traces and result in a compact process description

Performance Evaluation of the Control Plane in OpenFlow Networks

Online services and applications have grown rapidly in the last decade. The network is necessary for many services and applications. Many technologies are invented to meet the requirements of online services, such as micro-services and serverless computing. However, the traditional network architecture suffers from several shortages. It is difficult for the traditional network to adapt to new demands without massive reconfiguration. In traditional IP networks, it is complex to manage and configure the network devices since skilled technicians are required. Changing the policy of a network is also time consuming because network operators need to re-configure multiple network devices and update access control lists using low level commands. The management and configuration becomes more complex and challenging, when the traffic in a network changes frequently. SDN (Software-defined networking) is an innovative approach to manage networks more flexible. It separates the control plane from forwarding devices and uses a centralized controller to manipulate all the forwarding devices. The separation offers many benefits in terms of network flexibility and management. The controller can provide a global view of a network. Using the controller, network operators can manage and configure all the network devices at a high level interface. With SDN, a network can adapt to new demands by updating the applications in the controller. However, all these benefits come with a performance penalty. Since the controller manipulates all the forwarding devices, the performance of the controller impacts the performance of the whole network. In this thesis, we investigate the performance of SDN controllers. We also implement a benchmark tool for OpenFlow controllers. It measures the response time of an OpenFlow controller and fit a phase-type distribution to the response time. Based on the distribution of the response time, we build a queueing model for multiple controllers in an OpenFlow network and determine the optimal number of controllers that can minimize the response time of the controllers. We design an algorithm that can optimize the mapping relationship among the switches and controllers. The load of controllers can be balanced with the optimized mapping relationship

Statistical Analysis of Message Delay in SIP Proxy Server, Journal of Telecommunications and Information Technology, 2014, nr 4

Single hop delay of SIP message going through SIP proxy server operating in carriers backbone network is being analyzed. Results indicate that message sojourn times inside SIP server in most cases do not exceed order of tens of milliseconds (99% of all SIP-I messages experience less than 21 ms of sojourn delay) but there were observed very large delays which can hardly be attributed to message specic processing procedures. It is observed that delays are very variable. Delay components distribution that is to identied are not exponentially distributed or nearly constant even per message type or size. The authors show that measured waiting time and minimum transit time through SIP server can be approximated by acyclic phase-type distributions but accuracy of approximation at very high values of quantiles depends on the number outliers in the data. This nding suggests that modeling of SIP server with queueing system of GjPHjc type may server as an adequate solution

Eliminierung negativer Effekte autokorrelierter Prozesse an Zusammenführungen

Im Kern der vorliegenden Arbeit wird eine neue Vorfahrtstrategie zur Steuerung von Materialflüssen an Zusammenführungen vorgestellt. Das Hauptanwendungsgebiet stellen innerbetriebliche Transportsysteme dar, wobei die Erkenntnisse auf beliebige Transport- bzw. Bediensysteme übertragbar sind. Die Arbeit grenzt sich mit der Annahme autokorrelierter Ankunftsprozesse von bisheriger Forschung und Entwicklung ab. Bis dato werden stets unkorrelierte Ströme angenommen bzw. findet keine spezielle Beachtung autokorrelierter Ströme bei der Vorfahrtsteuerung statt. Untersuchungen zeigen aber, dass zum einen mit hoher Konfidenz mit autokorrelierten Materialflüssen zu rechnen ist und in diesem Fall zum anderen von einem erheblichen Einfluss auf die Systemleistung ausgegangen werden muss. Zusammengefasst konnten im Rahmen der vorliegenden Arbeit 68 Realdatensätze verschiedener Unternehmen untersucht werden, mit dem Ergebnis, dass ca. 95% der Materialflüsse Autokorrelation aufweisen. Ferner wird hergeleitet, dass Autokorrelation intrinsisch in Materialflusssystemen entsteht. Die Folgen autokorrelierter Prozesse bestehen dabei in längeren Durchlaufzeiten, einem volatileren Systemverhalten und höheren Wahrscheinlichkeiten von Systemblockaden. Um die genannten Effekte an Zusammenführungen zu eliminieren, stellt die Arbeit eine neue Vorfahrtstrategie HAFI – Highest Autocorrelated First vor. Diese priorisiert die Ankunftsprozesse anhand deren Autokorrelation. Konkret wird die Vorfahrt zunächst so lange nach dem Prinzip First Come First Served gewährt, bis richtungsweise eine spezifische Warteschlangenlänge überschritten wird. Der jeweilige Wert ergibt sich aus der Höhe der Autokorrelation der Ankunftsprozesse. Vorfahrt bekommt der Strom mit der höchsten Überschreitung seines Grenzwertes. Die Arbeit stellt ferner eine Heuristik DyDeT zur automatischen Bestimmung und dynamischen Anpassung der Grenzwerte vor. Mit einer Simulationsstudie wird gezeigt, dass HAFI mit Anwendung von DyDeT die Vorzüge der etablierten Vorfahrtstrategien First Come First Served und Longest Queue First vereint. Dabei wird auch deutlich, dass die zwei letztgenannten Strategien den besonderen Herausforderungen autokorrelierter Ankunftsprozesse nicht gerecht werden. Bei einer Anwendung von HAFI zur Vorfahrtsteuerung können Durchlaufzeiten und Warteschlangenlängen auf dem Niveau von First Come First Served erreicht werden, wobei dieses ca. 10% unter dem von Longest Queue First liegt. Gleichzeitig ermöglicht HAFI, im Gegensatz zu First Come First Served, eine ähnlich gute Lastbalancierung wie Longest Queue First. Die Ergebnisse stellen sich robust gegenüber Änderungen der Auslastung sowie der Höhe der Autokorrelation dar. Gleichzeitig sind die Erkenntnisse unabhängig der Analyse einer isolierten Zusammenführung und der Anordnung mehrerer Zusammenführungen in einem Netzwerk.:1 Einleitung 1 1.1 Motivation 1 1.2 Zielsetzung, wissenschaftlicher Beitrag 4 1.3 Konzeption 5 2 Grundlagen 7 2.1 Automatisierung, Steuern, Regeln 7 2.2 System, Modell 10 2.3 Stochastik, Statistik 14 2.3.1 Wahrscheinlichkeitsverteilungen 14 2.3.2 Zufallszahlengeneratoren 21 2.3.3 Autokorrelation als Ähnlichkeits- bzw. Abhängigkeitsmaß 24 2.4 Simulation 29 2.5 Warteschlangentheorie und -modelle 32 2.6 Materialflusssystem 35 2.7 Materialflusssteuerung 37 2.7.1 Steuerungssysteme 37 2.7.2 Steuerungsstrategien 40 2.8 Materialflusssystem charakterisierende Kennzahlen 46 3 Stand der Forschung und Technik 51 3.1 Erzeugung autokorrelierter Zufallszahlen 51 3.1.1 Autoregressive Prozesse nach der Box-Jenkins-Methode 52 3.1.2 Distorsions-Methoden 54 3.1.3 Copulae 56 3.1.4 Markovian Arrival Processes 58 3.1.5 Autoregressive Prozesse mit beliebiger Randverteilung 61 3.1.6 Weitere Verfahren 64 3.1.7 Bewertung der Verfahren und Werkzeuge zur Generierung 65 3.2 Wirken von Autokorrelation in Bediensystemen 68 3.3 Fallstudien über Autokorrelation in logistischen Systemen 75 3.4 Ursachen von Autokorrelation in logistischen Systemen 89 3.5 Steuerung von Ankunftsprozessen an Zusammenführungen 96 3.6 Steuerung autokorrelierter Ankunftsprozesse 100 4 Steuerung autokorrelierter Ankunftsprozesse an Zusammenführungen 105 4.1 Modellannahmen, Methodenauswahl, Vorbetrachtungen 106 4.2 First Come First Served und Longest Queue First 114 4.3 Highest Autocorrelated First 117 4.3.1 Grundprinzip 117 4.3.2 Bestimmung der Grenzwerte 127 4.3.3 Dynamische Bestimmung der Grenzwerte mittels „DyDeT“ 133 4.4 Highest Autocorrelated First in Netzwerken 150 4.5 Abschließende Bewertung und Diskussion 161 5 Zusammenfassung und Ausblick 167 Primärliteratur 172 Normen und Standards 194 Abbildungsverzeichnis 197 Tabellenverzeichnis 199 Pseudocodeverzeichnis 201 Abkürzungsverzeichnis 203 Symbolverzeichnis 205 Erklärung an Eides statt 209The work at hand presents a novel strategy to control arrival processes at merges. The main fields of application are intralogistics transport systems. Nevertheless, the findings can be adapted to any queuing system. In contrast to further research and development the thesis assumes autocorrelated arrival processes. Up until now, arrivals are usually assumed to be uncorrelated and there are no special treatments for autocorrelated arrivals in the context of merge controlling. However, surveys show with high reliability the existence of autocorrelated arrivals, resulting in some major impacts on the systems\' performance. In detail, 68 real-world datasets of different companies have been tested in the scope of this work, and in 95% of the cases arrival processes significantly show autocorrelations. Furthermore, the research shows that autocorrelation comes from the system itself. As a direct consequence it was observed that there were longer cycle times, more volatile system behavior, and a higher likelihood of deadlocks. In order to eliminate these effects at merges, this thesis introduces a new priority rule called HAFI-Highest Autocorrelated First. It assesses the arrivals\' priority in accordance to their autocorrelation. More concretely, priority initially is given in accordance to the First Come First Served scheme as long as specific direction-wise queue lengths are not exceeded. The particular thresholds are determined by the arrival processes\' autocorrelation, wherein the process with the highest volume gets priority. Furthermore, the thesis introduces a heuristic to automatically and dynamically determine the specific thresholds of HAFI-so called DyDeT. With a simulation study it can be shown that HAFI in connection with DyDeT, combines the advantages of the well-established priority rules First Come First Served and Longest Queue First. It also becomes obvious that the latter ones are not able to deal with the challenges of autocorrelated arrival processes. By applying HAFI cycling times and mean queue lengths on the level of First Come First Served can be achieved. These are about 10% lower than for Longest Queue First. Concomitantly and in contrast to First Come First Served, HAFI also shows well balanced queues like Longest Queue First. The results are robust against different levels of throughput and autocorrelation, respectively. Furthermore, the findings are independent from analyzing a single instance of a merge or several merges in a network.:1 Einleitung 1 1.1 Motivation 1 1.2 Zielsetzung, wissenschaftlicher Beitrag 4 1.3 Konzeption 5 2 Grundlagen 7 2.1 Automatisierung, Steuern, Regeln 7 2.2 System, Modell 10 2.3 Stochastik, Statistik 14 2.3.1 Wahrscheinlichkeitsverteilungen 14 2.3.2 Zufallszahlengeneratoren 21 2.3.3 Autokorrelation als Ähnlichkeits- bzw. Abhängigkeitsmaß 24 2.4 Simulation 29 2.5 Warteschlangentheorie und -modelle 32 2.6 Materialflusssystem 35 2.7 Materialflusssteuerung 37 2.7.1 Steuerungssysteme 37 2.7.2 Steuerungsstrategien 40 2.8 Materialflusssystem charakterisierende Kennzahlen 46 3 Stand der Forschung und Technik 51 3.1 Erzeugung autokorrelierter Zufallszahlen 51 3.1.1 Autoregressive Prozesse nach der Box-Jenkins-Methode 52 3.1.2 Distorsions-Methoden 54 3.1.3 Copulae 56 3.1.4 Markovian Arrival Processes 58 3.1.5 Autoregressive Prozesse mit beliebiger Randverteilung 61 3.1.6 Weitere Verfahren 64 3.1.7 Bewertung der Verfahren und Werkzeuge zur Generierung 65 3.2 Wirken von Autokorrelation in Bediensystemen 68 3.3 Fallstudien über Autokorrelation in logistischen Systemen 75 3.4 Ursachen von Autokorrelation in logistischen Systemen 89 3.5 Steuerung von Ankunftsprozessen an Zusammenführungen 96 3.6 Steuerung autokorrelierter Ankunftsprozesse 100 4 Steuerung autokorrelierter Ankunftsprozesse an Zusammenführungen 105 4.1 Modellannahmen, Methodenauswahl, Vorbetrachtungen 106 4.2 First Come First Served und Longest Queue First 114 4.3 Highest Autocorrelated First 117 4.3.1 Grundprinzip 117 4.3.2 Bestimmung der Grenzwerte 127 4.3.3 Dynamische Bestimmung der Grenzwerte mittels „DyDeT“ 133 4.4 Highest Autocorrelated First in Netzwerken 150 4.5 Abschließende Bewertung und Diskussion 161 5 Zusammenfassung und Ausblick 167 Primärliteratur 172 Normen und Standards 194 Abbildungsverzeichnis 197 Tabellenverzeichnis 199 Pseudocodeverzeichnis 201 Abkürzungsverzeichnis 203 Symbolverzeichnis 205 Erklärung an Eides statt 20

SLA Calculus

For modeling Service-Oriented Architectures (SOAs) and validating worst-case performance guarantees a deterministic modeling method with efficient analysis is presented. Upper and lower bounds for delay and workload in systems are used to describe performance contracts. The SLA Calculus allows one to combine model descriptions for single systems and to derive bounds for reaction time and capacity of composed systems with analytic means. The intended, but not exclusive modeling domain for SLA Calculus are distributed software systems with reaction time constraints. SOAs are a system design paradigm that encapsulate software functions in service applications. Due to their standardized interfaces and accessibility via networks, large systems can be composed from smaller services and presented as services again. A well-known implementation of the service paradigm are Web Services that allow applications with components connected by the Internet. Own services and those rented from providers can be transparently combined by users. Performance guarantees for SOAs gain importance with more complex systems and applications in business environments When a service is rented by a customer the provider agrees upon a Service Level Agreement (SLA) with conditions concerning interface, pricing and performance. Service reaction time in form of delay is an important part in many SLAs and subject to performance models discussed in this work. With SLAs providers implicate a maximum delay for their products when the customer limits the workload to their systems. Hence customers expect the contracted service provider to deliver the performance figures unless the workload exceeds the SLA. Since contract penalties could apply, providers have a natural interest in dimensioning their service in regard to the SLA. Even for maximum workloads specified in the contracts the worst-case delay has to hold. Moreover, due to the compositional nature of Web Services, customers become providers themselves when they offer their service compositions to others. Again, worst-case performance bounds are of major interest here. Analyzing models of SOAs is an option to plan, dimension and validate service performance. For system modeling and analysis many methods exist. Queueing Systems and simulation are two well-known approaches in computer science. They provide average and thus long-term performance numbers quite easily using, probabilistic workload and service process descriptions. Deriving system behavior in worst-case situations for performance guarantees is elaborative and can be impossible for more complex systems. Receiving delay bounds usable in SLAs for SOAs by model analysis is still a research issue. A promising candidate to model SOA with SLAs is Network Calculus, an analytical method to derive performance bounds for network components. Given deterministic descriptions for arrival to and service in a network node hard bounds for network delay and the required buffer memory in routers are computed. A fine-granular separation between short- and long-term goals is possible. Network Calculus models also feature composition of elements and fast analytical analysis. When applied to SOAs with SLAs the problem arises that SLAs are not suitable as a system description and information source for Network Calculus models. Especially the internal service capacity is not exposed by SLAs, since providers consider them as a business secret. Without service process descriptions Network Calculus models cannot be analyzed. The SLA Calculus is presented as a solution to this problem. As a novel contribution for deterministic model analysis for SOAs, SLA Calculus is an extension to Network Calculus. Instead of service process descriptions, it uses information on latency to characterize a system. Delay of services is not a scalar analysis result anymore, it becomes a process over time that is bound with Network Calculus-style curves, the delay curves. Together with arrival curves the performance contracts in SLAs are formalized by so-called SLA Delay Properties (SDPs) as a description for the service performance in worst-case. Service composition can be modeled by serial and parallel combination of SDPs. The necessary theorems for the resulting worst-case bounds are given and proved. We will present a method to transfer these performance figures to the missing service process description again. Apart from basic theory we will also consider solutions for practical modeling situations. An algorithm to extract arrival and delay curves from measurements, enables the modeler to include already existing systems without given SLAs as model elements. Finally, we will sketch a selection method in form of an optimization problem for services to support the dynamic service selection in SOAs with a Service Broker. SLA Calculus model analysis will deliver deterministic upper and lower bounds for workload capacities and response times. For upper bounds the worst-case is assumed, thus bounds are pessimistic. The advantage of SLA Calculus is the ability to compute these bounds very fast and to give system modelers a quick overview on system characteristics considering extreme situations. In other modeling methods a lengthy transient analysis would be required. The strict perspective towards worst-case brought up another analysis target: Until now, relatively little attention was paid to contract conformance between subsequent services within service compositions. When services offer different workload capacities the arrival rate to the system needs to be adjusted to avoid bottlenecks. Additionally, for service compositions no response time contract can be guaranteed without internal buffering to enforce a common arrival rate. SLA Calculus unveils the necessary buffer delays and is able to bound them

Journal of Telecommunications and Information Technology, 2014, nr 4

kwartalni