Congestion management in traffic-light intersections via Infinitesimal Perturbation Analysis

We present a flow-control technique in traffic-light intersections, aiming at regulating queue lengths to given reference setpoints. The technique is based on multivariable integrators with adaptive gains, computed at each control cycle by assessing the IPA gradients of the plant functions. Moreover, the IPA gradients are computable on-line despite the absence of detailed models of the traffic flows. The technique is applied to a two-intersection system where it exhibits robustness with respect to modeling uncertainties and computing errors, thereby permitting us to simplify the on-line computations perhaps at the expense of accuracy while achieving the desired tracking. We compare, by simulation, the performance of a centralized, joint two-intersection control with distributed control of each intersection separately, and show similar performance of the two control schemes for a range of parameters

Performance analysis of networks on chips

Modules on a chip (such as processors and memories) are traditionally connected through a single link, called a bus. As chips become more complex and the number of modules on a chip increases, this connection method becomes inefficient because the bus can only be used by one module at a time. Networks on chips are an emerging technology for the connection of on-chip modules. In networks on chips, switches are used to transmit data from one module to another, which entails that multiple links can be used simultaneously so that communication is more efficient. Switches consist of a number of input ports to which data arrives and output ports from which data leaves. If data at multiple input ports has to be transmitted to the same output port, only one input port may actually transmit its data, which may lead to congestion. Queueing theory deals with the analysis of congestion phenomena caused by competition for service facilities with scarce resources. Such phenomena occur, for example, in traffic intersections, manufacturing systems, and communication networks like networks on chips. These congestion phenomena are typically analysed using stochastic models, which capture the uncertain and unpredictable nature of processes leading to congestion (such as irregular car arrivals to a traffic intersection). Stochastic models are useful tools for the analysis of networks on chips as well, due to the complexity of data traffic on these networks. In this thesis, we therefore study queueing models aimed at networks on chips. The thesis is centred around two key models: A model of a switch in isolation, the so-called single-switch model, and a model of a network of switches where all traffic has the same destination, the so-called network of polling stations. For both models we are interested in the throughput (the amount of data transmitted per time unit) and the mean delay (the time it takes data to travel across the network). Single-switch models are often studied under the assumption that the number of ports tends to infinity and that traffic is uniform (i.e., on average equally many packets arrive to all buffers, and all possible destinations are equally likely). In networks on chips, however, the number of buffers is typically small. We introduce a new approximation specifically aimed at small switches with (memoryless) Bernoulli arrivals. We show that, for such switches, this approximation is more accurate than currently known approximations. As traffic in networks on chips is usually non-uniform, we also extend our approximation to non-uniform switches. The key difference between uniform and nonuniform switches is that in non-uniform switches, all queues have a different maximum throughput. We obtain a very accurate approximation of this throughput, which allows us to extend the mean delay approximation. The extended approximation is derived for Bernoulli arrivals and correlated arrival processes. Its accuracy is verified through a comparison with simulation results. The second key model is that of concentrating tree networks of polling stations (polling stations are essentially switches where all traffic has the same output port as destination). Single polling stations have been studied extensively in literature, but only few attempts have been made to analyse networks of polling stations. We establish a reduction theorem that states that networks of polling stations can be reduced to single polling stations while preserving some information on mean waiting times. This reduction theorem holds under the assumption that the last node of the network uses a so-called HoL-based service discipline, which means that the choice to transmit data from a certain buffer may only depend on which buffers are empty, but not on the amount of data in the buffers. The reduction theorem is a key tool for the analysis of networks of polling stations. In addition to this, mean waiting times in single polling stations have to be calculated, either exactly or approximately. To this end, known results can be used, but we also devise a new single-station approximation that can be used for a large subclass of HoL-based service disciplines. Finally, networks on chips typically implement flow control, which is a mechanism that limits the amount of data in the network from one source. We analyse the division of throughput over several sources in a network of polling stations with flow control. Our results indicate that the throughput in such a network is determined by an interaction between buffer sizes, flow control limits, and service disciplines. This interaction is studied in more detail by means of a numerical analysis

Some topics in web performance analysis

This thesis consists of four papers on web performance analysis. In the first paper we investigate the performance of overload control through queue length for two different web server architectures. The simulation result suggests that the benefit of request prioritization is noticeable only when the capacities of the sub-systems match each other. In the second paper we present an M/G/1/K*PS queueing model of a web server. We obtain closed form expressions for web server performance metrics such as average response time, throughput and blocking probability. The model is validated through real measurements. The third paper studies a queueing system with a load balancer and a pool of identical FCFS queues in parallel. By taking the number of servers to infinite, we show that the average waiting time for the system is not always minimized by routing each customer to the expected shortest queue when the information used for decision is stale. In the last paper we consider the problem of admission control to an M/M/1 queue under periodic observations with average cost criterion. The problem is formulated as a discrete time Markov decision process whose states are fully observable. A proof of the existence of the average optimal policy by the vanishing discounted approach is provided. We also show that the optimal policy is nonincreasing with respect to the observed number of customers in the system

Performance analysis of error recovery and congestion control in high-speed networks

In the past few years, Broadband Integrated Services Digital Network (B-ISDN) has received increasing attention as a communication architecture capable of supporting multimedia applications. Among the techniques proposed to implement B-ISDN, Asynchronous Transfer Mode (ATM) is considered to be the most promising transfer technique because of its efficiency and flexibility.In ATM networks, the performance bottleneck of the network, which was once the channel transmission speed, is shifted to the processing speed at the network switching nodes and the propagation delay of the channel. This shift is because the high-speed channel increases the ratio of processing time to packet transmission time and also the ratio of propagation delay to packet transmission time. The increased processing overhead makes it difficult to implement hop-by-hop schemes, which may impose prohibitably high processing at each switching node. The increased propagation delay overhead makes traffic control in ATM a challenge since a large number of packets can be in transit between two ATM switching nodes. Because of these fundamental changes, control schemes developed for traditional networks may not perform efficiently, and thus, new network architectures (congestion control schemes, error control schemes, etc.) are required in ATM networks.In this dissertation, we first present an extensive survey of various traffic control schemes and network protocols for ATM networks. In this survey, possible traffic control schemes are examined, and problems of those schemes and their possible solutions are presented. Next, we investigate two key research issues in ATM networks (and other types of high-speed networks): the effects of protocol-processing overhead and the efficiency of traffic control schemes.We first investigate the effects of protocol-processing overhead on the performance of error recovery schemes. Specifically, we investigate the performance trade-offs between link-by-link and edge-to-edge error recovery schemes. Our results show that for a network with high-speed/low-error-rate channels, an edge-to-edge scheme gives a smaller delay than a link-by-link scheme. We then investigate the effectiveness of a priority packet discarding scheme, a congestion control mechanism suitable for high-speed networks. We derive loss probabilities for each stream and investigate the impact of burstiness of traffic streams on the performance of individual streams

Numerical analysis of stochastic biochemical reaction networks

Numerical solution of the chemical master equation for stochastic reaction networks typically suffers from the state space explosion problem due to the curse of dimensionality and from stiffness due to multiple time scales. The dimension of the state space equals the number of molecular species involved in the reaction network and the size of the system of differential equations equals the number of states in the corresponding continuous-time Markov chain, which is usually enormously huge and often even infinite. Thus, efficient numerical solution approaches must be able to handle huge, possibly infinite and stiff systems of differential equations efficiently. In this thesis, we present efficient techniques for the numerical analysis of the biochemical reaction networks. We present an approximate numerical integration approach that combines a dynamical state space truncation procedure with efficient numerical integration schemes for systems of ordinary differential equations including adaptive step size selection based on local error estimates. We combine our dynamical state space truncation with the method of conditional moments, and present the implementation details and numerical results. We also incorporate ideas from importance sampling simulations into a non-simulative numerical method that approximates transient rare event probabilities based on a dynamical truncation of the state space. Finally, we present a maximum likelihood method for the estimation of the model parameters given noisy time series measurements of molecular counts. All approaches presented in this thesis are implemented as part of the tool STAR, which allows to model and simulate the biochemical reaction networks. The efficiency and accuracy is demonstrated by numerical examples.Numerische Lösungen der chemischen Master-Gleichung für stochastische Reaktionsnetzwerke leiden typischerweise an dem Zustandsraumexplosionsproblem aufgrund der hohen Dimensionalität und der Steifigkeit durch mehrfache Zeitskalen. Die Dimension des Zustandsraumes entspricht der Anzahl der molekularen Spezies von dem Reaktionsnetzwerk und die Größe des Systems von Differentialgleichungen entspricht der Anzahl der Zustände in der entsprechenden kontinuierlichen Markov-Kette, die in der Regel enorm gross und oft sogar unendlich gross ist. Daher müssen numerische Methoden in der Lage sein, riesige, eventuell unendlich grosse und steife Systeme von Differentialgleichungen effizient lösen zu können. In dieser Arbeit beschreiben wir effiziente Methoden für die numerische Analyse biochemischer Reaktionsnetzwerke. Wir betrachten einen inexakten numerischen Integrationsansatz, bei dem eine dynamische Zustandsraumbeschneidung und ein Verfahren mit einem effizienten numerischen Integrationsschema für Systeme von gewöhnlichen Differentialgleichungen benutzt werden. Wir kombinieren unsere dynamische Zustandsraumbeschneidungsmethode mit der Methode der bedingten Momente und beschreiben die Implementierungdetails und numerischen Ergebnisse. Wir benutzen auch Ideen des importance sampling für eine nicht-simulative numerische Methode, die basierend auf der Zustandsraumbeschneidung die Wahrscheinlichkeiten von seltenen Ereignissen berechnen kann. Schließlich beschreiben wir eine Maximum-Likelihood-Methode für die Schätzung der Modellparameter bei verrauschten Zeitreihenmessungen von molekularen Anzahlen. Alle in dieser Arbeit beschriebenen Ansätze sind in dem Software-Tool STAR implementiert, das erlaubt, biochemische Reaktionsnetzwerke zu modellieren und zu simulieren. Die Effizienz und die Genauigkeit werden durch numerische Beispiele gezeigt

Applications of stochastic modeling in air traffic management:Methods, challenges and opportunities for solving air traffic problems under uncertainty

In this paper we provide a wide-ranging review of the literature on stochastic modeling applications within aviation, with a particular focus on problems involving demand and capacity management and the mitigation of air traffic congestion. From an operations research perspective, the main techniques of interest include analytical queueing theory, stochastic optimal control, robust optimization and stochastic integer programming. Applications of these techniques include the prediction of operational delays at airports, pre-tactical control of aircraft departure times, dynamic control and allocation of scarce airport resources and various others. We provide a critical review of recent developments in the literature and identify promising research opportunities for stochastic modelers within air traffic management

Delay Performance and Cybersecurity of Smart Grid Infrastructure

To address major challenges to conventional electric grids (e.g., generation diversification and optimal deployment of expensive assets), full visibility and pervasive control over utilities\u27 assets and services are being realized through the integratio

Operational research and simulation methods for autonomous ride-sourcing

Ride-sourcing platforms provide on-demand shared transport services by solving decision problems related to ride-matching and pricing. The anticipated commercialisation of autonomous vehicles could transform these platforms to fleet operators and broaden their decision-making by introducing problems such as fleet sizing and empty vehicle redistribution. These problems have been frequently represented in research using aggregated mathematical programs, and alternative practises such as agent-based models. In this context, this study is set at the intersection between operational research and simulation methods to solve the multitude of autonomous ride-sourcing problems. The study begins by providing a framework for building bespoke agent-based models for ride-sourcing fleets, derived from the principles of agent-based modelling theory, which is used to tackle the non-linear problem of minimum fleet size. The minimum fleet size problem is tackled by investigating the relationship of system parameters based on queuing theory principles and by deriving and validating a novel model for pickup wait times. Simulating the fleet function in different urban areas shows that ride-sourcing fleets operate queues with zero assignment times above the critical fleet size. The results also highlight that pickup wait times have a pivotal role in estimating the minimum fleet size in ride-sourcing operations, with agent-based modelling being a more reliable estimation method. The focus is then shifted to empty vehicle redistribution, where the omission of market structure and underlying customer acumen, compromises the effectiveness of existing models. As a solution, the vehicle redistribution problem is formulated as a non-linear convex minimum cost flow problem that accounts for the relationship of supply and demand of rides by assuming a customer discrete choice model and a market structure. An edge splitting algorithm is then introduced to solve a transformed convex minimum cost flow problem for vehicle redistribution. Results of simulated tests show that the redistribution algorithm can significantly decrease wait times and increase profits with a moderate increase in vehicle mileage. The study is concluded by considering the operational time-horizon decision problems of ride-matching and pricing at periods of peak travel demand. Combinatorial double auctions have been identified as a suitable alternative to surge pricing in research, as they maximise social welfare by relying on stated customer and driver valuations. However, a shortcoming of current models is the exclusion of trip detour effects in pricing estimates. The study formulates a shared-ride assignment and pricing algorithm using combinatorial double auctions to resolve the above problem. The model is reduced to the maximum weighted independent set problem, which is APX-hard. Therefore, a fast local search heuristic is proposed, producing solutions within 10\% of the exact approach for practical implementations.Open Acces

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