Perfect simulation, monotonicity and finite queueing networks

International audienceTutorial on perfect sampling with applications to queueing network

Perfect simulation, monotonicity and finite queueing networks

International audienceTutorial on perfect sampling with applications to queueing network

Application Layer Feedback-based SIP Server Overload Control

A SIP server may be overloaded by emergency-induced call volume, "American Idol" style flash crowd effects or denial of service attacks. The SIP server overload problem is interesting especially because the costs of serving or rejecting a SIP session can be similar. For this reason, the built-in SIP overload control mechanism based on generating rejection messages cannot prevent the server from entering congestion collapse under heavy load. The SIP overload problem calls for a pushback control solution in which the potentially overloaded receiving server may notify its upstream sending servers to have them send only the amount of load within the receiving server's processing capacity. The pushback framework can be achieved by either a rate-based feedback or a window-based feedback. The centerpiece of the feedback mechanism is the algorithm used to generate load regulation information. We propose three new window-based feedback algorithms and evaluate them together with two existing rate-based feedback algorithms. We compare the different algorithms in terms of the number of tuning parameters and performance under both steady and variable load. Furthermore, we identify two categories of fairness requirements for SIP overload control, namely, user-centric and provider-centric fairness. With the introduction of a new double-feed SIP overload control architecture, we show how the algorithms meet those fairness criteria

Perfect sampling of Jackson Queueing Networks

We consider open Jackson networks with losses with mixed finite and infinite queues and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain may have an infinite state space. The main idea is to use a Jackson network with infinite buffers (that has a product form stationary distribution) to bound the number of initial conditions to be considered in the coupling from the past scheme. We also provide bounds on the sampling time of this new perfect sampling algorithm for acyclic or hyperstable networks. These bounds show that the new algorithm is considerably more efficient than existing perfect samplers even in the case where all queues are finite. We illustrate this efficiency through numerical experiments. We also extend our approach to non-monotone networks such as queueing networks with negative customers.On considère les réseaux de Jackson avec perte comportant des files finies et infinies, et l'on s'intéresse à l'efficacité des techniques d'échantillonnage de leur distribution stationnaire exacte. Nous démontrons que la simulation parfaite est possible même si la chaîne de Markov sous-jacente a un espace d'états potentiellement infini. L'idée principale est d'utiliser un réseau de Jackson aux files infinies (qui admet une distribution de forme-produit) pour borner les conditions initiales à considérer dans l'algorithme de simulation parfaite. Nous donnons également des bornes sur le temps d'échantillonnage de ce nouvel algorithme dans le cas des réseaux acycliques, ainsi que pour des réseaux hyperstables. Ces bornes prouvent que le nouvel algorithme est considérablement plus efficace que les échantillonneurs parfaits acuels, même dans le cas où toutes les files sont finies. Nous illustrons cette efficacité par des expériences numériques. Enfin, nous généralisons notre approche au cas des réseaux non-monotones comme les réseaux aux clients négatifs

Perfect sampling of Jackson Queueing Networks

We consider open Jackson networks with losses with mixed finite and infinite queues and analyze the efficiency of sampling from their exact stationary distribution. We show that perfect sampling is possible, although the underlying Markov chain may have an infinite state space. The main idea is to use a Jackson network with infinite buffers (that has a product form stationary distribution) to bound the number of initial conditions to be considered in the coupling from the past scheme. We also provide bounds on the sampling time of this new perfect sampling algorithm for acyclic or hyperstable networks. These bounds show that the new algorithm is considerably more efficient than existing perfect samplers even in the case where all queues are finite. We illustrate this efficiency through numerical experiments. We also extend our approach to non-monotone networks such as queueing networks with negative customers.On considère les réseaux de Jackson avec perte comportant des files finies et infinies, et l'on s'intéresse à l'efficacité des techniques d'échantillonnage de leur distribution stationnaire exacte. Nous démontrons que la simulation parfaite est possible même si la chaîne de Markov sous-jacente a un espace d'états potentiellement infini. L'idée principale est d'utiliser un réseau de Jackson aux files infinies (qui admet une distribution de forme-produit) pour borner les conditions initiales à considérer dans l'algorithme de simulation parfaite. Nous donnons également des bornes sur le temps d'échantillonnage de ce nouvel algorithme dans le cas des réseaux acycliques, ainsi que pour des réseaux hyperstables. Ces bornes prouvent que le nouvel algorithme est considérablement plus efficace que les échantillonneurs parfaits acuels, même dans le cas où toutes les files sont finies. Nous illustrons cette efficacité par des expériences numériques. Enfin, nous généralisons notre approche au cas des réseaux non-monotones comme les réseaux aux clients négatifs

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"

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

Modeling a healthcare system as a queueing network:The case of a Belgian hospital.

The performance of health care systems in terms of patient flow times and utilization of critical resources can be assessed through queueing and simulation models. We model the orthopaedic department of the Middelheim hospital (Antwerpen, Belgium) focusing on the impact of outages (preemptive and nonpreemptive outages) on the effective utilization of resources and on the flowtime of patients. Several queueing network solution procedures are developed such as the decomposition and Brownian motion approaches. Simulation is used as a validation tool. We present new approaches to model outages. The model offers a valuable tool to study the trade-off between the capacity structure, sources of variability and patient flow times.Belgium; Brownian motion; Capacity management; Decomposition; Health care; Healthcare; Impact; Model; Models; Performance; Performance measurement; Queueing; Queueing theory; Simulation; Stochastic processes; Structure; Studies; Systems; Time; Tool; Validation; Variability;

Online Modeling and Tuning of Parallel Stream Processing Systems

Writing performant computer programs is hard. Code for high performance applications is profiled, tweaked, and re-factored for months specifically for the hardware for which it is to run. Consumer application code doesn\u27t get the benefit of endless massaging that benefits high performance code, even though heterogeneous processor environments are beginning to resemble those in more performance oriented arenas. This thesis offers a path to performant, parallel code (through stream processing) which is tuned online and automatically adapts to the environment it is given. This approach has the potential to reduce the tuning costs associated with high performance code and brings the benefit of performance tuning to consumer applications where otherwise it would be cost prohibitive. This thesis introduces a stream processing library and multiple techniques to enable its online modeling and tuning. Stream processing (also termed data-flow programming) is a compute paradigm that views an application as a set of logical kernels connected via communications links or streams. Stream processing is increasingly used by computational-x and x-informatics fields (e.g., biology, astrophysics) where the focus is on safe and fast parallelization of specific big-data applications. A major advantage of stream processing is that it enables parallelization without necessitating manual end-user management of non-deterministic behavior often characteristic of more traditional parallel processing methods. Many big-data and high performance applications involve high throughput processing, necessitating usage of many parallel compute kernels on several compute cores. Optimizing the orchestration of kernels has been the focus of much theoretical and empirical modeling work. Purely theoretical parallel programming models can fail when the assumptions implicit within the model are mis-matched with reality (i.e., the model is incorrectly applied). Often it is unclear if the assumptions are actually being met, even when verified under controlled conditions. Full empirical optimization solves this problem by extensively searching the range of likely configurations under native operating conditions. This, however, is expensive in both time and energy. For large, massively parallel systems, even deciding which modeling paradigm to use is often prohibitively expensive and unfortunately transient (with workload and hardware). In an ideal world, a parallel run-time will re-optimize an application continuously to match its environment, with little additional overhead. This work presents methods aimed at doing just that through low overhead instrumentation, modeling, and optimization. Online optimization provides a good trade-off between static optimization and online heuristics. To enable online optimization, modeling decisions must be fast and relatively accurate. Online modeling and optimization of a stream processing system first requires the existence of a stream processing framework that is amenable to the intended type of dynamic manipulation. To fill this void, we developed the RaftLib C++ template library, which enables usage of the stream processing paradigm for C++ applications (it is the run-time which is the basis of almost all the work within this dissertation). An application topology is specified by the user, however almost everything else is optimizable by the run-time. RaftLib takes advantage of the knowledge gained during the design of several prior streaming languages (notably Auto-Pipe). The resultant framework enables online migration of tasks, auto-parallelization, online buffer-reallocation, and other useful dynamic behaviors that were not available in many previous stream processing systems. Several benchmark applications have been designed to assess the performance gains through our approaches and compare performance to other leading stream processing frameworks. Information is essential to any modeling task, to that end a low-overhead instrumentation framework has been developed which is both dynamic and adaptive. Discovering a fast and relatively optimal configuration for a stream processing application often necessitates solving for buffer sizes within a finite capacity queueing network. We show that a generalized gain/loss network flow model can bootstrap the process under certain conditions. Any modeling effort, requires that a model be selected; often a highly manual task, involving many expensive operations. This dissertation demonstrates that machine learning methods (such as a support vector machine) can successfully select models at run-time for a streaming application. The full set of approaches are incorporated into the open source RaftLib framework