Maximum likelihood estimation of closed queueing network demands from queue length data

We propose maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent stations. Our ML estimators are expressed in implicit form and require only to compute mean queue lengths and marginal queue length probabilities from an empirical dataset. Further, in the load-independent case, we provide an explicit approximate formula for the ML estimator together with confidence intervals

Maximum Likelihood Estimation of Closed Queueing Network Demands from Queue Length Data

Resource demand estimation is essential for the application of analyical models, such as queueing networks, to real-world systems. In this paper, we investigate maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent service times. Stemming from a characterization of necessary conditions for ML estimation, we propose new estimators that infer demands from queue-length measurements, which are inexpensive metrics to collect in real systems. One advantage of focusing on queue-length data compared to response times or utilizations is that confidence intervals can be rigorously derived from the equilibrium distribution of the queueing network model. Our estimators and their confidence intervals are validated against simulation and real system measurements for a multi-tier application

Maximum Likelihood Estimation of Closed Queueing Network Demands from Queue Length Data

Resource demand estimation is essential for the application of analyical models, such as queueing networks, to real-world systems. In this paper, we investigate maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent service times. Stemming from a characterization of necessary conditions for ML estimation, we propose new estimators that infer demands from queue-length measurements, which are inexpensive metrics to collect in real systems. One advantage of focusing on queue-length data compared to response times or utilizations is that confidence intervals can be rigorously derived from the equilibrium distribution of the queueing network model. Our estimators and their confidence intervals are validated against simulation and real system measurements for a multi-tier application

QMLE: a methodology for statistical inference of service demands from queueing data

Estimating the demands placed by services on physical resources is an essential step for the definition of performance models. For example, scalability analysis relies on these parameters to predict queueing delays under increasing loads. In this paper, we investigate maximum likelihood (ML) estimators for demands at load-independent and load-dependent resources in systems with parallelism constraints. We define a likelihood function based on state measurements and derive necessary conditions for its maximization. We then obtain novel estimators that accurately and inexpensively obtain service demands using only aggregate state data. With our approach, and also thanks to approximation methods for computing marginal and joint distributions for the load-dependent case, confidence intervals can be rigorously derived, explicitly taking into account both topology and concurrency levels of the services. Our estimators and their confidence intervals are validated against simulations and real system measurements for two multi-tier applications, showing high accuracy also in the presence of load-dependent resources

Learning Queuing Networks by Recurrent Neural Networks

It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive performance models from data. We focus on queuing networks, and crucially exploit a deterministic approximation of their average dynamics in terms of a compact system of ordinary differential equations. We encode these equations into a recurrent neural network whose weights can be directly related to model parameters. This allows for an interpretable structure of the neural network, which can be trained from system measurements to yield a white-box parameterized model that can be used for prediction purposes such as what-if analyses and capacity planning. Using synthetic models as well as a real case study of a load-balancing system, we show the effectiveness of our technique in yielding models with high predictive power

JMT – Performance Engineering Tools for System Modeling

We present the Java Modelling Tools (JMT) suite, an integrated framework of Java tools for performance evaluation of computer systems using queueing models. The suite offers a rich user interface that simplifies the definition of performance models by means of wizard dialogs and of a graphical design workspace. The performance evaluation features of JMT span a wide range of state-of-the-art methodologies including discrete-event simulation, mean value analysis of product-form networks, analytical identification of bottleneck resources in multiclass environments, and workload characterization with fuzzy clustering. The discrete-event simulator supports several advanced modeling features such as finite capacity regions, load-dependent service times, bursty processes, fork-and-join nodes, and implements spectral estimation for analysis of simulative results. The suite is open-source, released under the GNU general public license (GPL), and it is available for free download at http://jmt.sourceforge.net

Estimating customer impatience in a service system with unobserved balking

This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. The main objective is to estimate the customers' patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual queue-length process only. The main complication, and distinguishing feature of our setup, lies in the fact that customers who decide not to join are not observed, but, remarkably, we manage to devise a procedure to estimate the load they would generate. We express our system in terms of a multi-server queue with a Poisson stream of customers, which allows us to evaluate the corresponding likelihood function. Estimating the unknown parameters relying on a maximum likelihood procedure, we prove strong consistency and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. The performance of our approach is further assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized-hyperexponential distributions our method provides a robust estimation framework for any continuous patience-level distribution

A Review of Traffic Signal Control.

The aim of this paper is to provide a starting point for the future research within the SERC sponsored project "Gating and Traffic Control: The Application of State Space Control Theory". It will provide an introduction to State Space Control Theory, State Space applications in transportation in general, an in-depth review of congestion control (specifically traffic signal control in congested situations), a review of theoretical works, a review of existing systems and will conclude with recommendations for the research to be undertaken within this project