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

Monotonicity-Preserving Bootstrapped Kriging Metamodels for Expensive Simulations

Kriging (Gaussian process, spatial correlation) metamodels approximate the Input/Output (I/O) functions implied by the underlying simulation models; such metamodels serve sensitivity analysis and optimization, especially for computationally expensive simulations. In practice, simulation analysts often know that the I/O function is monotonic. To obtain a Kriging metamodel that preserves this known shape, this article uses bootstrapping (or resampling). Parametric bootstrapping assuming normality may be used in deterministic simulation, but this article focuses on stochastic simulation (including discrete-event simulation) using distribution-free bootstrapping. In stochastic simulation, the analysts should simulate each input combination several times to obtain a more reliable average output per input combination. Nevertheless, this average still shows sampling variation, so the Kriging metamodel does not need to interpolate the average outputs. Bootstrapping provides a simple method for computing a noninterpolating Kriging model. This method may use standard Kriging software, such as the free Matlab toolbox called DACE. The method is illustrated through the M/M/1 simulation model with as outputs either the estimated mean or the estimated 90% quantile; both outputs are monotonic functions of the traffic rate, and have nonnormal distributions. The empirical results demonstrate that monotonicity-preserving bootstrapped Kriging may give higher probability of covering the true simulation output, without lengthening the confidence interval.Queues

Response Surface Methodology's Steepest Ascent and Step Size Revisited

Response Surface Methodology (RSM) searches for the input combination maximizing the output of a real system or its simulation.RSM is a heuristic that locally fits first-order polynomials, and estimates the corresponding steepest ascent (SA) paths.However, SA is scale-dependent; and its step size is selected intuitively.To tackle these two problems, this paper derives novel techniques combining mathematical statistics and mathematical programming.Technique 1 called 'adapted' SA (ASA) accounts for the covariances between the components of the estimated local gradient.ASA is scale-independent.The step-size problem is solved tentatively.Technique 2 does follow the SA direction, but with a step size inspired by ASA.Mathematical properties of the two techniques are derived and interpreted; numerical examples illustrate these properties.The search directions of the two techniques are explored in Monte Carlo experiments.These experiments show that - in general - ASA gives a better search direction than SA.response surface methodology

Some queueing models of airport delays

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1990.Includes bibliographical references.by Basil R. Horangic.M.S

Alternative methods of investigating the time dependent M/G/k queue

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.Microfiche copy available in Archives and Aero.Bibliograpy: leaf 154.by Peeter A. Kivestu.M.S

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

Studies of Uncertainties in Smart Grid: Wind Power Generation and Wide-Area Communication

This research work investigates the uncertainties in Smart Grid, with special focus on the uncertain wind power generation in wind energy conversion systems (WECSs) and the uncertain wide-area communication in wide-area measurement systems (WAMSs). For the uncertain wind power generation in WECSs, a new wind speed modeling method and an improved WECS control method are proposed, respectively. The modeling method considers the spatial and temporal distributions of wind speed disturbances and deploys a box uncertain set in wind speed models, which is more realistic for practicing engineers. The control method takes maximum power point tracking, wind speed forecasting, and wind turbine dynamics into account, and achieves a balance between power output maximization and operating cost minimization to further improve the overall efficiency of wind power generation. Specifically, through the proposed modeling and control methods, the wind power control problem is developed as a min-max optimal problem and efficiently solved with semi-definite programming. For the uncertain communication delay and communication loss (i.e. data loss) in WAMSs, the corresponding solutions are presented. First, the real-world communication delay is measured and analyzed, and the bounded modeling method for the communication delay is proposed for widearea applications and further applied for system-area and substation-area protection applications, respectively. The proposed bounded modeling method is expected to be an important tool in the planning, design, and operation of time-critical wide-area applications. Second, the real synchronization signal loss and synchrophasor data loss events are measured and analyzed. For the synchronization signal loss, the potential reasons and solutions are explored. For the synchrophasor data loss, a set of estimation methods are presented, including substitution, interpolation, and forecasting. The estimation methods aim to improve the accuracy and availability of WAMSs, and mitigate the effect of communication failure and data loss on wide-area applications