Response time distribution in a tandem pair of queues with batch processing

Response time density is obtained in a tandem pair of Markovian queues with both batch arrivals and batch departures. The method uses conditional forward and reversed node sojourn times and derives the Laplace transform of the response time probability density function in the case that batch sizes are finite. The result is derived by a generating function method that takes into account that the path is not overtake-free in the sense that the tagged task being tracked is affected by later arrivals at the second queue. A novel aspect of the method is that a vector of generating functions is solved for, rather than a single scalar-valued function, which requires investigation of the singularities of a certain matrix. A recurrence formula is derived to obtain arbitrary moments of response time by differentiation of the Laplace transform at the origin, and these can be computed rapidly by iteration. Numerical results for the first four moments of response time are displayed for some sample networks that have product-form solutions for their equilibrium queue length probabilities, along with the densities themselves by numerical inversion of the Laplace transform. Corresponding approximations are also obtained for (non-product-form) pairs of “raw” batch-queues – with no special arrivals – and validated against regenerative simulation, which indicates good accuracy. The methods are appropriate for modeling bursty internet and cloud traffic and a possible role in energy-saving is considered

Promoting clean technologies under imperfect competition

energy-saving technological progress, vintage capital, market imperfections, natural monopoly, investment subsidies

Bounds for Markov Decision Processes

We consider the problem of producing lower bounds on the optimal cost-to-go function of a Markov decision problem. We present two approaches to this problem: one based on the methodology of approximate linear programming (ALP) and another based on the so-called martingale duality approach. We show that these two approaches are intimately connected. Exploring this connection leads us to the problem of finding "optimal" martingale penalties within the martingale duality approach which we dub the pathwise optimization (PO) problem. We show interesting cases where the PO problem admits a tractable solution and establish that these solutions produce tighter approximations than the ALP approach. © 2013 The Institute of Electrical and Electronics Engineers, Inc

Inference via low-dimensional couplings

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map---e.g., representing and evaluating it---grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization---to the non-Gaussian case---of the square-root Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure

Queueing models for cable access networks

abstract in thesi

Augmenting Bottom-Up Metamodels with Predicates

Metamodeling refers to modeling a model. There are two metamodeling approaches for ABMs: (1) top-down and (2) bottom-up. The top down approach enables users to decompose high-level mental models into behaviors and interactions of agents. In contrast, the bottom-up approach constructs a relatively small, simple model that approximates the structure and outcomes of a dataset gathered fromthe runs of an ABM. The bottom-up metamodel makes behavior of the ABM comprehensible and exploratory analyses feasible. Formost users the construction of a bottom-up metamodel entails: (1) creating an experimental design, (2) running the simulation for all cases specified by the design, (3) collecting the inputs and output in a dataset and (4) applying first-order regression analysis to find a model that effectively estimates the output. Unfortunately, the sums of input variables employed by first-order regression analysis give the impression that one can compensate for one component of the system by improving some other component even if such substitution is inadequate or invalid. As a result the metamodel can be misleading. We address these deficiencies with an approach that: (1) automatically generates Boolean conditions that highlight when substitutions and tradeoffs among variables are valid and (2) augments the bottom-up metamodel with the conditions to improve validity and accuracy. We evaluate our approach using several established agent-based simulations

Finding the Right Tree: Topology Inference Despite Spatial Dependences

© 1963-2012 IEEE. Network tomographic techniques have almost exclusively been built on a strong assumption of mutual independence of link processes. We introduce model classes for link loss processes with non-Trivial spatial dependencies, for which the tree topology is nonetheless identifiable from leaf measurements using multicast probing. We show that these classes are large in a well-defined sense, and we provide an algorithm, SLTD, capable of returning the correct topology with certainty in the limit of infinite data