Efficient Heuristics for the Simulation of Buffer Overflow in Series and Parallel Queueing Networks

Many of recent studies have proved the tail equivalence result for Egalitarian Processor Sharing system: [EQUATION], where B (resp. V) is service requirement (resp. sojourn time) of a customer; for PS, g = 1 - ρ. In this paper, we consider time-shared systems in which the server capacity is shared by existing customers in proportion to (dynamic) weights assigned to customers. We consider two systems, 1) in which the weight of a customer depends on it Age (attained service), and 2) in which the weight depends on the residual processing time (RPT). We allow for a parameterized family of weight functions such that the weight associated with a customer that has received a service (or, has a RPT) of x units is ω(x) = xα for some -∞ < α < ∞. We then study the sojourn time of a customer under such scheduling discipline and provide conditions on α for tail equivalence to hold true, and also give the value of g as a function of α

Proof-Pattern Recognition and Lemma Discovery in ACL2

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it

Generative models versus underlying symmetries to explain biological pattern

Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative models confirm the plausibility of an explanation and make testable hypotheses for further experiments. However, studies rarely consider the broad family of alternative models that match the same observed pattern. The symmetries that define the broad class of matching models are in fact the only aspects of information truly revealed by observed pattern. Commonly observed patterns derive from simple underlying symmetries. This article illustrates the problem by showing the symmetry associated with the observed rate of increase in fitness in a constant environment. That underlying symmetry reveals how each particular generative model defines a single example within the broad class of matching models. Further progress on the relation between pattern and process requires deeper consideration of the underlying symmetries

Condensation in stochastic particle systems with stationary product measures

We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the context of the equivalence of ensembles, providing a general characterization of the condensation transition for homogeneous and inhomogeneous systems in the thermodynamic limit. This leads to strengthened results on weak convergence for subcritical systems, and establishes the equivalence of ensembles for spatially inhomogeneous systems under very general conditions, extending previous results which were focused on attractive and finite systems. We use relative entropy techniques which provide simple proofs, making use of general versions of local limit theorems for independent random variables.Comment: 44 pages, 4 figures; improved figures and corrected typographical error