In a recent paper [5] it was shown that under suitable conditions stationary distributions of the (scaled) queue lengths process for a generalized Jackson network converge to the stationary distribution of the associated reflected Brownian motion in the heavy traffic limit. The proof relied on certain exponential integrability assumptions on the primitives of the network. In this note we show that the above result holds under much weaker integrability conditions. We provide an alternative proof of this result making (in addition to natural heavy traffic and stability assumptions) only standard independence and square integrability assumptions on the network primitives that are commonly used in heavy traffic analysis. Furthermore, under additional integrability conditions we establish convergence of moments of stationary distributions.

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Motivated by the prevalence of high dimensional low sample size datasets in modern statistical applications, we propose a general nonparametric framework, Direction-Projection-Permutation (DiProPerm), for testing high dimensional hypotheses. The method is aimed at rigorous testing of whether lower dimensional visual differences are statistically significant. Theoretical analysis under the non-classical asymptotic regime of dimension going to infinity for fixed sample size reveals that certain natural variations of DiProPerm can have very different behaviors. An empirical power study both confirms the theoretical results and suggests DiProPerm is a powerful test in many settings. Finally DiProPerm is applied to a high dimensional gene expression dataset.

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For many years now, firms have managed their research and development (R&D) by applying various approaches drawn from the discipline of technology roadmapping (TRM). The underlying rationale of these roadmapping approaches is to align firms' product and technology developments with their business goals. By visually representing firms' technology strategy, roadmaps support intra‐firm communication and facilitate the coordination of strategic decisions and activities within the technology management domain. Most previously published research on TRMs has focused on the design and implementation of roadmapping processes; that is, relatively few empirical or quantitative studies describe the use and evaluation of roadmapping techniques. This paper seeks to address this gap by conducting a survey of 186 different R&D units within stock market‐listed companies in Korea that have implemented TRM. The paper attempts to identify the antecedent factors behind firms' successful use of roadmaps, further identifying correlations between these antecedent factors through an analysis of the R&D units. It also empirically highlights these antecedent factors by empirically analyzing and verifying correlations between roadmap utilization and R&D performance.

We consider critically loaded single class queueing networks with infinite buffers in which arrival and service rates are state (i.e., queue length) dependent and may be dynamically controlled. An optimal rate control problem for such networks with an ergodic cost criterion is studied. It is shown that the value function (i.e., optimum value of the cost) of the rate control problem for the network converges, under a suitable heavy traffic scaling limit, to that of an ergodic control problem for certain controlled reflected diffusions. Furthermore, we show that near optimal controls for limit diffusion models can be used to construct asymptotically near optimal rate control policies for the underlying physical queueing networks. The expected cost per unit time criterion studied here is given in terms of an unbounded holding cost and a linear control cost ("cost for effort"). Time asymptotics of a related uncontrolled model are studied as well. We establish convergence of invariant measures of scaled queue length processes to that of the limit reflecting diffusions. Our proofs rely on infinite time horizon stability estimates that are uniform in control and the heavy traffic parameter, for the scaled queue length processes. Another key ingredient, and a result of independent interest, in the proof of convergence of value functions is the existence of continuous near optimal feedback controls for the diffusion control model. AMS 2000 subject classifications: primary 93E20; secondary 60H30, 60J25, 60K25, 93E15.