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We present a geometric interpretation of a product form stationary distribution for a d-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The d-dimensional SRBM data can be equivalently specified by d + 1 geometric objects: an ellipse and d rays. Using these geometric objects, we establish necessary and sufficient conditions for characterizing product form stationary distribution. The key idea in the characterization is that we decompose the d-dimensional problem to 1 2 d(d − 1) two-dimensional SRBMs, each of which is determined by an ellipse and two rays. This characterization contrasts with the algebraic condition of Harrison and Williams [14]. A d-station tandem queue example is presented to illustrate how the product form can be obtained using our characterization. Drawing the two-dimensional results in [1,7], we discuss potential optimal paths for a variational problem associated with the three-station tandem queue. Except Appendix D, the rest of this paper is almost identical to the QUESTA paper with the same title. R d + . Its data consists of a (nondegenerate) d × d covariance matrix Σ, a drift vector µ ∈ R d

We present a reconfigurable cluster-on-chip architecture and supporting parallel programming software library based on the well-known Message Passing Interface (MPI) standard. The intent is to allow designers to program multi-core reconfigurable systems on chip using the same or similar methodologies that yielded tremendous productivity improvements in the workstation and HPC cluster community. Additionally the architecture is designed to support native hardware processing modules to participate in the MPI network as fully-fledged peers.