The hex-cell is one of the interconnection networks used for parallel systems. The main idea of the hex-cell is that there are hexagon cells that construct the network;each one of those cells has six nodes. The perfor...The hex-cell is one of the interconnection networks used for parallel systems. The main idea of the hex-cell is that there are hexagon cells that construct the network;each one of those cells has six nodes. The performance of the network is affected by many factors one of the factors as load balancing. Until the moment of writing of this paper, there is no load balancing algorithm for this network. The proposed algorithm for dynamic load balancing on hex-cell is based on Tree Walking Algorithm (TWA) for load balancing on tree interconnection network and the ring all to all broadcast.展开更多
The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Xr. We introduce and study theoscillations of the walk:where ...The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Xr. We introduce and study theoscillations of the walk:where Φ(n) is an increasing sequence of positive numbers. We prove that for each $ belonging to a certain class of sequences of different orders, there are ξ 's depending on Φ such that 0 < OSCΦ(ξ) <∞. Exact Hausdorff dimension of the set of such ξ's is calculated. An application is given to study the local variation of Brownian motion. A general limsup deviation problem on trees is also studied.展开更多
文摘The hex-cell is one of the interconnection networks used for parallel systems. The main idea of the hex-cell is that there are hexagon cells that construct the network;each one of those cells has six nodes. The performance of the network is affected by many factors one of the factors as load balancing. Until the moment of writing of this paper, there is no load balancing algorithm for this network. The proposed algorithm for dynamic load balancing on hex-cell is based on Tree Walking Algorithm (TWA) for load balancing on tree interconnection network and the ring all to all broadcast.
文摘The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Xr. We introduce and study theoscillations of the walk:where Φ(n) is an increasing sequence of positive numbers. We prove that for each $ belonging to a certain class of sequences of different orders, there are ξ 's depending on Φ such that 0 < OSCΦ(ξ) <∞. Exact Hausdorff dimension of the set of such ξ's is calculated. An application is given to study the local variation of Brownian motion. A general limsup deviation problem on trees is also studied.
