Abstract
We analyze the following problem: Each node of the d-dimensional hypercube independently generates packets according to a Poisson process with rate A. Each of the packets is to be sent to a randomly chosen destination; each of the nodes at Hamming distance k from a packet's origin is assigned an a priori probability pk (1 _p)d- k. Packets are routed under a simple greedy scheme: each of them is forced to cross the hypercube dimensions required in increasing index-order, with possible queueing at the hypercube nodes. Assuming unit packet length and no other communications taking place, we show that this scheme is stable (in steady-state) if p < 1, where pde Ap is the load factor of the network; this is seen to be the broadest possible range for stability. Furthermore, we prove that the average delay T per packet satisfies T < AdE p , thus showing that an average delay of O(d) is attainable for any fixed p < 1. We also establish similar results in the context of the butterfly network. Our analysis is based on a stochastic comparison with a product-form network.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.