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<p>The authors analyze the problem in which each node of the binary hypercubeindependently generates packets according to a Poisson process with rate lambda ; eachof the packets is to be broadcast to all other nodes. Assuming unit packet length and noother communications taking place, it is observed that the system can be stable insteady-state only if the load factor rho identical to lambda (2/sup d/-1)/d satisfies rho>1 where d is the dimensionality (diameter) of the hypercube. Moreover, the authorsestablish some lower bounds for the steady-state average delay D per packet and deviseand analyze two distributed routing schemes that are efficient in the sense that stabilityis maintained for all rho > rho * where rho * does not depend on the dimensionality d ofthe network, while the average delay D per packet satisfies D>or=Kd(1+ rho ) for smallvalues of rho (with constant K). The performance evaluation is rigorous for one scheme,while for the other the authors resort to approximations and simulations.</p>
Index Termsrouting schemes; multiple broadcasts; hypercubes; packets; Poisson process; unit packetlength; dimensionality; lower bounds; average delay; distributed routing; performanceevaluation; approximations; simulations; hypercube networks; performance evaluation;queueing theory

G. Stamoulis and J. Tsitsiklis, "Efficient Routing Schemes for Multiple Broadcasts in Hypercubes," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 725-739, 1993.
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