THE EFFICIENCY OF GREEDY ROUTING IN HYPERCUBES AND BUTTERFLIES

STAMOULIS, GD; TSITSIKLIS, JN

dc.contributor.author	STAMOULIS, GD	en
dc.contributor.author	TSITSIKLIS, JN	en
dc.date.accessioned	2014-03-01T01:43:01Z
dc.date.available	2014-03-01T01:43:01Z
dc.date.issued	1994	en
dc.identifier.issn	0090-6778	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/24002
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.classification	Telecommunications	en
dc.subject.other	COMMUNICATION	en
dc.title	THE EFFICIENCY OF GREEDY ROUTING IN HYPERCUBES AND BUTTERFLIES	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1994	en
heal.abstract	We analyze the following problem: Each node of the d-dimensional hypercube independently generates packets according to a Poisson process with rate lambda. 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 p(k)(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 rho < 1, where rho=(def)lambda p 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 less than or equal to dp/1-rho, thus showing that an average delay of Theta(d) is attainable for any fixed rho < 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 queueing network.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE TRANSACTIONS ON COMMUNICATIONS	en
dc.identifier.isi	ISI:A1994PQ82000019	en
dc.identifier.volume	42	en
dc.identifier.issue	11	en
dc.identifier.spage	3051	en
dc.identifier.epage	3061	en