Summary: Math. Proc. Camb. Phil. Soc. (2008), 145, 471 c 2008 Cambridge Philosophical Society
doi:10.1017/S0305004108001242 Printed in the United Kingdom
First published online 29 April 2008
Spatial transportation networks with transfer costs:
asymptotic optimality of hub-and-spoke models
BY DAVID J. ALDOUS
Department of Statistics, 367 Evans Hall # 3860, U.C. Berkeley, CA 94720, U.S.A.
(Received 23 February 2007; revised 1 September 2007)
Consider networks on n vertices at average density 1 per unit area. We seek a network that
minimizes total length subject to some constraint on journey times, averaged over source-
destination pairs. Suppose journey times depend on both route-length and number of hops.
Then for the constraint corresponding to an average of 3 hops, the length of the optimal net-
work scales as n13/10
. Alternatively, constraining the average number of hops to be 2 forces
the network length to grow slightly faster than order n3/2
. Finally, if we require the network