 
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
471
Spatial transportation networks with transfer costs:
asymptotic optimality of hubandspoke models
BY DAVID J. ALDOUS
Department of Statistics, 367 Evans Hall # 3860, U.C. Berkeley, CA 94720, U.S.A.
email: aldous@stat.berkeley.edu
www.stat.berkeley.edu/users/aldous
(Received 23 February 2007; revised 1 September 2007)
Abstract
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 routelength 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
