  We consider assignment policies that allocate resources to users, where both
resources and users are located on a one-dimensional line. First, we consider
unidirectional assignment policies that allocate resources only to users
located to their left. We propose the Move to Right (MTR) policy, which scans
from left to right assigning nearest rightmost available resource to a user,
and contrast it to the Unidirectional Gale-Shapley (UGS) matching policy. While
both policies among all unidirectional policies, minimize the expected distance
traveled by a request (request distance), MTR is fairer. Moreover, we show that
when user and resource locations are modeled by statistical point processes,
and resources are allowed to satisfy more than one user, the spatial system
under unidirectional policies can be mapped into bulk service queueing systems,
thus allowing the application of many queueing theory results that yield closed
form expressions. As we consider a case where different resources can satisfy
different numbers of users, we also generate new results for bulk service
queues. We also consider bidirectional policies where there are no directional
restrictions on resource allocation and develop an algorithm for computing the
optimal assignment which is more efficient than known algorithms in the
literature when there are more resources than users. Numerical evaluation of
performance of unidirectional and bidirectional allocation schemes yields
design guidelines beneficial for resource placement. \np{Finally, we present a
heuristic algorithm, which leverages the optimal dynamic programming scheme for
one-dimensional inputs to obtain approximate solutions to the optimal
assignment problem for the two-dimensional scenario and empirically yields
request distances within a constant factor of the optimal solution.
