  Motivated by health care systems with repeated services that have both
personnel (nurse and physician) and space (beds) constraints, we study a
restricted version of the Erlang-R model. The space restriction policies we
consider are blocking or holding in a pre-entrant queue. We develop many-server
approximations for the system performance measures when either policy applies,
and explore the connection between them. We show that capacity allocation of
both resources should be determined simultaneously, and derive the methodology
to determine it explicitly. We show that the system dynamics is captured by the
fraction of needy time in the network, and that returning customers should be
accounted for both in steady-state and time-varying conditions. We demonstrate
the application of our policies in two case studies of resource allocation in
hospitals.
