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

The restricted Erlang-R Queue: Finite-size effects in service systems with returning customers