A Stochastic Service Network Model with Application to Hospital Facilities

This paper presents a methodology for estimating expected utilization and service level for a class of capacity constrained service network facilities operating in a stochastic environment. A semi-Markov process describes the flows of customers (patients) through a network of service units. We model the case where one of the units has finite capacity and no queues are allowed to form. We show that the expected level of utilization and service can be computed from a simple linear relationship based on (a) the equilibrium arrival rates at each unit which are associated with the case of infinite capacity, (b) mean holding times for each unit, and (c) the probability that the finite capacity unit is at full capacity. We use Erlang's loss formula to calculate the probability of full capacity, show this calculation to be exact for two cases, and recommend its use as an approximation in the general case. We test the accuracy of the approximation on a set of published data. In the discussion, we present a technique for analyzing collected patient flow data using the results of this methodology.