  In the current work, we consider diversion of childbirth patients who arrive
seeking emergency admission to public primary health centers (PHCs). PHCs are
the first point of contact for an Indian patient with formal medical care, and
offer medical care on an outpatient basis, and limited inpatient and childbirth
care. In this context, real-time prediction of the wait time of the arriving
patient becomes important in order to determine whether the patient must be
diverted to another PHC or not. We study this problem using a discrete event
simulation that we develop of medical care operations in two PHCs in India. We
approximate the labour room service at each PHC as an M/G/1 queueing system and
show how the accuracy of real-time delay predictors impacts the extent of the
change in operational outcomes at each PHC. We simulate patient diversion using
actual delays as well as the delay estimates generated by various delay
predictors based on the state of the system such as queue-length, elapsed
service time, and observed delay histories. The simulation of the diversion
process also incorporates travel time between the PHCs. We also propose a new
delay predictor that incorporates information regarding the system state as
well as the service time distribution. We compare the operational outcomes at
both PHCs without diversion and with diversion using the above delay
predictors. We show numerically that more accurate delay predictors lead to
more equitable distribution of resources involved in provision of childbirth
care across both PHCs.
