On the Design of a Shared Waiting Room

Abstract

We investigate the design of a waiting area of a service system where different types of customers seek different services, provided by designated servers. We examine two waiting room designs: The designated waiting room, where each server has its own designated waiting area, and the shared waiting room, where all customers are waiting together. In the designated waiting room design, customers observe the number of customers waiting for each service, whereas in the shared waiting room, customers cannot distinguish which service the other customers are waiting for, but can still observe the total number of customers in the waiting room and make a joining/balking decision accordingly. Assuming two types of customers that have similar characteristics seeking service from two different servers, we show that all customers adopt an identical pure equilibrium threshold. We find the shared waiting room design achieves higher throughput than the designated waiting room design when the congestion rate is low. However, the designated waiting room is always preferable in terms of social welfare. Furthermore, we extend our analysis to the asymmetric case, where types differ from each other in terms of arrival rate, service reward, per unit-time waiting cost, and service duration. Finding the equilibrium strategies in these cases is more challenging and requires an iterative process. We show that mixed equilibrium thresholds can emerge, and that the designated waiting room does not always improve system performance, even when considering social welfare.