Is it Worth the Wait? Service Choice and Externalities When Waiting is Expensive

We study how rational customers choose between two congested service facilities with finite buffer space and unknown service value when waiting is expensive. Customers observe an imperfect private signal indicating which service facility may provide more service value, as well as the queue lengths at the service facilities before making their choice. If more customers choose the same service facility because of their private information, longer queues will form at the service facility and therefore a long queue may be an indication of higher quality. On the other hand, a long queue also implies more waiting time to obtain the service. We characterize the equilibrium queue-joining behavior of arriving customers in the presence of such positive and negative externalities. We find that when the waiting costs are positive, it might be rational for customers to join the longer queue, even if the private information suggests joining the shorter queue. How the information is distributed among customers, and the buffer sizes play key roles in determining the customer choice behavior: In markets in which all of the customers have the same signal strength, there has to be enough waiting space available allowing for variability in queue length observations to make customers infer high service value from long queues. However, in markets in which customers have different signal strengths, the less informed customers join the longest queue even when there is not much variability in the queue lengths due to limited waiting space. The customers join the longer queue when the arrival rates are low as then the queue length information is the least contaminated by the spillovers due to capacity constraints. Finally, we find that depending on the arrival rate and waiting costs, these externalities provide strong incentives to both service facilities or to either the high-quality or the low-quality service facility to co-locate physically or virtually