Efficient Ignorance: Information Heterogeneity in a Queue

Abstract

How would the growing prevalence of real-time delay information have an impact on a service system? We consider a single-server queueing system where customers arrive according to a Poisson process and service takes an exponential time. There are two streams of customers, one informed about real-time delay and one uninformed. We characterize the equilibrium behavior of customers who may balk in such a system and investigate how a larger fraction of informed customers affects the system performance measures, i.e., throughput and social welfare. We show that the impacts of growing information prevalence on system performance measures are determined by the equilibrium joining behavior of uninformed customers. Perhaps surprisingly, we find that throughput and social welfare can be unimodal in the fraction of informed customers. In other words, some amount of information heterogeneity in the population can lead to strictly more efficient outcomes, in terms of the system throughput or social welfare, than information homogeneity. For example, under a very mild condition, throughput of a system with offered load being 1 will always suffer if there are more than 58% of informed customers in the population. Moreover, it is shown that for an overloaded system with offered load sufficiently higher than 1, social welfare always reaches its maximum when some fraction of customers are uninformed of the congestion in real time.