Efficient Ignorance: Information Heterogeneity in a Queue

Abstract

How would the growing prevalence of real-time delay information affect a service system? We consider a single-server queueing system where customers arrive according to a Poisson process and the service time follows an exponential distribution. There are two streams of customers, one informed about real-time delay and the other uninformed. The customers' uninformed behavior may be due to information ignorance or rational behavior in the presence of an information fee. We characterize the equilibrium behavior of customers with information heterogeneity and investigate how the presence of a larger fraction of informed customers affects the system performance measures, i.e., throughput and social welfare. We show that the effects 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 in a system with an offered load of 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.

Keywords: Service Operations; Queueing System; Information Heterogeneity; Non-Monotonic Behavior