Benefits of Using Imperfect Information in Controlling an M/M/1 Queueing System

In this paper, we analyze an M / M / 1 queueing system where there are incentive conflicts among customers. Self-interested customers' decisions whether to join the system or not may not necessarily induce a socially optimal congestion level. As a way to alleviate the over-congestion, toll imposition was used in Naor's paper [3]. Instead of using a toll mechanism, we study the usefulness of imperfect information on system state (queue size, for example) as a way to reduce the over-congestion by self-interested customers. The main conclusion of this paper is that by purposefully giving fuzzy or imperfect information on the current queue size we can improve the congestion in the system. This result might look contradictory to rough intuition since perfect information should give better performance than imperfect information. We show how this idea is verified. In deriving this result, we use the concept of Nash equilibrium (pure and mixed strategy) as introduced in game theory. In some real situations, using imperfect information is easier to apply than imposing a toll, and thus the result of this paper has practical implications.