Information Freshness in Service Queues With Strategic Customers

We examine a scenario in which a service provider updates its queue length information to customers at a specific frequency. Customers decide whether to join the queue based on the most recent update. Our objective is to determine the optimal updating frequency that benefits both the service provider and customers. Using a two-dimensional continuous-time Markov process, we model the actual and announced queue length processes. By proving the identical distributions of these two processes under a Poisson updating scheme, we derive closed-form solutions for customers’ utility functions. Our findings demonstrate that customers adopt a generalized mixed-threshold strategy at equilibrium, and their certainty about whether to join the queue or balk does not always increase with fresher information. Furthermore, we reveal that due to customers’ different sensitivities to information freshness, system performance metrics such as throughput and total customer utility exhibit non-monotonic behavior in response to the updating frequency. Consequently, providing fresher information does not necessarily lead to improved system performance. To address this, we propose algorithms to determine the optimal updating frequency for each system performance metric and identify the conditions under which different updating frequencies are optimal. We demonstrate that any positive updating frequency can achieve customer utility no worse than the no-information system. Additionally, in systems with high customer arrival rates, updating with a positive updating frequency can improve throughput. Furthermore, we prove conditions under which a positive and finite updating frequency can yield higher throughput and total customer utility compared to real-time information systems.