Feedback Increases the Capacity of Queues with Bounded Service Times
K. R. Sahasranand, Aslan Tchamkerten
TL;DR
The paper proves that full feedback increases the capacity of FIFO queues whenever the service time has bounded support, by introducing a generalized feedback framework that interpolates between weak and full feedback. It shows a monotone relationship in the generalized feedback parameter and derives a strict separation between full and weak feedback capacities for bounded service times in both discrete and continuous time, while proving equality for unbounded service times. The approach combines convex/variational analysis, operator theory, and discrete/continuous-time arguments to establish when the generalized feedback yields strictly higher capacity and when the bounds collapse. The results resolve longstanding questions in timing channels, provide structural insight into when feedback helps, and highlight open problems for unbounded service times. Practically, the findings clarify the design of feedback mechanisms in timing-based communication systems and their impact on achievable rates under bounded versus unbounded service-time distributions.
Abstract
In the "Bits Through Queues" paper, it was hypothesized that full feedback always increases the capacity of first-in-first-out queues, except when the service time distribution is memoryless. More recently, a non-explicit sufficient condition under which feedback increases capacity was provided, along with simple examples of service times meeting this condition. While this condition yields examples where feedback is beneficial, it does not offer explicit structural properties of such service times. In this paper, we show that full feedback increases capacity whenever the service time has bounded support. This is achieved by investigating a generalized notion of feedback, with full feedback and weak feedback as particular cases.