Queue length as an implicit communication channel

We attempt to bridge queuing theory and information theory by considering queue lengths as communication channels conveying information about system parameters. A toy problem is proposed and an information-theoretic lower bound is derived on the queue-length/cost tradeoff which matches (in an order sense) the performance of back-pressure algorithms. The proof is based on the idea of “communication simulation,” which gives a “reduction” that uses a queuing system with a certain performance to simulate a communication system with the corresponding performance. The result suggests that there is a fundamental performance penalty to following the minimalist aesthetic of avoiding explicit protocol information.