Observability and reconstructibility of hidden Markov models: Implications for control and network congestion control

This paper addresses the observability and reconstructibility of the hidden Markov model. A rank condition for observability of the time-invariant hidden Markov model is proven. This condition is reminiscent of deterministic linear systems theory. Additionally, the externally controlled case is studied by way of simulations of a hidden Markov model which represents a computer network with sources running Transmission Control Protocol (TCP). This permits the comparison of congestion control methods based on their quantified reconstructibility properties. Simulation results elucidate the dual purpose of the control signal, which simultaneously regulates the system while ensuring persistent reconstructibility.