# Flow control as a stochastic control problem with incomplete information

##
Boris Miller

### Institute for Information Transmission Problems

### Résumé:

The nonlinear stochastic control problem related with the Internet
flow control is considered. The state of the link is described by
hidden Markov process while the loss flow is described by the
counting process with the intensity depending on the current
transmission rate and unobserved link state. The control is
the transmission rate that has to be chosen as non-anticipating
process depending on the observation of the loss process.
The aim of the control is to maximize some performance criterion
characterizing the quantity of successively transmitted infromation
and losses. We state the problem with incomplete information where
the flow intensity plays a dual role. On one hand it of course has
an impact on transmission rate and on the other hand provokes the
arrival of the information about the link state via the loss process.
It is a new manifestation of the incompelete infromation stochastic
control problem which admits a reduction to the stochastic control
problem with complete observations and sometimes even to a
deterministic control problem. We overview various statements
of this problem that could be interesting in the context of modelling
and optimization of the IP wired and wireless networks and provide
a more detail analysis of one particular setting.