The challenge of stabilizing control for queueing systems with unobservable server states

We address the problem of stabilizing control for complex queueing systems where servers follow unobservable Markovian environments. The controller needs to assign servers to queues without full information about the servers´ states. A control challenge is to devise a policy that matches servers to queues in a way that takes state estimates into account and updates these estimates in the best way possible. Maximally attainable stability regions are non-trivial. We present the model, the control problem, and some preliminary methods for analysis and control. We illustrate basic phenomena and then focus on the simplest possible model having a single queue, a fixed state server, and a two state server. For this case, we begin analysis of a partially observable Markov decision process (POMDP) hinting at some structural properties. We also show how to use a quasi-birth-death (QBD) process for analysis and control.