  We study a multiclass M/M/1 queueing control problem with finite buffers
under heavy-traffic where the decision maker is uncertain about the rates of
arrivals and service of the system and by scheduling and admission/rejection
decisions acts to minimize a discounted cost that accounts for the uncertainty.
The main result is the asymptotic optimality of a $c\mu$-type of policy derived
via underlying stochastic differential games studied in [16]. Under this
policy, with high probability, rejections are not performed when the workload
lies below some cut-off that depends on the ambiguity level. When the workload
exceeds this cut-off, rejections are carried out and only from the buffer with
the cheapest rejection cost weighted with the mean service rate in some
reference model. The allocation part of the policy is the same for all the
ambiguity levels. This is the first work to address a heavy-traffic queueing
control problem with model uncertainty.
