  This paper considers a Markovian model for the optimal dynamic routing of
homogeneous traffic to parallel heterogeneous queues, each having its own
finite input buffer and server pool, where buffer and server-pool sizes, as
well as service rates, may differ across queues. The main goal is to identify a
heuristic index-based routing policy with low complexity that consistently
attains a nearly minimum average loss rate (or, equivalently, maximum
throughput rate). A second goal is to compare alternative policies, with
respect to computational demands and empirical performance. A novel routing
policy that can be efficiently computed is developed based on a second-order
extension to Whittle's restless bandit (RB) index, since the latter is constant
for this model. New results are also given for the more computationally
demanding index policy obtained via policy improvement (PI), including that it
reduces to shortest queue routing under symmetric buffer and server-pool sizes.
A numerical study shows that the proposed RB index policy is nearly optimal
across the instances considered, and substantially outperforms several
previously proposed index policies.
