  Motivated by time-sensitive e-service applications, we consider the design of
effective policies in a Markovian model for the dynamic control of both
admission and routing of a single class of real-time transactions to multiple
heterogeneous clusters of web servers, each having its own queue and server
pool. Transactions come with response-time deadlines, staying until completion
if the latter are missed. Per job rejection and deadline-miss penalties are
incurred. Since computing an optimal policy is intractable, we aim to design
near optimal heuristic policies that are tractable for large-scale systems.
Four policies are developed: the static optimal Bernoulli-splitting (BS)
policy, and three index policies, based respectively on individually optimal
(IO) actions, one-step policy improvement (PI), and restless bandit (RB)
indexation. A computational study demonstrates that PI is the best of such
policies, being consistently near optimal. In the pure-routing case, both the
PI and RB policies are nearly optimal.
