  A problem of much current practical interest is the replacement of the wiring
infrastructure connecting approximately 200 sensor and actuator nodes in
automobiles by an access point. This is motivated by the considerable savings
in automobile weight, simplification of manufacturability, and future
upgradability.
  A key issue is how to schedule the nodes on the shared access point so as to
provide regular packet delivery. In this and other similar applications, the
mean of the inter-delivery times of packets, i.e., throughput, is not
sufficient to guarantee service-regularity. The time-averaged variance of the
inter-delivery times of packets is also an important metric.
  So motivated, we consider a wireless network where an Access Point schedules
real-time generated packets to nodes over a fading wireless channel. We are
interested in designing simple policies which achieve optimal mean-variance
tradeoff in interdelivery times of packets by minimizing the sum of
time-averaged means and variances over all clients. Our goal is to explore the
full range of the Pareto frontier of all weighted linear combinations of mean
and variance so that one can fully exploit the design possibilities. We
transform this problem into a Markov decision process and show that the problem
of choosing which node's packet to transmit in each slot can be formulated as a
bandit problem. We establish that this problem is indexable and explicitly
derive the Whittle indices. The resulting Index policy is optimal in certain
cases. We also provide upper and lower bounds on the cost for any policy.
Extensive simulations show that Index policies perform better than previously
proposed policies.
