  We consider a polling system with two queues, exhaustive service, no
switch-over times and exponential service times. The waiting cost depends on
the position of the queue relative to the server: It costs a customer c per
time unit to wait in the busy queue (where the server is) and d per time unit
in the idle queue (where no server is). Customers arrive according to a Poisson
process. We study the control problem of how arrivals should be routed to the
two queues in order to minimize expected waiting costs and characterize
individually and socially optimal routing policies under three scenarios of
available information at decision epochs: no, partial and complete information.
In the complete information case, we develop a new iterative algorithm to
determine individually optimal policies, and show that such policies can be
described by a switching curve. We conjecture that a linear switching curve is
socially optimal, and prove that this policy is indeed optimal for the fluid
version of the two-queue polling system.
