  Polling systems with losses are useful mathematical objects that can model
many practical systems like travelling salesman problem with recurrent
requests. One of the less studied yet an important aspect in such systems is
the disparity in the utilities derived by the individual stations. Further, the
random fluctuations of the travel conditions can have significant impact on the
performance. This calls for a scheduler that caters to the fairness aspect,
depends upon the travel conditions and the dynamic system state.
  Inspired by the generalized alpha-fair schedulers of wireless networks, we
propose a family of schedulers that further considers binary knowledge of the
travel conditions. These schedulers are opportunistic, allocate the server to a
station with bad travel condition only when the station has accumulated too
little a utility by the decision epoch. We illustrate that the disparities
among the individual utilities diminish to zero, as fairness factor increases,
and further that the price of fairness decreases as the number of stations
increase.
