  We consider a slotted wireless network in an infrastructure setup with a base
station (or an access point) and N users. The wireless channel gain between the
base station and the users is assumed to be i.i.d., and the base station seeks
to schedule the user with the highest channel gain in every slot (opportunistic
scheduling). We assume that the identity of the user with the highest channel
gain is resolved using a series of contention slots and with feedback from the
base station. In this setup, we formulate the contention resolution problem for
opportunistic scheduling as identifying a random threshold (channel gain) that
separates the best channel from the other samples. We show that the average
delay to resolve contention is related to the entropy of the random threshold.
We illustrate our formulation by studying the opportunistic splitting algorithm
(OSA) for i.i.d. wireless channel [9]. We note that the thresholds of OSA
correspond to a maximal probability allocation scheme. We conjecture that
maximal probability allocation is an entropy minimizing strategy and a delay
minimizing strategy for i.i.d. wireless channel. Finally, we discuss the
applicability of this framework for few other network scenarios.
