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A time-slotted queueing system for a wireless downlink with multiple flows and a single server is considered, with exogenous arrivals and time-varying channels. It is assumed that only one user can be serviced in a single time slot. Unlike much recent work on this problem, attention is drawn to the case where the server can obtain only partial information about the instantaneous state of the channel. In each time slot, the server is allowed to specify a single subset of flows from a collection of observable subsets, observe the current service rates for that subset, and subsequently pick a user to serve. The stability region for such a system is provided. An online scheduling algorithm is presented that uses information about marginal distributions to pick the subset and the Max-Weight rule to pick a flow within the subset, and which is provably throughput-optimal. In the case where the observable subsets are all disjoint, or where the subsets and channel statistics are symmetric, it is shown that a simple scheduling algorithm-Max-Sum-Queue-that essentially picks subsets having the largest squared-sum of queues, followed by picking a user using Max-Weight within the subset, is throughput-optimal.