The efficient antenna scheduling strategy for data relay satellites (DRSs) is essential to optimize the throughput or delay of the satellite data relay network.However,these two objectives conflict with each other since the user satellites (USs) with higher priorities take up more transmission time of DRSs' antennas for greater throughput but the USs storing more packets cause a severer waiting delay to the whole network.To balance the conflicting metrics for meeting the delay-throughput integrated requirements,we formulate the antenna scheduling as a stochastic non-convex fractional programming,which is challenging to be solved.For the tractability,we equivalently transform the fractional programming to a parametric problem and implement the Lyapunov drift to guarantee the constraint of mean rate stability.By proposing a delay and throughput tradeoff based antenna scheduling algorithm,we further transform the parametric problem to a solvable weight matching problem.Simulation results reveal the feasible region of the preference control parameter for integrated QoS cases and its variation relationship with network delay and throughput.