Queue-Aware ISAC Power Allocation Under Imperfect CSI: Integer-Service Analysis and Anchored Lyapunov Look-Ahead

We study power allocation for a multiuser integrated sensing and communication (ISAC) downlink with bursty queues and imperfect channel state information (CSI). Starting from a long-run utility–backlog objective, we derive its common task reward and online score. Integer departures are represented by threshold events of indefinite Gaussian quadratic forms, accounting for estimation error in both signal and interference. Their moments give the conditional one-slot task reward and characterize the error of an efficient plug-in score. An anchored quadratic Lyapunov look-ahead corrects its reward-greedy action with a bounded nominal loss. Across five CSI-error levels, the rule reduces mean queue exceedance by 27.4–43.9% (0.49–0.99 percentage points) relative to the plug-in maximizer, with mean reward loss below 0.01 per slot. The rule achieves higher reward and lower exceedance than DPP, SAC and PPO; its advantage over freshly retrained learning baselines extends to five configurations with 9–23 power-allocation variables using fixed candidate budgets. For the seven-variable system, a fused implementation reproduces all 25 confirmation trajectories and achieves a one-core p99 decision time of 0.274–0.311,ms.