Model-parallel inference over dynamic edge systems requires scheduling decisions that account for not only instantaneous resources but also future resource contention and reliable service commitments. Existing edge-inference designs, however, predominantly optimize performance metrics based on current or short-term system states, without explicitly coupling current assignments with future commitment fulfillment. To address this issue, we propose PROMISE, a predictive rolling-horizon framework for commitment-aware model-parallel inference under spatio-temporal edge dynamics. PROMISE jointly models stochastic task generation, mobility-induced communication variations, privacy-aware model partitioning, and load-dependent edge computing capability. We introduce committed completion time (CCT) as an endogenous service decision and formulate joint SD--ES mapping and CCT determination to balance commitment fulfillment and service reward. To address cross-timeslot coupling, PROMISE estimates future task arrivals and computational workloads over an adaptive horizon and embeds them into certainty-equivalent ES-state rollout. A progress-aware surrogate then evaluates feasible current-stage mappings, while the corresponding CCTs are analytically recovered from predicted completion times. Only the first-stage decisions are committed, and the optimization is repeated with newly observed states in a receding-horizon manner. Numerical experiments demonstrate robust scheduling performance under diverse system scales and workload dynamics, while Raspberry-Pi-based experiments validate the practical feasibility and key system characteristics of model-parallel edge inference.

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