Closed-Form and Boundary Expressions for Task-Success Probability in Status-Driven Systems

Status-driven task offloading appears in many systems such as vehicular coordination, UAV control, and compute-first networking, where an user-side node (or access point, AP) forwards user tasks based on periodically received server status. Whether a task ultimately succeeds depends not only on the freshness of this information, but also on server-side blocking and the random status-link and task-link delays that separate the forwarding decision from the task’s actual arrival at the server. Despite its practical relevance, the effect of these factors on the task-success probability has not been rigorously analyzed. This paper develops a unified analytical framework for quantifying the task-success probability in a multi-threaded status-driven system. By characterizing the state-dependent AP forwarding rule through its stationary long-run forwarding probability and representing all delays via their Laplace transforms, we obtain a closed-form expression for the success probability along with analytical upper and lower bounds. These expressions jointly capture resource blocking, information staleness, and bidirectional link delays in a tractable way. Experiments show that the theory and bounds closely match empirical success rates, with errors within 1.0% (upper bound) and 1.6% (lower bound).