In a distributed real-time system, uneven task arrivals temporarily overload some nodesand leave others idle or underloaded. Consequently, some tasks may miss their deadlineseven if the overall system has the capacity to meet the deadlines of all tasks. Aneffective load-sharing (LS) scheme is proposed as a solution to this problem. Upon arrival of a task at a node, the node determines whether the node can complete the task in time under the minimum-laxity first-served policy. If the task cannot be guaranteed, or if guarantees of some other tasks are to be violated as a result of the addition of this taskto the existing schedule, the node looks up the list of loss-minimizing decisions anddetermines the best node among a set of nodes in its physical proximity, called its buddyset, to which the task(s) may be transferred. This list of decisions is periodically updatedusing Bayesian decision analysis and prior/posterior state distributions. These probabilitydistributions are derived from the information collected via time-stamped state-regionchange broadcasts within each buddy set. By characterizing the inconsistency between anode's "observed" state and the corresponding true state with prior and posteriordistributions, the node can first estimate the states of other nodes, and then use themto reduce the probability of transferring a task to an "incapable") node. Moreover, the useof prior and posterior distributions and Bayesian analysis has made the proposed schemerobust to the variation of design parameters that usually require fine-tuning for adaptiveLS. The performance of the proposed scheme is evaluated via simulation, along with fiveother schemes: no LS, LS with state probing, LS with random selection, LS with focusedaddressing, and perfect LS.