In order to consider the impact that out-of-tolerance rollback will have on the predictive system, consider how simulation error occurs. A predictive management system LP may deviate from the real object because either the LP does not accurately represent the actual entity or because events outside the scope of the predictive network management system may effect the entities being managed. Ignore events outside the scope of the simulation for now and consider error form inaccurate simulation modeling only.
Because of this possibility for prediction error, a method of determining the amount of error in a predicted result needs to be developed. A function of total accumulated error in a predicted result, , is described by Equations 1 and 2. is the error introduced by the virtual message injected into the predictive system by the driving process. The error introduced by the output message produced by the computation of each LP is represented by the computation error function, . The actual time taken by the LP to calculate and output the next virtual message is . Note that the LP topology may not necessarily be a feed-forward network as described by Equations 1 and 2; it may include a cycle. Note also that is the greatest lower bound of all sub-sequential limits of as approaches .
The driving process is indicated by . is the total accumulated error in the virtual message output by the LP from the driving process. is the accumulated error in actual time units from generation of the virtual message from the driving process. For example, if a prediction result is generated in the third LP from the driving process, then the total accumulated error in the result is . If 10 represents the number of time units after the initial message was generated from the driving process then would be the amount of total accumulated error in the result.