Incremental Verification of Timing Constraints for Real-Time Systems

Testing constraints for real-time systems are usually verified through the satisfiability of propositional formulae. In this paper, we propose an alternative where the verification of timing constraints can be done by counting the number of truth assignments instead of boolean satisfiability. This number can also tell us how “far away” is a given specification from satisfying its safety assertion. Furthermore, specifications and safety assertions are often modified in an incremental fashion, where problematic bugs are fixed one at a time. To support this development, we propose an incremental algorithm for counting satisfiability. Our proposed incremental algorithm is optimal as no unnecessary nodes are created during each counting. This works for the class of path RTL. To illustrate this application, we show how incremental satisfiability counting can be applied to a well-known rail-road crossing example, particularly when its specification is still being refined.

The Benefits of Re-Evaluating Real-Time Fulfillment Decisions

At the time of a customer order, the e-tailer assigns the order to one or more of its order fulfillment centers, and/or to drop shippers, so as to minimize procurement and transportation costs, based on the available current information. However this assignment is necessarily myopic as it cannot account for all future events, such as subsequent customer orders or inventory replenishments. We examine the potential benefits from periodically re-evaluating these real-time order-assignment decisions. We construct near-optimal heuristics for the re-assignment for a large set of customer orders with the objective to minimize the total number of shipments. We investigate how best to implement these heuristics for a rolling horizon, and discuss the effect of demand correlation, customer order size, and the number of customer orders on the nature of the heuristics. Finally, we present potential saving opportunities by testing the heuristics on sets of order data from a major e-tailer.