A Study of Combinatorial Optimization Problems in Industrial Computer Systems

A combinatorial optimization problem is an optimization problem where the number of possible solutions are finite and grow combinatorially with the problem size. Combinatorial problems exist everywhere in industrial systems. This thesis focuses on solving three such problems which arise within two different areas where industrial computer systems are often used. Within embedded systems and real-time systems, we investigate the problems of allocating stack memory for an system where a shared stacks may be used, and of estimating the highest response time of a task in a system of industrial complexity. We propose a number of different algorithms to compute safe upper bounds on run-time stack usage whenever the system supports stack sharing. The algorithms have in common that they can exploit commonly-available information regarding timing behaviour of the tasks in the system. Given upper bounds on the individual stack usage of the tasks, it is possible to estimate the worst-case stack behaviour by analysing the possible and impossible preemption patterns. Using relations on offset and precedences, we form a preemption graph, which is further analysed to find safe upper-bounds on the maximal preemptions chain in the system. For the special case where all tasks exist in a single static schedule and share a single stack, we propose a polynomial algorithm to solve the problem. For generalizations of this problem, we propose an exact branch-andbound algorithm for smaller problems and a polynomial heuristic algorithm for cases where the branch-and-bound algorithm fails to find a solution in reasonable time. All algorithms are evaluated in comprehensive experimental studies. The polynomial algorithm is implemented and shipped in the developer tool set for a commercial real-time operating system, Rubus OS. The second problem we study in the thesis is how to estimate the highest response time of a specified task in a complex industrial real-time system. The response-time analysis is done using a best-effort approach, where a detailed model of the system is simulated on input constructed using a local search