Charlemagne's challenge: the periodic latency problem.

Latency problems are characterized by their focus on minimizing the waiting time for all clients. We study periodic latency problems, a non-trivial extension of standard latency problems. In a periodic latency problem each client has to be visited regularly: there is a server traveling at unit speed, and there is a set of n clients with given positions. The server must visit the clients over and over again, subject to the constraint that successive visits to client i are at most qi time units away from each other. We investigate two main problems. In problem PLPP the goal is to find a repeatable route for the server visiting as many clients as possible, without violating their qi's. In problem PLP the goal is to minimize the number of servers needed to serve all clients. In dependence on the topol- ogy of the underlying network, we derive polynomial-time algorithms or hardness results for these two problems. Our results draw sharp separation lines between easy and hard cases.Latency problem; Periodicity; Complexity;

An Average-Case Analysis for Rate-Monotonic Multiprocessor Real-time Scheduling

We introduce the "First Fit Matching Periods" algorithm for static-priority multiprocessor scheduling of periodic tasks with implicit deadlines and show that it yields asymptotically optimal processor assignments if utilization values are chosen uniformly at random. More precisely we prove that the expected waste is upper bounded by O(n^(3/4) * (log n)^(3/8)). Here the waste denotes the ratio of idle times, cumulated over all processors and n gives the number of tasks. The algorithm can be implemented to run in time O(n log n) and even in the worst case, an asymptotic approximation ratio of 2 is guaranteed. Experiments yield an expected waste proportional to n^0.70, indicating that the above upper bound on the expected waste is almost tight

Scheduling periodic tasks with slack

We consider the problem of nonpreemptively scheduling periodic tasks on a minimum number of identical processors, assuming that some slack is allowed in the time between successive executions of a periodic task. We prove that the problem is NP-hard in the strong sense. Necessary and sufficient conditions are derived for scheduling two periodic tasks on a single processor, and for combining two periodic tasks into one larger task. Based on these results, we propose an approximation algorithm