In the periodic packet routing problem a number of tasks periodically create packets which have to be transported through a network. Due to capacity constraints on the edges, it might not be possible to find a schedule which delivers all packets of all tasks in a feasible way. In this case one aims to find a feasible schedule for as many tasks as possible, or, if weights on the tasks are given, for a subset of tasks of maximal weight. In this paper we investigate this problem on trees and grids with row-column paths. We distinguish between direct schedules (i.e. schedules in which each packet is delayed only in its start vertex) and not necessarily direct schedules. For these settings we present constant factor approximation algorithms, separately for the weighted and the cardinality case. Our results combine discrete optimization with real-time scheduling. We use new techniques which are specially designed for our problem as well as novel adaptions of existing methods.
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