Simultaneous Budget and Buffer Size Computation for Throughput-Constrained Task Graphs

Modern embedded multimedia systems process multiple concurrent streams of data processing jobs. Streams often have throughput requirements. These jobs are implemented on a multiprocessor system as a task graph. Tasks communicate data over buffers, where tasks wait on sufficient space in output buffers before producing their data. For cost reasons, jobs share resources. Because jobs can share resources with other jobs that include tasks with date-dependent execution rates, we assume run-time scheduling on shared resources. Budget schedulers are applied, because they guarantee a minimum budget in a maximum replenishment interval. Both the buffer sizes as well as the budgets influence the temporal behaviour of a job. Interestingly, a trade-off exists: a larger buffer size can allow for a smaller budget while still meeting the throughput requirement. This work is the first to address the simultaneous computation of budget and buffer sizes. We solve this non-linear problem by formulating it as a second-order cone program. We present tight approximations to obtain a non-integral second-order cone program that has polynomial complexity. Our experiments confirm the non-linear trade-off between budget and buffer sizes.