Control mechanisms of stream processing applications (SPAs) that ensure latency bounds at minimal runtime cost mostly target a specific infrastructure, e.g., homogeneous nodes. With the growing popularity of the Internet of Things, fog, and edge computing, SPAs are more often distributed on het- erogeneous infrastructures, triggering the need for a holis- tic SPA-control that still considers heterogeneity. We there- fore combine individual control mechanisms via the latency- distribution problem that seeks to distribute latency budgets to individually managed components of distributed SPAs for a lightweight yet effective end-to-end control. To this end, we introduce a hierarchical control architecture, give a formal definition of the latency-distribution problem, and provide both an ILP formulation to find an optimal solution as well as a heuristic approach, thereby enabling the combi- nation of individual control mechanisms into one SPA while ensuring global cost minimality. Our evaluations show that both solutions are effective—while the heuristic approach is only slightly more costly than the optimal ILP solution, it significantly reduces runtime and communication overhead.