Focusing on low-level task management of interconnected virtual machines, we present preliminary results on the use of “network calculus” for parallel processing (fork-join) systems, as in MapReduce. We derive a probabilistic bound that the delay through a single parallel processing stage exceeds a threshold, including under redundant tasking to reduce delays at barriers (joins). We conclude with an overview of recent research on energy-efficient cloud operations - work in collaboration with Bhuvan Urgaonkar, IBM Research, and students.