  We study network response to queries that require computation of remotely
located data and seek to characterize the performance limits in terms of
maximum sustainable query rate that can be satisfied. The available resources
include (i) a communication network graph with links over which data is routed,
(ii) computation nodes, over which computation load is balanced, and (iii)
network nodes that need to schedule raw and processed data transmissions. Our
aim is to design a universal methodology and distributed algorithm to
adaptively allocate resources in order to support maximum query rate. The
proposed algorithms extend in a nontrivial way the backpressure (BP) algorithm
to take into account computations operated over query streams. They contribute
to the fundamental understanding of network computation performance limits when
the query rate is limited by both the communication bandwidth and the
computation capacity, a classical setting that arises in streaming big data
applications in network clouds and fogs.
