  This paper investigates the use of a networked system ($e.g.$, swarm of
robots, smart grid, sensor network) to monitor a time-varying phenomenon of
interest in the presence of communication and computation latency. Recent
advances in edge computing have enabled processing to be spread across the
network, hence we investigate the fundamental computation-communication
trade-off, arising when a sensor has to decide whether to transmit raw data
(incurring communication delay) or preprocess them (incurring computational
delay) in order to compute an accurate estimate of the state of the phenomenon
of interest. We propose two key contributions. First, we formalize the notion
of $processing$ $network$. Contrarily to $sensor$ $and$ $communication$
$networks$, where the designer is concerned with the design of a suitable
communication policy, in a processing network one can also control when and
where the computation occurs in the network. The second contribution is to
provide analytical results on the optimal preprocessing delay ($i.e.$, the
optimal time spent on computations at each sensor) for the case with a single
sensor and multiple homogeneous sensors. Numerical results substantiate our
claims that accounting for computation latencies (both at sensor and estimator
side) and communication delays can largely impact the estimation accuracy.
