  Recently, an idling mechanism has been introduced in the context of
distributed \emph{first order} methods for minimization of a sum of nodes'
local convex costs over a generic, connected network. With the idling
mechanism, each node $i$, at each iteration $k$, is active -- updates its
solution estimate and exchanges messages with its network neighborhood -- with
probability $p_k$, and it stays idle with probability $1-p_k$, while the
activations are independent both across nodes and across iterations. In this
paper, we demonstrate that the idling mechanism can be successfully
incorporated in \emph{distributed second order methods} also. Specifically, we
apply the idling mechanism to the recently proposed Distributed Quasi Newton
method (DQN). We first show theoretically that, when $p_k$ grows to one across
iterations in a controlled manner, DQN with idling exhibits very similar
theoretical convergence and convergence rates properties as the standard DQN
method, thus achieving the same order of convergence rate (R-linear) as the
standard DQN, but with significantly cheaper updates. Simulation examples
confirm the benefits of incorporating the idling mechanism, demonstrate the
method's flexibility with respect to the choice of the $p_k$'s, and compare the
proposed idling method with related algorithms from the literature.
