Time-critical networking requires low-latency decisions from sparse and bursty telemetry, where fixed-step neural inference waste computation. We introduce Network-Optimised Spiking (NOS), a two-state neuron whose variables correspond to normalised queue occupancy and a recovery resource. NOS combines a saturating excitability nonlinearity for finite buffers, service and damping leaks, graph-local inputs with per-link gates and delays, and differentiable resets compatible with surrogate gradients and neuromorphic deployment. We establish existence and uniqueness of subthreshold equilibria, derive Jacobian-based local stability tests, and obtain a scalar network stability threshold that separates topology from node physics through a Perron-mode spectral condition. A stochastic arrival model aligned with telemetry smoothing links NOS responses to classical queueing behaviour while explaining increased variability near stability margins. Across chain, star, and scale-free graphs, NOS improves early-warning F1 and detection latency over MLP, RNN, GRU, and temporal-GNN baselines under a common residual-based protocol, while providing practical calibration and stability rules suited to resource-constrained networking deployments. Code and Demos: https://mbilal84.github.io/nos-snn-networking/

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