In this paper a novel and efficient computational implementation of a Spiking Neuron-Astrocyte Network (SNAN) is reported. Neurons are modeled according to the Izhikevich formulation and the neuron-astrocyte interactions are intended as tripartite synapsis and modeled with the previ- ously proposed nonlinear transistor-like model. Concerning the learning rules, the original spike-timing dependent plasticity is used for the neural part of the SNAN whereas an ad-hoc rule is proposed for the astrocyte part. SNAN performances are compared with a standard spiking neural network (SNN) and evaluated using the polychronization concept, i.e., number of co-existing groups that spontaneously generate patterns of polychronous activity. The astrocyte-neuron ratio is the biologically inspired value of 1.5. The proposed SNAN shows higher number of polychronous groups than SNN, remarkably achieved for the whole duration of simulation (24 hours).