Information transfer may not be limited only to synapses. Therefore, the processes and dynamics of biological neuron-astrocyte coupling and intercellular interaction within this domain are worth investigating. Existing models of tripartite synapse consider an astrocyte as a point process. Here, we extended the tripartite synapse model by considering the astrocytic processes (synaptic and perinodal) as compartments. The scattered extrinsic signals in the extracellular space and the presence of calcium stores in different astrocytic sites create local transient [Ca2+]. We investigated the Ca2+ dynamics and found that the increase in astrocytic intracellular [Ca2+] enhances the probability of neurotransmitter release. However, the period in which the extrasynaptic glutamate lingers in the extracellular space may cause excitotoxicity. We propose further biological investigation on intercellular communication, considering that unconventional sources (nonsynaptic) of glutamate may improve information processing in neuron-astrocyte networks.