Accumulation of amyloid-beta (Aβ) is associated with synaptic dysfunction and destabilization of astrocytic calcium homeostasis. A growing body of evidence support astrocytes as active modulators of synaptic transmission via calcium-mediated gliotransmission. However, the details of mechanisms linking Aβ signaling, astrocytic calcium dynamics, and gliotransmission are not known. We developed a biophysical model that describes calcium signaling and the ensuing gliotransmitter release from a single astrocytic process when stimulated by glutamate release from hippocampal neurons. The model accurately captures the temporal dynamics of microdomain calcium signaling and glutamate release via both kiss-and-run and full-fusion exocytosis. We investigate the roles of two crucial calcium regulating machineries affected by Aβ: plasma-membrane calcium pumps (PMCA) and metabotropic glutamate receptors (mGluRs). When we implemented these Aβ-affected molecular changes in our astrocyte model, it led to an increase in the rate and synchrony of calcium events. Our model also reproduces several previous findings of Aβ associated aberrant calcium activity, such as increased intracellular calcium level and increased spontaneous calcium activity, and synchronous calcium events. The study establishes a causal link between previous observations of hyperactive astrocytes in Alzheimer's disease (AD) and Aβ-induced modifications in mGluR and PMCA functions. Analogous to neurotransmitter release, gliotransmitter exocytosis closely tracks calcium changes in astrocyte processes, thereby guaranteeing tight control of synaptic signaling by astrocytes. However, the downstream effects of AD-related calcium changes in astrocytes on gliotransmitter release are not known. Our results show that enhanced rate of exocytosis resulting from modified calcium signaling in astrocytes leads to a rapid depletion of docked vesicles that disrupts the crucial temporal correspondence between a calcium event and vesicular release. We propose that the loss of temporal correspondence between calcium events and gliotransmission in astrocytes pathologically alters astrocytic modulation of synaptic transmission in the presence of Aβ accumulation.