The biophysical model of short-term plasticity in tripartite synapse due to the astrocytic extrasynaptic slow inward currents is well known. Multiple biophysical models have been developed for the elements of this mechanism and well known. In this paper, we reproduced the following sequence of events: an action potential arrival on axon action potential leads to opening of calcium volage gated channels and further exocytosis of glutamate filled vesicles with presynaptic membrane. The increased synaptic glutamate concentration leads to activation of the metabotropic astrocyte glutamate receptor. Its activation leads to increase of inositol 1,4,5-trisphodphate concentration in astrocyte cytosol and activation of metabotropic 1,4,5-trisphodphate receptor on the endoplasmatic reticulum membrane. This activation leads to calcium release from endoplasmatic reticulum buffer and further exocytosis of the glutamate filled vesicles with astrocyte outer membrane. This slow glutamate release cascade activate two types of glutamate extrasynaptic receptors on postsynaptic neuron dendrite membrane. Alongside with these slow extrasynaptic inward currents the fast synaptic currents due to activation of two types of synaptic glutamate receptors are also reproduced. For both slow and fast currents we propose the simplified model reflecting complex dynamics of the synaptic transmission. This model independently reproduce slow and fast glumatergic postsynaptic currents with sufficient precision. This model will let us consider the features of the tripartite synapse – the short-term plasticity in future large-scale realtime simulation tasks.