Astrocytes　have　important　functions　in　the　central　nervous　system　(CNS)　and　are　significant　in　our　understanding　of　the　neuronal　network.　Astrocytes　modulate　neuronal　firings　at　both　single　cell　level　of　tripartite　synapses　and　the　neuron-glial　network　level.　Astrocytes　release　adenosine　triphosphate　(ATP)　and　glutamate　into　the　neuron-glial　network.　These　gliotransmitters　diffuse　over　the　network　to　form　long　distance　signals　to　regulate　neuron　firings.　In　this　paper,　we　study　a　neuron-glial　network　model　that　includes　a　diffusion　of　astrocytic　ATP　and　glutamate　to　investigate　how　long　distance　diffusion　of　the　gliotransmitters　affects　the　information　processing　in　a　neuronal　network.　We　find　that　gliotransmitters　diffusion　can　compensate　for　the　failure　of　information　processing　of　interneuron　network　firings　induced　by　defectively　coupled　synapses.　Moreover,　we　find　that　calcium　waves　in　astrocyte　network　and　firings　in　interneuron　network　are　both　sensitive　to　the　glutamate　diffusion　rate　and　feedback　intensities　of　astrocytes　on　interneurons.