A self-inflating tire assembly includes an air tube mounted within a tire sidewall groove. The air tube is in contacting engagement with opposite angled groove surfaces surrounding the air tube. A segment of the air tube is flattened from an expanded diameter to a flat diameter by bending and compression of the groove in a rolling tire footprint to force air evacuated from the flattened segment along a tube air passageway. The sidewall groove extends into an annular, axially extending, sidewall surface such as an axially oriented surface of a tire chafer protrusion located in non-contacting relationship with the rim. The opposite groove surfaces comprise a rubber composition, the rubber composition comprising: a diene based rubber; from 0.25 to 5 parts by weight, per 100 parts by weight of rubber (phr), of a self-lubrication agent capable of migrating from the rubber composition to the groove surface and disposing on the groove surface as a liquid; and from 1 to 15 parts by weight, per 100 parts by weight of rubber (phr), of a vulcanization modifier for use in the second rubber composition include α,ω-bis(N,N′-dihydrocarbylthiocarbamamoyldithio)alkanes, bismaleimides, and biscitraconimides.