The only thing that comes to mind is a flowable, non shrink grout, similar to what's used under steel column base plates to make up the difference between the plate and the column base/footing, sometimes there's a discrepancy, between the steel fabricated and the footing elevation, this material is structural, but I am not sure about bonding, abrasion resistance and or weathering, maybe someone knows of another similar or newer material, portland cement based with structural properties, that can be used to fill, is non sag and will bond.
On the other hand, if the joints between the (substrate) ie; existing concrete to existing concrete can be cleaned, prepared, possibly primed for a sealant,(caulk) that may be another alternative, but it needs to achieve a bond, with adequate resistance to pull out, (this is a common test with sealants) and something that is also elastomeric enough to tolerate expansion and possibly compression, and not lose its bond. There are joint sealants for concrete, our local masonry supply house, would have something used commercially. It has to be compatible with the substrate, may require cleaning and priming depending on what the material is.
With bituminous asphaltic concrete, (asphalt paving) and you have either one side of the substrate,(the joint) is a bituminous material, or both sides of the joint, are bituminous, you will likely need a material that is bituminous, (asphalt, tar, etc.) to achieve a bond, but also elastomeric enough to not fail under the conditions of a paved roadway. Is there a fine cold patch or similar, possibly a driveway sealer with filling properties, perhaps a roofing patch material, fibrous or similar, substrate may have to be prepped, possibly heated, way out of my league on that, but N.Y.S. D.O.T. commonly seals cracks in asphalt paved roads, that material, along with the specified installation instructions may just suffice. In both you may want to apply substantial dose of weed killer prior too, I have seen that called for in similar repair specifications. Not sure how many lineal feet you have, but the material quantity would not to appear to be that costly from what you describe, the results however could be disappointing, these kinds of materials and repairs may not be the most durable under the conditions, at worst it will be a maintenance item at some point again.