Coming into the off season and looking at my options of cross training. Bang for buck, If someone only has time to add running or strength training to their trainer roads time, which will make you a faster cyclist come next year?
Cycling specific weight training will make you a faster cyclist than cross training something that will just work your already developed aerobic system and crush your joints.
Running does not work your muscles the same way that cycling does, so the impact on making you faster on the bike won’t be there (look up eccentric vs concentric muscle contractions). I find that running helps round out my general athletic abilities, but it has not made me faster on the bike. So, I agree with @ErickVH that you will get far more bang for your buck by introducing strength training.