From Herod’s appointment by Rome in 39 BC, to the end of the Herods in 73 AD, was 111 years. However, from Herod’s appointment in 39 BC, it was another 3 years before his actual accession, after deposing his predecessor Antigonus, in the year 36 BC. This reduces the overall 111 years to 108 years.
The best treatise for defining the beginning and end of the rule of the first of the Herods, commonly referred to as “Herod the Great,” is an article by William Filmer, in Oxford’s “Journal of Theological Studies,” October 1966. He dates the rule of Herod the Great from his accession in 36 BC to his passing in very early in 1 BC — rather than the former but imprecise date of 4 BC for the death of Herod.