Recent ACC and CACC systems provide a consumer with a discrete and finite set of choices of time headway settings. Heterogeneity of traffic results from consumers' preference for different time headways even if the vehicles are of the same make and model. In this paper, we study string stability associated with this type of heterogeneity. We show that if time headways are in a decreasing order in a vehicle string for CACC and in increasing order for ACC, string stability can be guaranteed. We provide a method to choose the associated control gains so that the same set of gains can be used for all headway settings. We also investigate how errors propagate if one were to rearrange the vehicles in a random order. By doing so, it is found that for a finite, discrete choice of time headways, the maximum spacing error of a vehicle for any rearrangement of vehicles can be bounded irrespective of the size of the platoon implying that heterogeneity will not contribute significantly to string instability for nominal maneuvers of the leading vehicle in the string. We provide numerical results to corroborate the results in this paper.