Cache-related pre-emption delays (CRPD) have been integrated into the schedulability analysis of sporadic tasks with constrained deadlines for fixed-priority pre-emptive scheduling (FPPS). This paper generalizes that work by integrating CRPD into the schedulability analysis of tasks with arbitrary deadlines for fixed-priority pre-emption threshold scheduling (FPTS). The analysis is complemented by an optimal threshold assignment algorithm that minimizes CRPD. The paper includes a comparative evaluation of the schedulability ratios of FPPS and FPTS, for constrained-deadline tasks, taking CRPD into account.