When the bursty (BRST) inter-arrival time distribution is arbitrarily fixed, the blocking probability in the BRST/GI/c/c increases, as the log-convex or log-concave service time density function becomes stochastically less variable. This implies that the BRST/D/c/c with constant service times has the maximum blocking probability in the BRST/GI/c/c systems. Since it is impossible to obtain the strict blocking probability in the BRST/D/c/c the tight upper bound of the strict blocking probability has been expected for a long time. In this paper, we propose not only the upper bound but also the lower bound in which the proposed lower bound assures that the proposed upper bound is tight. For the numerical calculations of the upper and lower bounds, we introduce an asymmetric 2-hyper-exponential inter-arrival time density with the coefficient of bias r^-1 which is greater than or equal to 1. Here, as r^-1 increases, the inter-arrival time becomes stochastically more variable and the blocking probability in the BRST/D/c/c increases. The numerical examples for r^-1(≥ 1) illustrate that the proposed upper bound of the blocking probability in the BRST/D/c/cis very close to the proposed lower bound. In result, the proposed upper bound BLK^(U)(D) is closer to the strict blocking probability BLK(D). In particular, if r^-1 ≥ 2, then we  have BLK^(U)(D) ≈ BLK(D). However, letting  BLK(M) be the strict blocking probability BLK(M) in the BRST/M/c/c the difference between BLK(D) and BLK(M) is remarkable for 1 ≤ r^-1 ≤ 10. As r^-1 increases, the difference becomes smaller little by little and when r^-1 is beyond 100,  BLK(D) is nearly equal to BLK(M). Moreover, when r^-1 > 1000, BLK(D) and BLK(M) such that BLK(D) = BLK(M) are nearly equal to 1. We have that if r^-1 → ∞, then both BLK(D) and BLK(M) converge to 1.

GI/GI/∞, GI/GI/c/c, bursty, completely monotone, generalized Erlang, asymmetric hyper-exponential, heavy tail, blocking probability, effect of service time variation, stochastically more (less) variable, paradoxical behavior.