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To reduce contention in optical burst switched networks, data bursts are preceded by the so-called burst control packets, which are sent a given offset time in advance in order to advertise the switch of the forthcoming burst arrivals. However, this policy of one-way in-advance reservation produces the so-called path length priority effect, which benefits BCP reservations with high offset values against those with smaller offset times. This effect not only brings an unfair treatment to bursts with different offset values, but also leads to a serious degradation of global network performance. This work presents a new detailed analytical study to quantify the blocking probability perceived by BCP reservations with continuous-time uniformly distributed offset time values. In addition, it shows how to apply such theoretical values onto a proactive discarding algorithm which reduces such unfairness and achieves an equalized picture of the blocking probability with respect to the offset time.