A similar entry appears in the Wheel of Time Companion confirming the information available in the main story arc.
Author: Atarah al'Norahn
When Rand plans to go to Alcair Dal as quickly as possible, Rhuarc tells him that he must not reach the site too quickly, or the clans that are not there yet will lose honor. Bruan and the Nakai Aiel have the farthest to go, and Rhuarc thinks it will take them a month to get there. Seana replies that she has walked Alsera's dreams twice, and that Alsera says Bruan means to run the whole way to Alcair Dal from Shiagi Hold and will be there in less than a month.
(Reference: The Shadow Rising, Chapter 49)