http://www.ibiblio.org/pub/academic/history/marshall/militar...
I wish I had a link to the source (I'll dig it up when I have more time). I discovered this while researching "fox walking", the toe-first method of human locomotion that some believe is the natural means of human motion, before the advent of stiff-soled shoes. This skill appeared to become mostly lost in the indigenous populations after the Spanish introduced horses to the Americas.
A search on "native american" and "ultrarunning" should render some good links for those who are curious.
As an aside, as anyone who's ever read Stephen King's "The Long Walk" can attest, sustaining a 4mph walk is quite tough. I mean, who hasn't read that story and tried keeping that pace with GPS in hand?
Their forced marches were to make them march longer, not faster. I'm saying 2 miles/hour because the Romans only managed around 1.5 with weight.
I'm not arguing that the Romans were slackers. Given the effort it takes to setup a Roman castra, the marching might be the least strenuous part of the soldier's day. Also, my daily walk is on paved sidewalk across mostly level ground, while the Romans often didn't have such advantages.
For an able bodied person walking through a shopping mall, three miles an hour is perfectly healthy and reasonable.