Bus-Wait Formula

This morning, I headed out the door late. About 20 minutes late. I normally would catch a 7:58 bus at the end of my block. But I was so late today that thought I might be able to catch the 8:18 bus. 

After getting to the stop at 8:15 and waiting for two minutes, I decided to walk the route and maybe beat the bus there. Its a mile to the station, mainly uphill. And I thought back to this NY Times article about the walk/wait dilemma.

Here are my assumptions: 

• walking straight from my place to the station takes 15 minutes, no bus involved 
• riding the bus from my stop to the station takes five minutes

Based on that: 

• I save ten minutes if I don't have to wait for the bus at all
• I save five minutes if the bus picks me up after I wait only five minutes at my stop
• I save no time if I wait ten minutes - I arrive at the same time I would have if I had walked
• I lose time by waiting more than ten minutes
  

Above is the bus line map. 

This morning, after waiting for two minutes and walking for 15 minutes, not a single bus caught up to or passed me. I can only guess how late I would have been by waiting at my stop.

I obviously don't agree with the belief that this problem is "is in essence trivial" like this wikipedia page does.