Quote:
Originally Posted by cybele
Well, I am glad you are back, you always have some good ideas and facts and figures and so forth.
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Thanks
Just because I feel like it I'm going to present a little tidbit on highway capacity.
The capacity of a highway is driven by the average speed of the vehicles and the spacing of the vehicles. Drivers are supposed to keep a 2 second spacing which roughly corresponds to a safe reaction time and the natural spacing inclination drivers feel safe with.
Speed is actually the smallest portion of that factor unless the average speed runs extremely low.
Calculation:
65 miles per hour ----> 0.136 seconds for the average length vehicle to pass
a point
30 miles per hour ----> 0.295 seconds
10 miles per hour ----> 0.886 seconds
So therefore, assuming 1.4 average occupancy and 2 second separation the highway capacity per hour per lane per given station is as follows:
65mph : 2360 people per hour
30mph (heavy congestion): 2196 people per hour
10mph (traffic stops most of the time, usually due to hyper merging, an accident, construction, or a combination): 1746 people per hour
What occurs usually is that traffic will hit a critical limit and people will naturally slow down and thus reduce the capacity. Then people will start shuffling lanes which will further slow down traffic and reduce capacity. Then as merging becomes difficult traffic feeding onto the highway can cause an intermittent full stop.
Keeping in mind that average speed is what is key, not intermittent stops, unless there is a dire issue, traffic will flow at average rates over 10 mph even during the roughest rush hour. Let's factor in the affect of one HOT lane and three normal lanes versus four normal lanes, then finally one HOV lane and three normal lanes.
The toll of the HOT lane is designed to discourage some to use the lane and thus keep it relatively clear. The capacity of a normal four lane highway (per direction) is 9440 assuming 65 mph average (the OTP speed limit).
An assumption that the HOT lane discourages only 25% of travelers in any given situation is reasonable and probably generous. The calculated average capacity of such a lane is 2.31 according to at least one source. Therefore at 65 miles per hour, such a system would have a per hour capacity of 10,000 people per hour. This of course assumes that the normal lane occupancy rate stays the same (error correction).This is clearly better than normal lanes alone.
An HOV lane system would have a capacity, using the same methodology, of 10,937.
Taken alone, this would indicate that adding a toll to an HOV lane would be counter intuitive to a goal of increasing transportation capacity and would actually lower the critical congestion point.
Now what happens at rush hour takes a bit of mathematical magic. The HOT lane would reach congestion when 3,893 people try to use it, the same point an HOV would, however 25% of people are discouraged to use it according to this model. So there are a few scenarios. To summarize, the HOT would only provide an advantage over the HOV if between 10,937 and 12,250 people try to use the highway system. Any more or any less and the HOV system would move more traffic or be generally no different. This is actually the best case scenario, because if the HOT discouraged more than 40% of people, the traffic capacity would be so severely lowered that the highway system would be worse than if there were no high occupancy lanes at all no matter what the traffic situation.
Note: Several assumptions are made here to simplify the calculations . Also the best case for HOT lanes, the scenario where the HOT is at full free-flowing 65 mph capacity and the other lanes are fully congested (10 mph case) would have a capacity of 9,131 versus 5,238 for four normal lanes and 8188 at for HOV (at 10 mph). Effectively the result, in the very best and unlikely case would be to cause congestion 1,000 cars earlier to allow the passage of 1000 more cars after congestion is created. Or a 9% decrease in highway capacity to raise it 11% after all the cars can't move, but only for cars that pay a toll. The rest would be stuck in traffic that may not have congested if the HOT was an HOV.
It is an interesting trade off, but I don't really see why someone would actually advocate HOT. Perhaps to raise money or to punish poor drivers or drivers in general.