Jim has been observing traffic flows at intersections.
To make things easier Jim only studies 4-way intersections and defines the inside of the intersection to be the square of road shared by the two intersecting roads. A car on the inside of the intersection is said to be "on the intersection".

He
observes that the through-put of an intersection is limited by the number of cars allowed on the inside of the intersection at any one time. For a 4-way intersection 2 cars are allowed on the inside of the intersection at any one time. These cars travel in opposite directions on the same road. To increase the service time (and thus decrease the average wait time) at the intersection more cars must be allowed on the intersection at any one time.

Jim decides to allow twice as many cars (4) onto the intersection but insists that these cars exit the intersection before any others are allowed on. These cars travel in opposite directions on both roads. These cars may turn away from the opposing traffic flow but not against it (ie right hand turns in the UK, left hand turns in the US).

The inside of the intersection must be of sufficient size to allow the 4 cars to slide past each other in much the same way a round about works.

Jim believes the average wait at such an intersection is half that of existing ones.

Jim was never in Melbourne (being a figment of my imagination). I have seen a hook turn or two and Jim has disallowed them. c.f. "turning against the opposing traffic flow"

We are puzzled as to why this well stated, clearly thought out idea has attracted fishbones. We think that Jim is improving and is not deserving of such opprobium in this case. We will give Jim our croissant.

We think that while this is a simple enough idea, it can equally well be addressed by the judicious use of roundabouts (traffic circles, rotarys) which are common in the UK, but relatively rare in other countries where the "four-way stop" as described in the idea has been adopted in preference.

<aside> We are mildly puzzled by the continuing use of the third person singular, but are reluctant to criticise openly since this may attract attention to our own use of the first person plural. </aside>

I like this idea – mostly because in Meredith’s mind John overcomplicates everything Jim and Helen say… If Jim were to drive on one-way streets with 4-way intersections and staggered turning at those intersections (left/right) on a grid… Jim and Helen could theoretically get from point A to point B without stopping.

// it can equally well be addressed by the judicious use of roundabouts

Roundabouts are really good but flawed in heavy traffic, since the flow on one road can prevent other traffic from entering. The solution in the UK is to add traffic lights to occasionally steam the dominate flow onto the turning circle. The Chiswick roundabout (in the UK) is an example of this. Turning circles are also alot bigger than 4-way intersections. London has alot of mini roundabouts, that are effectively 4-way intersections that obey roundabout rules, i.e. at the intersection you always giveway to your right.

Jim would allow cars arriving at an intersection at the same time to always enter but they must leave before other cars are allowed to enter, hence the "single car phase" title.

Red lights on all intersecting roads might be triggered by a car, or cars entering an intersection. And green lights on all intersecting roads might be triggered by a car, or cars leaving an intersection. The difference in the phase of the lights here and those used at the Chiswick roundabout is that they are all on the same phase. The Chiswick roundabout uses the standard alternating phasing.

How does Jim propose to indicate to approaching vehicles that there are fewer than 4 cars in the intersecion? Forcing approaching cars to stop defeats Jim's intent.

Indeed, Jim might find that the average speed for that intersection drops; as everyone must slow down (if not stop) on approach (much like a traffic circle).

[phoenix] There is no need to indicate that there are fewer than 4 cars on the intersection. Under peek conditions you can calculate the total and average wait time at the intersection. Hint assume a constant service time and you do the math...

Perhaps it's my public school education, but...
Sorry, I'm still not buying either the time savings or the lack of indicators.

What, exactly, stops the fifth (or greater) car from entering the intersection and/or synchronizes its movement with the other cars in the intersection?

Assume 32 cars arrive at the intersection simultaneously (8 from each direction). How long does it take them to get though your intersection? How long does it take them to get through a 'normal' intersection (where we'll assume no turns, traffic must stop while opposing traffic moves through the intersection, but 8 cars can move through the intersection at once)?

I completely agree with the theory of traffick circles and am more than willing to impart the sought after confectionary for Jim’s thinking, but….I’m afraid Jim has overlooked one very important factor.

My driving experience in the UK is forever being spoilt by the infuriating politeness that locals apply when it comes to making decisions at traffick circles. The larger ones are rarely a problem, but at the ones applied to small four-way crossings, I can’t help but get aggitated, when such effective and pure logic meets it’s match.. Instead of speeding up the flow of traffick, it has exactly the opposite effect. People are forever stopping because I presume it just doesn’t seem polite to drive into the circle and push in front of the person sitting just a few metres away.

I have often considered jumping out of my car and approaching the “nice” person sitting there waving at me impatiently to proceed, and share with them the wonderfull logic which ought to make traffick circles a pleasure to deal with, but then that would probably slow the whole process down even more.

I know that it could be argued that at least people are slowing down for the intersection, which I approve of, but it need not bring everyone to a standstill.

Assume it takes one second to traverse the inside of an intersection.

At a normal intersection, 16 cars will drive straight through taking 8 seconds. The other 16 will then drive through taking a further 8 seconds. The total wait is 184 seconds since each of the other 16 cars waits 8 seconds plus the time it takes to clear their respective queues which is 7 seconds (the first car does not wait).

At a Jim intersection 4 of the 32 cars will drive straight through making 28 cars wait 1 second, the next 4 cars drive through making 24 cars wait a further 1 second, and so on. The total wait is 112 seconds.

Not half its true but better...

The performance of the Jim intersection can be improved by making the inside of the intersection bigger, c.f. really big roundabouts. A Jim intersection that can handle 8 cars at a time as a 48 second total wait with a 1 second service time and a 96 second total wait with a 2 second service time...

What baffles me is why we don't have a "left turn on red" rule in the UK. I have driven in states that have a "right turn on red" rule (unless otherwise posted) and it improves traffic flow with seemingly little disruption, cost or potential increase in accidents.

What about T intersections; if the top of the T has two lanes one of those can "bypass" the intersection altogether. It bugs me the number of times I have to stop at a two lane T junction when I am driving accross the top of the T.