TOLL X-LANES & FREE:That Snub-Nosed Bullet Graph on 91X

Last issue (TRnl#31 Sept 98 p3) we wondered about the condition, described in the Sullivan Report, of the X-lanes and the free lanes each running 1.5k to 2k veh/hr/lane, the former at free flow speeds like 65mph while alongside the free lanes were experiencing stop&go and 32mph average speeds. Did this reflect that backward sloping curve of volume versus speed, a curve whose shape we characterized as like a snub-nosed bullet.

Most traffic engineering texts shows such a curve (though they didn’t think of a memorable name!) and the TRB’s Highway Capacity Manual shows an idealized parabola (see nearby). It is an area where engineers and economists have labored mightily to try explain traffic flows.

We asked a bunch of experts what they thought about our idea that the 91X/91-free speed/volume relationship represented points above one another on the snub nose bullet. As you’ll see we turned up a variety of views.

Joe El Harake, Caltrans liaison engineer to the toll roads in Orange county told us he thinks the parabolic curve has been in evidence during the rush hours with slower speeds in the free lanes the result of overloading, and free flow on the X-lanes arising from the tolls deterring excessive entry. Bob Foote former director of research at the Port Authority in New York says that the PA pioneered experiments in the 1960s using signal metering on approaches to the Holland Tunnel searching for the optimum traffic flow near the nose of the snub bullet on the graph.

Joy Dahlgren of UC Berkeley notes that 91X/91-free could be following a parabola or hitting the wall of a vertical section of the graph. She says she hasn’t done any independent work on it but that both shapes are supported in the literature.

Kenneth Small

Ken Small an economist at UC Irvine who has done extensive work on traffic congestion says any equilibrium on 91X is purely between the toll rate and the speed differential plus other perceived advantages of the X-lanes. He doubts that there is any equilibrium in the relation Sullivan reported of the X-lanes and free lanes carrying similar volumes at very different speeds. He thinks that coincidence of volumes is “dumb luck.” Small and other economists have pointed out that the lower backward sloping part of the curve cannot represent an equilibrium. The backward sloping section “defies commonsense” as a static representation because it suggests that curtailing the amount of demand for roadspace will worsen congestion.

Small says that any speed-flow curve will have discontinuities. The 70th St Lake Murray Blvd data he displayed (see nearby) show more of a ship’s stern profile than any bullet shape with most of the readings on the deck of the stern, a bunch with just the slightest backward slope and a smattering “underwater.”

Economists studying congestion have concluded that static analysis doesn’t get you very far because in these conditions of hypercongestion the issue is one of shocks and dynamic effects. With Xuehao Chu Small wrote in a paper “Hypercongestion” that steady state analysis cannot explain it because the condition doesn’t persist: “Rather hypercongestion occurs as a result of transient demand surges and can be fully analyzed only within a dynamic model. Even if the dynamic model is converted to a static one through the use of time averaging, the appropriate specification of average cost depends on the underlying dynamics.”

He wrote us: “Since the bottom part of the curve can’t express the cause-effect relationship, yet it is based on known engineering measurements, then there must be some other factor at work. We haven’t really pinned that other factor down, but in some cases it is simply a downstream bottleneck. If, for example, your diagram represents westbound traffic, the bottleneck could be the 91-55 interchange. If it represents eastbound traffic, the bottleneck could be the Riverside County line where 6 lanes reduce to 5; or it could be caused by entering traffic from the I-15 or some other feeder road. I don’t know whether there is really a bottleneck constricting the traffic in the regular lanes. This, I think, would be the most fruitful way to research the phenomenon further. Of course, what’s really happening may be lots more complicated than a single bottleneck. There may be complex interactions between traffic entering and leaving the 91 and the 55 for some miles on either end of the CPTC project and the speeds observed on the regular lanes. Modeling this accurately is hard, but I suspect some current computer models are up to it.”

Nagui Rouphail

Nagui Rouphail, engineer prof at North Caolina State Univ wrote us: “If you think of ‘demand’ as the number of cars wishing to pass that point over a certain time interval, that demand is easily measured ar 4:00 am, but very difficult to estimate during the rush hour. So the same volume has two very different operating speeds, depending on the congestion level on the facility. The general shape you showed is reasonably OK. It represents the relationship between speed and volume for a uniform section of highway not the entire facility. Typically, the speed line is fairly flat with volume until a volume of about 1300-1400 vph/lane, where it begins curving down. The highest volume i.e. the farthest point on the volume scale, or capacity, ranges from 2000-2400 vph/lane depending on the road geometry, trucks and other factors. The speed at capacity hovers around 50mph. Basically, if the average traffic speed is above 50mph or so, the “volume” that is counted on the road is equivalent to the “demand” for travel on the facility. Therefore, the volume measured on 91X lanes during the rush hour represents unfettered demand “for the price”.

“Turning our attention to the lower half of the curve, again, the shape of the curve seems OK, except in the case where volume are very low, at which point speed is zero. The “volumes” that are measured under these conditions have NOTHING to do with “demand” on the facility. One does not “chose” to travel at 32 mph. These are the results of a bottleneck that is downstream of the point where the speed measurements are taken. So, on the free lanes, if you have a bottleneck downstream whose capacity is less than the segment you took your speed measurements on, then what comes out of your section is basically the maximum throughput of the most severe bottleneck on the facility. In these cases, therefore, the “demand” on the free lanes cannot be directly measured, but, for sure it is MUCH higher than the maximum observed flow.

“Therefore, in my opinion, the fact that the observed DEMAND on 91X lanes

and the counted VOLUME on the free lanes are equivalent is purely coincidental. I disagree that the throughput potential is the same. The way you measure throughput is how many vehicle-miles you can move per hour. Clearly the 91X lanes have a higher throughput capacity.”

Tim Lomax

Tim Lomax of Texas Transp Inst: “You are right about your bullet nose graph. It’s a fairly well understood phenomenon in the last several updates of the highway capacity manual. Its why you can’t just use volume to estimate speed or level of service or several other values. It has been revised to show the behavior of folks who drive 50+mph in bumper to bumper conditions until the freeway stops all of a sudden.

“The freeway speeds don’t slow much until the speeds drop to stop and go. This is in contrast to the gradual drop from 60/70 mph to 30/35 in the HCM versions before 1985. A variety of factors seem to contribute — the law of unintended consequences is at work here, too. Seat belts, better brakes, third tail lights, air bags, low truck percentages all contribute to longer sight distances (through the glass) which makes it easier to see brakes, and thus easier to drive closer. Obviously tinted windows and pick-ups/SUVs have the opposite effect. Pressure or time crunched travelers help to speed traffic right up to the “edge”.

“The highest volumes are seen where the road falls away so that drivers can see a long way away. The high volumes are also seen downstream of bottleneck areas because there is enough traffic stored up to force the flow.”

James Schoen

Jim Shoen of Catalina Engineering, Tuscon AZ told us he thought much of the difference in speeds between the X-lanes and the free lanes could be accounted for by the turbulence caused by entry and exit movements on the free lanes. There are 6 intermediate interchanges, 9 ramps each side, in the stretch of 91 alongside 91X whereas the X-lanes of course are a simple “pipe” — in one end and out the other. The capacity of the 91X lanes would have to be 2400 veh/lane/hour and could be as high as 2600 he says.

“The operators of the 91X lanes want to meter traffic at the entry point, either physically (i.e. a gate at a toll plaza) or by making tolls prohibitive, in order to keep the volumes below capacity. This will ensure that the 91X lanes are operating at significantly higher speeds than the mixed use lanes during peak periods.”

Bob Foote

Bob Foote formerly of the PANYNJ thinks that metering of traffic is the best way to smooth traffic flows: “The object of metering is to increase throughput on the most critical sections of the trunk road, by forestalling shock wave formation. It is a tricky, dicey operation requiring balancing demand approaching the bottleneck, with the ability of the bottleneck lanes to accommodate traffic when traffic is moving through at that speed and density providing the highest flow. Too much demand and shock waves are generated: too little and available capacity is underused. This is a 15 second by 15 second decision process, requiring intimate knowledge of speed and space-mean density on the approach to the bottleneck, and beyond.

“Our 1960 experiments at the Holland Tunnel demonstrated with metering, throughput can be increased by about 5%.

Part of this is due to more optimal speed/density more of the time, and part is due to the reduction in disabled vehicles to be expected when vehicles move at more constant speeds compared with stop/go conditions inherent in shockwaves. There is also a reduction in raw vehicle hours present on the road when density is low and speed high, compared with high density/low speed. The less presence, the less likelihood of breakdown. And the reduction in acceleration/deceleration makes a big difference in emissions,which is an especially valuable byproduct of the metering operation in tunnels.

“Our experiments also showed this relatively small increase in throughput had a major impact on approach congestion. To the extent the metering operation succeeds in raising throughput, the number of vehicles waiting at the on-ramp is lessened and overall delays are reduced. It isn’t a zero sum game

“Pricing elasticity is an important new variable, which I fear introduces random noise in a process which has plenty of variables already. The benefits of pricing the X-lane derive from operating it at sub-capacity, which is great for the premium payers as long as the margin of capacity exists.”

Foote favors further efforts to optimize flows with metering of entering traffic: “I’m convinced the benefits we demonstrated (in the 1960s) are worth pursuing, even more now when urban road construction is prohibitive or impossible. And I’m sure the technology available today could do a far better job than we did with our 4K, 8K and 16K on-line DECs and HP’s.”

The 1960s effort he says fizzled out as new management at the PA displayed no interest in maintaining the system and its components were not replaced as they wore out. (Contacts: bobfoote@ewol.com joy@uclink.berkeley.edu rouphail@mindspring.com ksmall@uci.edu t-lomax@tamu.edu SchoenJim@aol.com)