Introduction / Summary
We set up a model, in which the optimal number of the tollbooths in the toll plaza can be calculated under the condition that lane number is given. First of all, we defined 'the optimal' as the maximal number of vehicles passing through within a definite period of time, which can be attained, i.e., the outflow rate of a toll plaza. Considering drivers' complaint, we added a constraint condition that the total waiting time of a vehicle should be less than 5 minutes when traffic comes stable. Secondly, under the extreme condition assuming that the number of tollbooths equals that of lanes, we gradually increased the number of tollbooths using computer simulation and finally obtained the optimal. We have discovered that when traffic is blocked up, the former congestion will gradually decrease and the latter congestion will gradually increase along with the increase of tollbooths，while the latter congestion will aggravate the former congestion, which is consistent with fact. The optimal number of tollbooths will emerge in the phase when the latter congestion aggravates the former congestion, from there on, the increase of the tollbooths should make the whole highway section blocked more heavily. There are quite a few factors which can affect the optimal number, among which we take two as relatively major: charging time at the tollbooth and the speed at which vehicles leave out-pool back for highway. The result of sensitivity analysis is as below: fluctuation of charging time at the tollbooth affects target little, while that of the latter affects much.
Finally, using our model, we analyzed the real highway section's vehicle flow rate (of 4 lanes) and got 7 tollbooths, which is the same as the reality.
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Content
Content............................................................................................................................. 2 Problem Restatement.......................................................................................................... 3 Terms and Definition.......................................................................................................... 3 Assumptions ..................................................................................................................... 4
About Interstate-95 .............................................................................................. 4 About the weather ................................................................................................ 4 About the driver .................................................................................................. 4 About the vehicles ............................................................................................... 4 About the tollbooths ............................................................................................. 5 About the in-pool & out-pool ................................................................................ 5 Some Facts Derived from Assumptions................................................................... 5
Analysis and Model Design................................................................................................. 6
Overview ............................................................................................................ 6 Analysis ............................................................................................................. 6 Modeling ............................................................................................................ 7 Model Result Analysis...................................................................................................... 10
Single Lane Case ................................................................................................11 Multilane case ................................................................................................... 13 Special (n-n) case............................................................................................... 14 The answer to the question raised in the problem ................................................... 16
Model Verification ........................................................................................................... 17
Data Acquisition ................................................................................................ 17 Simulation ........................................................................................................ 19
Model Sensitivity............................................................................................................. 20
Sensitivity of minLeavingIntervalInSingleLane...................................................... 20 Sensitivity of serving time of tollbooths ................................................................ 21
Further Work ................................................................................................................... 23 Model Strength and Weakness ........................................................................................... 23 References ...................................................................................................................... 24
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The Optimal Number of Tollbooths
Problem Restatement
Some busy toll roads are multi-lane highways with some toll plazas scattered all over. Since no one is willing to experience continuous traffic disruption, it is desirable to limit the amount of time spent on toll plazas.
Commonly a toll plaza is made of tollbooths, a much larger number of which is located than the entering travel lanes so as to fit well into the roaring traffic inflow. Vehicles fan out to tollbooths to be served, and then take trouble in squeezing out of the bottleneck at the departure of toll plaza, finally go back to a normal number of lanes. Chances are that congestion happens in the bottleneck when traffic is heavy. Congestion at the entry of toll plaza is also possible as long as the inflow rate is overwhelming, though the possibility is not so high. Make a model to determine the optimal number of tollbooths in a barrier-toll plaza, given the freedom to define what the word “optimal” means in the context of paper. Pay special attention to the situation where the number of tollbooths is the same as that of travel lanes and compare that situation on effectiveness with current practice.
Terms and Definition
We assume the toll plaza as [Figure 1]:
Figure 1: The top view of a toll plaza.
A list of relevant variables, constants, and parameters is in [Table 1]. Terms In-pool Out-pool Definitions Space for the vehicles to pass the toll before going to the tollbooths Space for the vehicles to leave the toll plaza when paid for the toll Team # 708 Page 4 of 24
Terms Inflow Outflow Interval Distance numOfLanes numOfBooths The former congestion The latter congestion numOfWaitingInFormer numOfWaitingInLatter minLeavingIntervalInSingleLane The total waiting time maxDriverTolerance (n-m) deployment [abbr. (n-m)] Ci Co α η Definitions The traffic flow into the in-pool The traffic flow into the out-pool The word “Interval” can be either separation in time or in space. Here we just use it in time delay, while the word “Distance” is used for space. The number of Lanes in the highway. The number of tollbooths in the plaza. The 50% filled state in in-pool. The 50% filled state in out-pool. The number of vehicles waiting in the former congestion. The number of vehicles waiting in the latter congestion The minimal interval between two vehicles getting out of the departure in one lane. The total time for one vehicle from entering In-pool to getting out of Out-pool. The maximal total waiting time that a driver can tolerate. A toll plaza configuration with numOfLanes = n & numOfBooths = m The time constant used in the former congestion The time constant used in the latter congestion The second term’s coefficient of time delay in out-pool The third term’s coefficient of time delay in out-pool A diagram with x-axis labeled U and y-axis labeled V Table 1: Terms and Definitions
U-V diagram Assumptions
About Interstate-95
1. According to reference [1], the AADT (Annual Average Daily Traffic) of Interstate-95 in year 2001 is 60,414.
2. According to reference [1], Interstate-95 has 8 lanes and 4 lanes in each direction.
About the weather
1. We assume the weather is fine and has no bad effect on characteristics of the vehicles.
About the driver
1. Usually, the range of reaction time of the human beings is from 200ms to 300ms. We assume it is 250ms.
2. maxDriverTolerance = 5min.
About the vehicles
1. It is assumed that the arrival of vehicles is a bit stochastic, but stationary in the long hurl. As
usual, we model the arrival time of vehicles as Poisson distributed random variables, with the
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intervals following the probability density function:
e-xx0 f(x)x00With 1/λthe average traffic flow rate. 2. Vehicles are homogeneous.
a) All vehicles are in the same length of 4.5m.
b) The distance between two vehicles waiting paying for the toll is the 1.5m.
c) Empirically, it takes a vehicle about 25sec ~ 30sec (27sec on average) to speed up from
0km/h to 80km/h.
d) Empirically, the vehicle has to slide 40m until it can brake at a speed of 80km/h
e) The distance between two vehicles in the same lane getting out of the departure of the
toll plaza is at least 10m so as to avoid collision.
About the tollbooths
1. All the tollbooths are independent. They provide the service for the vehicles independently,
thus they have no idea of correlating the service time to avoid the congestion in the out poll which as the empirical parameter shows is 60s.
About the in-pool & out-pool
1. Empirically, the distance between the entry of toll plaza and each tollbooth is 200m. So does
each tollbooth to the departure. (shown in [Figure 1])
2. The capacity of the in-pool & out-pool is based on their shapes. 3. Ci = 16sec. 4. Co = 20sec 5. η = 5sec. 6. α = 10sec.
Some Facts Derived from Assumptions
1. The acceleration and deceleration of a vehicle can be evaluated:
AccelerationΔvΔt(80/3.6)m/s27sec0.8ms2
(mentioned in Assumption: vehicles. 2. c)) Deceleration v22s(80/3.6)2m/s222*40m6.2ms2
(mentioned in Assumption: vehicles. 2. d))
2. minLeavingIntervalInSingleLane can be evaluated:
Interval = 5sec (mentioned in Assumption: vehicles. 2.e) and acceleration value)
Notes. If we assume a vehicle won’t start to leave until its precedent is on its way with 10m distance, then according to acceleration data, we can derive:
LeavingInterval 2*10m0.8m/s25sec
3. The pool size of both in-pool and out-pool satisfies the following function:
poolSize10*numOfBooths20*numOfLanes
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Note: We can derive the expressions from increment analysis.
If numOfBooths increase by one, the pool will increase by 10 slots. If doing so, the area of pool will grow by one triangle, as shown in the following figure.
How many vehicles the triangle can hold? The triangle has a height of 200 meters long and a bottom, able to hold one vehicle (a tollbooth there). We assume each vehicle is 4.5 meters long and shares a free space of 5.5 meters with its neighbors. By division, 20 vehicles are able to pile in a rectangle with height of 200 meters and width of 1 vehicle, whose area is twice as much as that of triangle. Thus such a triangle can hold 10 vehicles, which is just the coefficient associated with numOfBooths.
On the other hand, if numOfLanes increase by one, the process of analysis is almost the same except that another tollbooth has to be added so as to prevent congestion. Thus the coefficient associated with numOfLanes is 20.
Figure 2: Illustration on increment analysis
Analysis and Model Design
Overview
Our goal is to set up a model to get to know the behavior of toll plaza serving, and then try to use that model to work out the optimal number of tollbooths, with respect to the number of lanes and the definition of “optimal” we raised.
Analysis
Two places are hot spots of congestion, the place before the tollbooths where there could be a very long line (“the former congestion”) and the place before the departure of toll plaza (“the latter congestion”).
The former congestion is related to the serving time of tollbooths, the smaller the serving time is, the less probable will this congestion happen. The latter congestion is related to the leaving rate of the departure and the number of vehicles staying in that position.
These two kinds of congestion are not uncorrelated. Once the latter congestion happens, the former one will happen sooner or later as the only drain of the traffic flow is blocked. However,
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the former congestion will not have such effects.
We can image that the former congestion will happen if the arrival of the vehicles has exceeded the capacity of the tollbooth because of the insufficient tollbooths. On the other hand, if there are too many tollbooths, the vehicles will rush to the departure where is easily blocked after they paid for fees. As a result, the latter congestion happens. Hence, there must exist a reasonable number where the chance of the congestions is in the minimum, which guarantees the maximal traffic flow.
Modeling
There are three parts in modeling.
1. The way to model “the former congestion”
First of all, each vehicle has to take a constant time Ci to pass through in-pool. As soon as the vehicles enter the toll plaza, they will be in line waiting for a certain tollbooth, which, generally speaking, has the shortest line. And then they will go into the in-pool. If the in pool is full, the former congestion will happen as no vehicles can enter the plaza any more.
Each tollbooth serves one vehicle at a time. When finished, the vehicle will leave to out-pool as long as out-pool is not full. If out-pool is full, the \"latter congestion \"will happen and the vehicle has to stay in the position with the side effect of disabling the corresponding tollbooth (no more vehicles can come and be served) until out-pool releases somewhat.
Because of the statement above, it is not identical to classic queuing theory. The number of serving windows keep changing over time rather than remaining constant, as is usually assumed.
2. The way to model “the latter congestion”
As to model “the latter congestion”, several factors or constraints are under consideration before modeling.
The capacity of out-pool is finite. It is not only based on the dimension of the plaza, but also for the sake of suppressing the latter congestion, actively rather than passively. Once out-pool is full, no more vehicles are allowed to pass through tollbooths.
Furthermore, such a traffic flow cannot be modeled as the kind of “flow” which is just like an ideal, frictionless flow in hydrodynamics. Since all the drivers have their own will to drive that no one can have a control over and there is congestion, which means vehicles are generally very close together, it makes sense that vehicles will surely affect each other in the drain of the plaza, which is not the characteristic of an ideal flow. Another important one is a special case: if numOfLane is equal to numOfBooth, then it’s reasonable to assume that there should be no “the latter congestion”. In such a case, no bottleneck exist, every vehicle passing through booths can go along without any disturbance. Our model should include such a case, though naturally.
Finally, we can make the following model:
Any vehicle to go out should endure the following three delays:
A constant interval Co which signifies the distance between the tollbooths and the
departure. An interval signifies the time the vehicle has to take to squeeze through out-pool,
as shown the black area in Figure 2.
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Figure 3: The demonstration on time delay of second term in out-pool.
(Modeling in details) In order to get through out-pool, the vehicle has to cross the trapezoid above.
Since the quantity h should be very small in contrast with the dimension of out-pool, the trapezoid can be regarded as a simple rectangle with the same width as the highway and a height h.
Thus, the area of the trapezoid is proportional to h.
And naturally, the time needed to cross the trapezoid is proportional to the quantity h.
So the time needed to cross the trapezoid is proportional to the area.
On the other hand, the area is proportional to numOfWaitingInLatter, given that each vehicle shares the same area from the top view. Then we have the following expression as the second delay time.
t2hnumOfWaitingInLatterwidthOfHighwaynumOfWaitingInLatternumOfLanes
αis a constant coefficient, we use 10 sec.
An interval signifies that when the vehicle is at the edge of the plaza, how much
extra time is needed to get out of the plaza, including turning and avoiding collision.
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Figure 4: The demonstration on time delay of second term in out-pool.
(Model in details) Here probability method is used to derive the expression of this third delay term.
If the vehicle lies in the rectangle area (with a probability of numOfLanes / numOfBooths), no extra time is needed to get out.
If it lies in the triangle area, some time is needed to squeeze itself to get out. This amount of time is inverse proportional to the width of highway, i.e., numOfLanes, since the wider the highway, the easier it can escape.
By evaluating the expectation, we get: t3(1numOfLanes)1(1numOfLanes)numOfBoothsnumOfLanesnumOfBoothsnumOfLanes
as the time cost in this term (η is a constant coefficient, we use 5sec).
Besides, any two successive vehicles should not get out in one lane within the time
of minLeavingIntervalInSingleLane. If there are multiple lanes, the minimal interval essentially becomes minLeavingIntervalInSingleLane / numOfLanes. At last, we define the delay time in the latter congestion as the following:
TimeDelayInOutPoolConumOfWaitingInLatternumOfLanesnumOfLanes(1)numOfBoothsnumOfLanes
3. The way to define “optimal”
One naturally way to define “optimal” is to maximize the outflow rate from the departure, with respect to numOfBooths.
But we notice that there is another factor not to be considered so far – the satisfaction of vehicle drivers. No one will accept such a situation that from the departure comes out 5sec
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each – the fastest rate to turn out a vehicle in one lane – but one hour has to be spent over passing the whole plaza! Furthermore, that’s also a good subjective measure to inspect drivers’ psychological factor. So the total waiting time of vehicles is yet another important one that shouldn’t be neglected. It needs to be minimized to achieve good traffic condition.
Now we have two objective variables to reach their extremes, respectively. But it is difficult to make it work. One way to solve that is to look the outflow rate as the objective variable and the total waiting time as a constraint. Each solution should have a waiting time short enough to some extent to be feasible, among which one that maximizes the outflow emerges.
Finally, the definition of “optimal” is:
Given the amount of inflow and numOfLanes, find the maximal outflow (and its corresponding inflow-outflow curve) with respect to numOfBooths, subject to the constraint that the corresponding total waiting time is not more than maxDriveTolerance(5min).
Model Result Analysis
We made a simulation program to simulate the model.
For every fixed amount of inflow rate, a stationary traffic inflow of about two hours is
generated, as an excitation, to feed into the model to get the outflow corresponding to that fixed amount, as well as total waiting time. Keep changing the amount, repeating the process above, and then an inflow-outflow curve is produced.
One the curve is available; it needs cutting off according to the information provided by total waiting time so as to fit into the constraint. The following one contains two curves, one (curve in blue) is inflow (vehicles/sec) versus outflow (vehicles/sec) and the other (curve in red) is inflow versus total waiting time (min).
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Figure 5: The inflow-outflow diagram, Demonstrating the part of curve being cut off.
Obviously, the red curve makes a sudden turn and increases nearly exponentially when it reaches the value of five minutes. That is the sign of congestion. It fits very well in our assumption of maxDriveTolerance, also a reasonable result to tell.
Now as written in the previous chapter, the corresponding blue curve, which shares the same inflow amount with the red one above 5 minutes line, will be cut off, infeasible to the following optimal-finding process. That’s why different curves below have different supports in their domains. We find some very good results derived from the model, as shown below. Most of the diagrams below are inflow-outflow curves, except for the special case of (n-n).
Single Lane Case
In the basic case of single lane, the model shows that (1-1) deployment is far from sufficient. The corresponding curve terminates as early as inflow rate is approximately 0.087(vehicles/second), i.e., one vehicle per 11.5 seconds, because the serving rate that one tollbooth can achieve is totally overwhelmed by roaring inflow rate of traffic.
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Figure 6: The inflow-outflow diagram of (1-n) case, both axes in vehicles per second.
In contrast, (1-3) made quite good improvements while (1-n) (n>3) did poor jobs again, as the diagram shown below:
Figure 7: The inflow-outflow diagram of (1-n) case, scaled version.
The green line is optimal solution for (1-n) deployment
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It is not surprised to get such a result. Because with the increase of n, the latter congestion comes to be more and more serious, which made the total waiting time of one vehicle roars, and finally disqualifies some potentially better solutions when the inflow rate increases.
All the curves have a line of y = x as their semi-asymptotes (intersects at x = 0). That identity line indicates an ideal situation, if no traffic disruption.
Multilane case
Since Interstate-95 has eight lanes and four in each direction, we consider (4-n) deployment (n≥4).
As usual, (4-4) made a trivial and poor result. (4-7) deployment is the best one.
Figure 8: The inflow-outflow diagram of (4-n) case, both axes in vehicles per second.
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Figure 9: The inflow-outflow diagram of (4-n) case, scaled version.
Compare optimal solution (1-2) with (4-7), the ratio of numOfLanes to numOfBooths is different. Furthermore, in the 4 lanes case, optimal solution is not as apparent as in the single-lane case. That’s because with the increase of numOfLanes, the serving rate becomes more and more powerful with four or more tollbooths, while the ability of out-pool to discharge appears to be the primary factor that affects the overall turnover.
Here is a table for some relationship between numOfLanes and optimal numOfBooths:
numOfLanes 1 2 3 4 Optimal numOfBooths 3 4 5 7
Table 2: relationship between numOfLanes and optimal numOfBooths
Special (n-n) case
As mentioned in the previous chapter, the (n-n) case deserves special attention. No the latter congestion here. But in all (n-n) cases, toll plazas suffer the same problems of the former congestion. That is to say, in order to make the outflow higher and keep total waiting time in a low rate, we exchange the latter congestion for the former congestion to some extent, as in the case of (1-2) and (4-7).
Here is the diagram of (n-n).
(1-1) case.
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Figure 10: The inflow-outpool’s occupancy diagram of (1-n) case,
x-axis in vehicles/sec, y-axis in percentage
(4-4) case
Figure 11: The inflow-outpool’s occupancy diagram of (4-n) case,
x-axis in vehicles/sec, y-axis in percentage
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One can easily get the idea that (n-n) deployment is always lower than 10% on the percentage of out-pool occupancy, for all inflow traffic. That result is within our grasp, as we analyzed before, there should be no latter congestion in (n-n) deployment. Note that (4-5) is just like (4-4) with no exponential growth, but there is not the case on the relationship of (1-1) and (1-2). That indicates the bottleneck effect is not so serious in (4-5) than in (1-2), understandable in real life.
The answer to the question raised in the problem
Under what conditions is (n-n) deployment more or less effective than the current practice? By inspecting what have been discussed, the answer is easily found.
For the current setting of serving time (60sec), obviously the current practice, allocate more tollbooths than lanes, is much better than allocating the same number in both sides. Because usually vehicles come much faster than single tollbooth can deal with. On the other hand, if serving time can be dramatically reduced to a certain low level (20 sec or less), then (n-n) deployment, free of the latter congestion, will surely perform much better; but (n-m) deployment will suffer more latter congestion, because inflow to out-pool will be overwhelming. So (n-n) is better if more advanced technical achievement is utilized to enhance the productivity of tollbooths. In such a situation, (n-n) will be dominant with the advantage not only of efficiency, but also of financial cost.
The example is listed below. From the two diagrams we know there exists a serving time lying between 40 seconds and 45 seconds that acts as the boundary of the two situations.
Figure 12: The situation that (4-7) is better than (4-4)
With the serving time > 45 seconds
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Figure 13: The situation that (4-4) is better than (4-7).
With the serving time < 45 seconds
Model Verification
In this chapter, we intend to check our model by some real data to prove it is truthful. That is the way from theory to practice. What we used for optimal-finding is stationary random flow; but real traffic flow is non-stationary and inhomogeneous. A rigorous inspection.
Data Acquisition
We use a real daily traffic flow diagram for our simulation on whole day traffic. This flow diagram is from reference [2]:
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Figure 14: The original diagram from reference [2]
Since there is no corresponding table available in the context, we have to sample some discrete points and get a closely approximately diagram in MatLab®:
Figure 15: The extracted diagram from reference [2]
(Some details are left out, but it is insignificant.)
The data were gathered for the three interstates located in the Hampton Roads region
(Charlottesville, Virginia), I-, I-2, and I-5, rather than I-95, so the daily flow is actually different. But it is believed that the curve should share the same shape over most of the interstate highways. So our way to make it fit into I-95 is to evaluate the area surrounded by the curve and x-axis, the daily traffic flow on I-, I-2 and I-5. On the other hand, the average traffic flow on I-95 from reference [1] is known. By scaling, we thus get the correspond counterpart on I-95, which is:
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Figure 16: The extracted and transformed diagram to fit in Interstate-95, from reference [2] Note that at its peak, traffic flow reaches 0.18/second in rush hour, i.e., 5.5 seconds one vehicle. That is also a reasonable quantity.
Simulation
We feed that non-stationary flow into our model as excitation, and get the corresponding response. We use (4-5) ~ (4-10) deployment for this simulation. The following figure shows the average delay for every 10 minutes slots.
Figure 17: The time-delay diagram from [Figure 12]
each unit in x-axis is 5 minutes; y-axis in minutes
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The following is in details:
Figure 18: The scaled time-delay diagram, green line for optimal solution of (4-7) deployment
The green line that indicates (4-7) deployment, enjoys the minimum delay over almost the
whole x-axis, wins over any other deployments. This result proves (4-7) is the optimal solution once again, though from another angle. Since the data to be tested are real-time, it is much more convictive than the stationary counterpart we have used in the early stage.
Model Sensitivity
Some parameters are quite crucial in this model. Here, we plan to analyze three major ones to reveal effects they take, respectively.
Here we examine the sensitivity of model by changing some parameters a little bit, then take a look at how the curve changes. The curve we origin from is the optimal solution we derived, (4-7).
Sensitivity of minLeavingIntervalInSingleLane
Act as a crucial quantity in the whole model, minLeavingIntervalInSingleLane controls the maximal rate of turnover at the departure for one lane. Just like the figure below, this quantity is sensitive:
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Figure 19: The inflow-outflow diagram,
x-axis in second/vehicles(Note! Not the same as previous ones),
y-axis in vehicles/seconds
We can infer that minLeavingIntervalInSingleLane is somewhat the turning point of curves, given the curve is represented in the domain of coming intervals, rather than the domain of inflow rate. It is sensitive partly because it represents for a door laying at the rear of plaza.
Sensitivity of serving time of tollbooths
We change serving time in the range [45 sec, 80 sec] with steps of 5sec. The following figure shows the model’s very robustness.
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Figure 20: The inflow-outflow diagram, x-axis and y-axis in vehicles/seconds
Figure 21: The inflow-outflow diagram, scaled version.
In the range of [45 sec, 65 sec], the curve clusters together like a “bundle”. We can tell that in the neighbor of 60 sec, which we currently set as serving time, the model is relatively
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independent of the value of serving time. So it is less important to look back into how we derived the current amount.
When the efficiency of tollbooths degrades one more step (70sec, 75sec, 80sec), out of the range above, the curve begins to drop down. It’s believed that the capacity of the whole toll system becomes insufficient to hold traffic inflow, with the diminishing amount of ability to serve. Thus, the former congestion comes to life.
Further Work
From our work above, it is more important to get rid of the latter congestion than get rid of the former congestion.
One way is found to be more important to control the latter congestion: The automatic assignment of serving time, or synchronization among each tollbooth. In the rest of this paper, independence of each tollbooth is assumed. That is simple, but not so hopeful in suppress the congestion.
Consider the following system: One lane and two tollbooths and a randomized inflow. Chances are that two vehicles could leave for the departure at the same time and block each other in out-pool, only to delay some extra interval, as inferred by our model. If tollbooths are made to be synchronized, i.e., never make it possible to have vehicles occupying the same time slots to go out, then such extra intervals could be prevented. That is for (1-2) case.
For some cases with multiple lanes and booths, the strategy could be much more complicated. Aim for that kind of strategy could be embodied as minimizing numOfWaitingInLatter, given current inflow that could be detected real-time.
Model Strength and Weakness
Strength
Based on some assumptions of quantity, either empirically or from some references, we derived two-level quantities to be used in this model. That reveals the linkage of different quantities and is more suitable than just assuming a lot without any inference. Use generalized analysis, able to fit into any toll plaza on the earth.
The definition of “optimal” is both subjective and objective, including psychological factors.
Many of the features this model produced are corresponding to things that really happen. Thus it is reasonable.
Consider (n-n) special case (no later congestion here), without piecewise mathematical forms to fit the real world more naturally.
We use real data to verify the effectiveness of this model to be truthful. No financial cost included.
Weakness
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References
[1] 2003-2022 Long Range Transportation Plan Seacoast MPO. August 2003.
[2] Sarah B. Medley and Michael J. Demetsky. Final Report Development of Congestion Performance Measures Using Its Information. January 2003.
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