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Analysis of Downstream Queues on Upstream Capacity Expansion of Urban Signalized Intersection
JOURNAL OF TRANSPORTATION SYSTEMS ENGINEERING AND INFORMATION TECHNOLOGY Volume 12, Issue 3, June 2012 Online English edition of the Chinese language journal Cite this article as: J Transpn Sys Eng & IT, 2012, 12(3), 98−108.
RESEARCH PAPER
Analysis of Downstream Queues on Upstream Capacity Expansion of Urban Signalized Intersection YU Xin1,*, SULIJOADIKUSUMO Goro2, PREVEDOUROS Panos1 1 Department of Civil and Environmental Engineering, University of Hawaii at Manoa, 2540 Dole Street, 383, Honolulu, HI 96822, USA 2 Hawaii Department of Transportation, 869 Punchbowl Street, Honolulu, HI 96813, USA
Abstract: Signalized intersection is a fundamental component of an urban transportation system and appropriate treatments for intersection related congestion and safety issues are increasingly growing in importance. The most direct and intuitive approach to alleviate the recurring congestion is to cope with the peak hour disparity between travel demand and supply at the bottleneck intersections by expanding intersection capacity. However, intersection treatments such as adding lanes, turning movement restrictions, and grade separation that were traditionally applied to improve intersection capacity may not realize the expected benefits of relieving congestion and reducing delay as the traffic conditions at the downstream intersections can be greatly deteriorated by increased upstream arrivals. Additionally, the extended queue generated from downstream intersections can spill back into the upstream intersection and diminish the performance of the upstream treatment. This phenomenon is frequently observed in large urban areas where the traffic volume is heavy, intersection spacing is short and cycle length is long. This study was conducted to provide traffic engineers with a simple, practical and step-by-step analysis method to identify the occurrence and the type of queue spillback (Cyclic and Sustained), to determine the effects of downstream queues on upstream capacity, and to select the best capacity expansion treatment. The theory and methods for measuring the consequence of downstream queue effects and quantifying the potential capacity cutoff are developed based on the updated queue size and intersection capacity estimation methodologies for signalized intersections in the Highway Capacity Manual 2010 (HCM 2010). A spreadsheet-based computational tool was developed to assist in the process of capacity constraint identification and calculation. A case study is presented to demonstrate the practical use of the analysis method. Key Words: urban traffic; signalized intersection; queue spillback; capacity expansion
1
Introduction
An intersection where traffic flows in different directions converge plays an essential role in the urban transportation network. Most of the signalized intersections are located in urbanized areas and allow for heavy traffic of motorized and non-motorized vehicles as well as that of pedestrians. A properly designed, timed, and maintained traffic signal can be expected to provide for the orderly and efficient movement of intersection users and to reduce the frequency and severity of certain types of conflicts. However, for a variety of reasons such as population, economic and auto ownership growth, increasing traffic demand can quickly exceed the capacity of urban intersections during peak periods. As a consequence, the traffic level of service deteriorates, and the safety risk
increases. Severe traffic congestion also causes unnecessary and excessive fuel consumption, emissions, and noise pollution. Furthermore, the sharply deteriorated traffic conditions are not only restricted at a single intersection. Queues can grow long at a saturated intersection and block driveways, access roads, and adjacent major intersections; so, the negative effects of intersection congestion can be both local and regional. Capacity expansion at a signalized intersection by adding lanes, channelizing, converting to grade-separated structures, restricting certain movements, or reducing signal phases are the most direct approaches that are used to alleviate the deteriorating traffic conditions. Additional capacity is expected to address the peak-period imbalance between travel
Received date: Jan 9, 2012; Revised date: Mar 7, 2012; Accepted date: Apr 4, 2012 *Corresponding author. E-mail: [email protected] Copyright © 2012, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(11)60206-7
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demand and supply in a short term, but the congestion will reoccur over the long term due to latent demand. However, instead of investigating the cost effectiveness of intersection capacity expansion in the long term, this study is aimed at discussing how to determine and measure the immediate and interactive impacts between a signalized intersection capacity expansion and its downstream congestion. In reality, the benefits of capacity improvement in a non-isolated intersection can be significantly diminished by downstream queues. Since expanded upstream capacity will increase traffic demand and queue size at downstream intersections, the extended queue generated from downstream intersections can quickly use up the queue storage and overspread all the space between intersections, which results in queue spillback and lane blockage. When downstream queues spread back into upstream and prevent vehicles from entering the upstream intersection on green, the actual traffic-carrying capacity of the upstream intersection would be much lower than its design capacity.
The queue interaction between two paired intersections also creates many safety concerns, especially for grade-separated structures where hazardous rear-end collisions may occur when the exiting high-speed traffic suddenly comes across the stopped, queuing traffic. Sideswipe crashes may also be observed, as existing vehicles make an unexpected and unsafe lane changes in order to avoid hitting the back of the queue. A simplified example as indicated in Fig. 1 is used to demonstrate the queue interaction between two closely spaced intersections (Intersection A and B). The eastbound through the approach of Intersection A is carrying 2,000 peak-hour vehicles. The before-treatment condition through the capacity of Intersection A is 1,600 veh/h and that of its downstream intersection (Intersection B) is 1,200 veh/h. The back-of-queue size that aggregated on the upstream segments of both intersections would be 400 veh/h, if the midblock traffic generation and the contribution of left and right turns at Intersection A are minimal and ignorable.
Fig. 1 Demonstration of downstream queue effects on intersection capacity
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
Provided one through lane is added to Intersection A and the through capacity theoretically increased from 1,600 to 2,000 vehicles per hour, the back-of-queue on the eastbound through of Intersection A is expected to be eliminated, but the queue size at its downstream Intersection B would be increased to 800 veh/h, which is twice more than the before-treatment condition. However, if the link between two intersections can only process 600 queuing vehicles per hour, then the remaining 200 vehicles are unable to enter Intersection A and have to stay on its upstream segment, resulting in the operational capacity of Intersection A eastbound through being down to 1,800 vehicles per hour. The downstream queue spillback affects any upstream movement for which the intended destination is being blocked. However, the effects of queue interaction are restricted to the nearest downstream intersections. As shown in the example just cited, the volume exiting Intersection B toward further downstream (1,200 veh/h) remains unchanged after deploying the treatment used in Intersection A. The HCM methodology used in estimating signalized intersection delay and the level of service does not take into account the effect of queue spillback from a downstream signal and is unable to provide an accurate estimation if spillback is present[1]. Simulation models are recommended and also commonly accepted by traffic engineers for modeling intersection operations when the queue interaction between two closely spaced signalized intersections is suspected. Although simulation models can measure the interactions of individual vehicles, conducting a network-wide analysis of queue evolvement, and providing detailed and visual information on queue effects, traffic simulation are always a time- and resource-consuming and data-intensive endeavor. To address these deficiencies, this study is designed to provide a quick and practical analysis method by often using readily available data and standard engineering parameters that evaluate the interactions between downstream queues and upstream capacity. The method can be used to assist traffic engineers in examining the application of capacity expansion treatment at urban major intersections. Through measuring and comparing the potential capacity loss for different capacity expansion alternatives, the most beneficial and effective option can be identified, and whether significant additional resources should be utilized for a traffic simulation or further detailed analysis can also be determined.
2
Literature review
A large body of research exists highlighting the effects of queue interactions at closely spaced signalized intersections in an urban road network, especially the potential upstream capacity cutoff caused by downstream queue spillback. Kittelson & Associates‘s research found that queue spillback is one of the most common causes of flow restriction at
congested intersections[2]. The Traffic Timing Manual has recommended that the performance measures of intersection treatments should include queue lengths, and the objectives are to minimize the time period during which the queue spillback or spillover exists and to manage queue interactions between intersections during oversaturated conditions. According to the AASHTO Green Book[3], upgrading an existing at-grade intersection to interchange in an urbanized area may create a queue spillback problem and affect traffic on the interchange off ramp. NCHRP Report 345 exploited the design and operation of single-point urban interchange and indicated that queue spillback from the downstream intersection was found to have an adverse effect on the safety of the off-ramp maneuver and led to a significant reduction in the efficiency of the off-ramp movements[4]. Papageorgiou presented an overview of the approaches that optimize the use of the traffic signal for an urban road network and concluded that isolated intersection control strategies, especially increasing intersection capacity, can dissipate queues at a maximal flow rate so as to minimize the travel delay at an isolated intersection. However, as for an intersection group rather than an isolated intersection, over-saturation’s forward transfer cannot alleviate the global saturation degree; hence, the potential for an increase in the travel delay of an intersection group and the risk of capacity loss do exist[5]. Many researchers have also been devoted to the identification and evaluation of downstream queues interfering with capacity, delay, and level of service of its upstream intersection. The City of Portland, Oregon, presented a traffic micro-simulation model that simulates the upstream capacity affected by the downstream queue built-in and spillback. The model needs the EMME/2 type network data as input, plus the lane configuration of adjoining intersections[6]. A new series of the traffic analysis module was integrated with the recent versions of Trafficware’s Synchro Studio, which examine how queues can reduce capacity through spillback, and a new queue-delay factor was introduced to measure the additional delay incurred by the capacity loss[7]. Elefteriadou conducted a research on the method used for the operational analysis of the internal overflowing queue blockage of diamond interchange ramp terminals on at-grade intersections based on the results of simulations to predict different measures[8]. Another research project led by the Texas Tech University found that both the Synchro and Elefteriadou’s methods overestimate delay and queue effects under a certain condition. It introduced an open-source mathematical model based on the HCM 2000 delay model[9]. There is more research on the intersection capacity estimation by considering queue effects under various conditions. For example, a complex genetic algorithm (GA)-based program that is capable of capturing the dynamic interactions of spillback queues among lane groups and
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
between neighboring intersections due to high demand, geometric constraints, or signal settings was described by Liu and Chang[10]. A simulation-based algorithms was developed by Gordo to control spillback from the ramp meters of upstream interchange of freeways for the high-amplitude limit cycle operation[11]. Ahmed and Abu-Lebdeh developed a macroscopic model for a hypothetical two-signal system to estimate the delay at signalized intersections caused by downstream congestion, using basic traffic flow properties and control parameters at neighboring intersections[12]. The Virginia Transportation Research Council reviewed a variety of computer programs that are capable of analyzing capacity at signalized intersections and recommended TRAF-NETSIM for capacity simulation analysis at non-isolated intersections where queuing and spillback are potential problems[13]. While reviewing these models, one can observe that most of these analytic approaches on queuing effects between intersections are either data intensive and require network-wide simulation models or compute intensive and need system-wide mathematical programming models. Network or system-wide simulation models are generated from a set of data, including traffic distributions, road system topographic maps, and characteristics of each link and node. It may be difficult and expensive to conduct a network- or system-wide investigation to gather the necessary information for applying these models, especially in the early stage of alternative screenings or for a minor/temporary intersection improvement project with a limited budget, such as signal optimization and temporary left-turn restriction. Therefore, a careful planning-level downstream effect analysis is essential to determine whether such effort should be expended and to develop a prioritized list of potential capacity expansion projects for major intersections. For example, in the primary
urban center of Honolulu with a population of approximately 500,000, about three dozen major intersections should be investigated. The method introduced in this article assists in determining whether significant additional resources should be expended for investigating a given site, so that most promising locations can be selected for subsequent analyses.
3
Methodology
The study described a systematic analysis method to determine whether queue spillback-related capacity cutoff will occur during the analysis period and to measure how the increased capacity at the subject (upstream) intersection deteriorates downstream traffic conditions. The full set of the analysis method shown in Fig. 2 consists of two interactive processes: evaluation process and calculation process. The evaluation process is used to identify the performance of the proposed treatments for the subject intersection. The calculation process focuses on the analysis of the traffic operation and the queuing condition at the downstream intersections and estimates the maximum rate of downstream traffic arrivals from the upstream intersection (i.e., the threshold of queue spillback). The threshold value is an essential input for the evaluation process in determining the feasibility and effectiveness of treatments. Although queue spillback may also occur due to oversaturation at unsignalized intersections and access points between major intersections, this study only considers the queue interactions between the paired signalized intersections, because the method described in this study is developed based on the HCM 2010 back-of-queue size and the capacity analysis procedures for signalized intersections.
Fig. 2 Flow chart of analysis method on downstream queue effects
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
3.1 Calculation process The methodology used in the calculation process is based on the queue accumulation and intersection capacity estimation methods introduced in the newly released HCM 2010. The queuing calculation in HCM 2010 is derived from Akcelik’s research[14] on the estimation of the full-stop rate at signalized intersections for uniform arrivals. Akcelik’s method was extended by Olszewski[15] for the platooned arrival type and the Texas Transportation Institute[16] for the coordinated actuated signal system. HCM 2010 further refined the estimation technique of back-of-queue size by eliminating slowing and partially stopped vehicles. An acceleration-deceleration delay da term is used to distinguish between a fully and a partially stopped vehicle[1]. da =
1.47(Sa − Ss )2 1 1 ( + ) 2Sa ra rd
where, Sa=average speed in the intersection approach (mi/h); it can be estimated by a posted speed limit Spl with the equation Sa=0.90(25.6+0.47 Spl); Ss=threshold speed defined for a stopped vehicle=5.0 (mi/h); ra=acceleration rate = 3.5 (ft/s2); rd=deceleration rate = 4.0 (ft/s2). The idea behind the derivation of the methodology in the calculation process is to investigate the capacity constraint of downstream queues by reversing and integrating the HCM procedures of intersection capacity and queue size estimation. According to HCM 2010[1], the queue size in any lane of a certain lane group can be estimated by accounting for the queue caused by the signal cycling through its phase sequence and the effect of random and cycle-by-cycle fluctuations in over-capacity demand. The provided signal timings and the queue storage capacity at two adjacent signalized intersections are known, through solving the inverse function of the arrival rate element in HCM queue size and intersection capacity estimation models, the downstream arrivals, subject to avoidance of queue spillback, for a certain lane group of the downstream intersection can be calculated by the equation given next: gQs ⎧ ⎪ qi = C ((Q − d s ) P − gs ( P − 1)) ⎪ a ⎨ g ( P − 1)(CQ + 450 gs ) ⎪q = ⎪⎩ i C 2 (d a P + g ( P − 1)) + 450Cg ( P − 1)
with
Q=
(Q < s (d a
P + g )) P −1
(Q ≥ s (d a
P + g )) P −1
(1)
D + Lv Lv
where, qi=traffic flow rate from the subject intersection to a lane group in its signalized downstream approach (veh/s/ln); Q=maximal back-of-queue size limited by the storage capacity of the road linking the two intersections, that is, the
maximum backward distance in vehicles over which the queue extends from the stop line of downstream intersections during a typical cycle (veh); s=adjusted saturation flow per second per lane in the lane group in the downstream approach (veh/s/ln). Note that the saturation flow of shared and exclusive lanes varies and should be estimated by using the methods defined in HCM 2010; g=effective green time for the lane group in the downstream approach (s); C=cycle length of the downstream intersection (s); D=specified distance between the exit of the subject intersection and the stop line of its downstream intersection. It approximates the intersection spacing if both are at-grade intersections (ft); Lv=average spacing between vehicles in a stopped queue, assumed to be 25 ft[16]; P=proportion of the vehicles arriving on green. Equation (1) is applicable for an individual lane; the arrival rate and saturation flow for the lane group have to be converted into individual lane values before applying this equation. The unequal lane utilization in a lane group is not reflected in the calculation, and no initial queue at the start of each analysis period is assumed. The inequalities in the parentheses of Equation (1) are used to determine the type of queue spillback (cyclic or sustained) by measuring whether the lane group in the downstream approach operates under capacity. Based on the definition in Chapter 17 of HCM 2010[1], if the intersection spacing and effective green time allow the downstream approach operating under this capacity, then queue spillback occurs. This spillback can be classified as cyclic spillback and may result from the long downstream cycle length and/or the poor quality of signal progression between intersections. If there is oversaturation at the downstream intersection, then the sustained spillback occurs. The impedance of sustained spillback could not be mitigated until either the downstream capacity is increased or the upstream demand is reduced. The proportion of all vehicles arriving during green (i.e., Parameter “P” in Eq. (1)) is recommended to be observed in the field, because it has a significant impact on the estimation of queue backup and capacity constraint. It can also be estimated by arrival type and platoon ratio at the downstream approach according to HCM (i.e., P=Rp g/C, in which “Rp” is platoon ratio and the default value of “Rp” can be computed by Rp=Arrival Type/3) (1). Downstream arrival type depends on the type of capacity expansion treatments deployed in the upstream intersection. If full or partial grade-separation treatment is applied, then downstream traffic arrivals can be assumed to have a random and uniform arrival flow profile. If adding lane or other at-grade capacity improvement treatments are used, then a dispersed and moderately dense platooned
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arrival type may be more appropriate. Arrival Type 4 (Rp=1.33) is commonly used to establish signal progression for the peak period or travel direction if signals at the paired intersections are properly coordinated. Other arrival types, such as type 1 (Rp=0.33) and 2 (Rp=0.67), can be used if traffic engineers presume a poor coordinated signalization. The progression for the off-peak hours or uninterrupted flow is usually characterized as Arrival Type 3 (Rp=1.00). Therefore, if the arrivals are effectively random, then the proportion of vehicles arriving on green equals the green/cycle ratio (i.e., P=g/C), and Eq. (1) can be rewritten as given next: gs (C − d a − g ) Qs ⎧ (Q < ) (2) ⎪qi = (C − d a − g ) s + Q ⎪ ⎨ (C − g )(CQ + 450 gs ) ⎪q = ⎪⎩ i C (C 2 − C (d a + g − 450) − 450 g )
C−g
gs (C − d a − g ) (Q ≥ ) C−g
The downstream arrival rate calculated by Eq. (1) (for platooned arrivals) or Eq.(2) (for uniform arrivals) is only the proportion of total approaching traffic and contributes to the longest queue found in one of the lane groups in the downstream approach. It has to be repeated for each lane group in order to determine the global maximal downstream arrival rate under the constraint of queue storage capacity, intersection configuration, and signalization. Once the arrival rate for each lane group in the downstream approach is computed, then the maximal downstream arrival rate that can be accommodated by the downstream approach and queuing space is calculated by using the equation given next: qmax=min(qiNi/Pi) (3) where, qmax=maximum arrivals at the downstream approach so as to avoid the queue generated from any downstream lane group from spilling back into the subject intersection (veh/s); Ni=number of lanes in a lane group of the downstream approach; Pi=proportion of lane group volume in the entire approaching volume. At any higher downstream arrival rate than the maximal rate (qmax) during an average signal cycle, the longest spillback queue generated in a certain downstream lane group will prevent upstream vehicles which are approaching that lane group from entering the intersection. Therefore, the downstream arrival capacity (Cda) can be computed with Eq. (4): Cda=3600qmax (4) The upstream departure volume, plus the traffic gained or lost at midblock access points (if not negligible), should not exceed the downstream arrival capacity in order to avoid queue spillback. The restriction of upstream departure volume imposes a constraint on the traffic-carrying capacity of the upstream intersection. The capacity constraint estimated by Eqs. (3) and (4) is derived from the longest queue at the downstream approach and is a conservative estimate. When the queue spillback
occurs and blocks some lanes or movements at the upstream intersection, then some other lanes or lane groups may still have space to receive the oncoming traffic. However, in order to minimize the potential of queue spillback and related traffic operations and safety concerns, it could be more scientific and reasonable to determine the subject intersection capacity constraint by considering the longest downstream queue, because there will always be a certain amount of weaving and lane changing between the entrance and the exit, and the different movements may interfere with each other so that the queue in one lane may spread across the other lanes and eventually block all the traffic. Due to the complexity involved in the formulation of the calculation process and in order to reduce the chances of error, if attempting to calculate by hand, an interactive spreadsheet tool is developed by using Microsoft Excel 2007 to quickly execute the calculation process. The spreadsheet user is taken through this computerized tool where traffic and geographic information at the downstream intersection is collected, and the calculation is automatically processed. As shown in Fig. 3, the spreadsheet tool is a one-page worksheet containing three sections: Inputs, Summary, and Output. The user is required to select the lane group and enter data, including the downstream intersection geographic and signal timing information, in the green boxes of the input section. The summary section includes the intermediary outputs during the calculation process, such as the acceleration/deceleration delay, the types of queue spillback, and the order of spillback occurrence. These values provide a handy review and assist in understanding the final output. Especially, this section specifies “the determinant lane group,” which would most likely generate the longest queue and be the first one that creates queue spillback and lane blockage at the upstream intersection. The value of the downstream arrival capacity presented in the output section of the worksheet is used as a crucial input for the evaluation process to justify the feasibility of a capacity expansion treatment and, if justified, to determine the potential loss in capacity during the analysis period. 3.2
Evaluation process
As shown in Fig. 2, a four-step evaluation procedure that was proposed to examine the performance of upstream capacity expansion treatment and to determine the capacity loss resulting from downstream queues is described in the next few paragraphs. Identify the treatment and its downstream intersections affected by the proposed treatment. During this step, the downstream intersections that will experience higher traffic demand after treatment should be identified. It depends on the approach where the treatment will be deployed. For example, adding through lanes on westbound at an upstream intersection may only affect its westbound downstream
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Downstream capacity constraint calculation worksheet
Downstream Intersection
Test Example
Analyzed by:
Xin Yu
Test Example
Project:
Test Example
Agency or Organization:
23-Feb-12
Date and Time:
Location:
University of Hawaii
Inputs A. Downstream intersection condition
Units
Posted Speed Limit
mi/hr
25
Distance to Upstream Int (D)
ft
900
Estimated Cycle Length (C)
sec
120
Select Lane Group (LG)
-
TH+RT
TH
RT
No. of Lanes
-
1
2
1
veh/s/ln
0.25
0.48
0.45
-
0.25
0.65
0.1
sec
25
25
25
-
3
3
3
mi/hr
34
sec
10
ft
25
veh
37
B. Lane configuration and signal timing
Saturation flow % LG Vol in Total Approaching Vol (Pi) Effective Green (g) Arrival Type
NA
Summary Avg. Approach Speed (Sa) Acc/Dec Delay (da) Veh Spacing in Queue (Lv) Max Back-of-Queue Size (Q )
-
TH+RT
TH
RT
% Veh Arriving on Green (P)
Lane Group (LG)
-
0.21
0.21
0.21
Cyclic or Sustained Spillback
-
Sustained
Sustained
Sustained
veh/s/ln
0.11
0.15
0.14
Max. Arrival Rate to LG (qi) Order of Spillback Occurrence
-
1
2
3
Determinant Lane Group
-
YES
NO
NO
Output Downstream Arrival Capacity (Rounded to the nearest 5)
veh/h
NA
1560
Fig. 3 Example calculation process using spreadsheet tool
intersection, and conversion to a four-way interchange may affect all the approaches and their associated downstream intersections. (ii) Identify Before-Treatment Downstream Arrival Volume. As depicted in Fig. 4, the before-treatment volume of each entry movement toward the downstream segment needs to be obtained. It can measure data in the field or forecasted volume for future years. The traffic entering and exiting from the driveways and access points between the two intersections may be assumed to be nonexistent or negligible if no midblock volume data are available or are in the preliminary planning stage. However, if the number of vehicles generated from the driveways, stop-controlled intersections, and access points within the downstream segment are available or suspected to be significant, then the amount should be
included in the estimation of total arrival volume. (iii) Determine the feasibility of capacity expansion at the subject intersection. This step is designed to examine whether the existing intersections condition and the queue storage capacity of link segments can accommodate an upstream capacity expansion. The determination of the downstream queuing condition in the calculation process (i.e., the determination of the determinant lane group and the downstream arrival capacity) should be done before conducting this step. If downstream arrival volume under the no-build condition computed in the previous step has already been higher or equal to the downstream arrival capacity, then queue spillback from the downstream intersection may already occur at the base condition. In this case, an upstream capacity improvement project cannot be justified, because the
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
Subject intersection
Downstream intersection
-Entry movements -Downstream segment
Fig. 4 Entry movements and downstream segment between two signalized intersections
implementation of a capacity expansion treatment would be counter-productive and have a negative effect on the traffic operations and safety at both subject and downstream congestions. (iV) If potentially feasible, determine the possible capacity cutoff. If the downstream arrival capacity has not been reached under the no-build condition, then the additional capacity at the upstream intersection may be possible. However, due to a potential increase in downstream arrivals, the extended downstream queues still have the possibility of restricting the upstream departure volume. Regardless of the treatment types, if the downstream arrival capacity is not more than the sum of the base downstream arrival volume and the capacity increment obtained from the treatment (i.e., the design capacity of the treatment facility), then the difference between the downstream arrival capacity and the sum would be the potential capacity loss. A positive capacity loss means the treatment may be unable to operate at a full capacity during the analysis period.
4
Case study
A case study is described in this part that illustrates the practical application of the analysis method. The subject intersection used in the case study is on the urban arterials Vineyard Boulevard and Punchbowl Street in downtown Honolulu, Hawaii. The eastbound (EB) and westbound (WB) of the subject intersection have been experiencing heavy congestion during peak periods. A partial grade-separation treatment by using one underpass though lanes and an at-grade treatment by adding one regular through lanes are proposed to be implemented in congested approaches to expand the intersection capacity. Since the grade-separated underpass lane theoretically obtains 100% green time at a signalized intersection and allows for uninterrupted through movement, in the urban condition, one underpass lane is anticipated to provide 1,620 veh/h additional through capacity for each of
the approaches (=default 1800 veh/h×0.9 area type factor). Considering the alternative adding lane treatment, given the through movement green-cycle ratio (0.37) at the subject intersection, the estimated additional capacity per regular through lanes is 600 veh/h, only about 2/5 of the underpass lane capacity. However, the expected capacity of the treatments added to the subject intersection may be negated by the downstream queues. The four-step evaluation process is applied to assess the capacity expansion treatments for this intersection. Step 1: In the first step, the downstream intersections that are suspected to be directly affected by the increased traffic arrivals from the subject intersection should be identified. As shown in Fig. 5, the subject intersection immediately connects to a signalized intersection: Vineyeard Boulevard and Queen Emma Street (V-Q Intersection) on its west end and the signal spacing is approximately 635 ft. Since the EB downstream approach connects a freeway on-ramp (midblock Miller Street is a right in/right out stop-controlled access point), no queue spillback effects on the subject intersection from the downstream freeway on-ramp is assumed. Note that a heavy congested freeway could also generate a queue on its access points, and the queue spillback may occur and affect adjacent intersections along the freeway on and off ramps. However, this study only accounts for the effects between signalized intersections and the queue spillback from freeway ramps, which is beyond the scope of this research. The WB approach of V-Q Intersection (i.e. the WB downstream approach of the subject intersection) has two through lanes, one exclusive left turn lane and one shared right/through lane. The posted speed limit is 30 mi/h. The percentage of left turns in the total WB approaching volume is averagely 18% for peak periods. The V-Q intersection signal timing plan during the peak periods is 160 s cycle length, 22 seconds green for the WB left turn, and 80 s for the WB through and right turn. The signalization of intersections is assumed to be properly coordinated.
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
downstream arrival rate exceeds its arrival capacity; so, the left-turn lane group of the V-Q intersection is the determinant lane group, and the queues in this lane group constrain the capacity of the upstream intersection.
N
The queue spillback at the left-turn lane group can be classified as sustained spillback, and the through/right-turn lane group generates cyclic spillback during the analysis period. According to HCM 2010 (1), the queue at the through/right-turn lane group is only growing during the red indication and will begin to dissipate once the green light presents. However, the sustained spillback at the left -urn lane occurs at some point during the analysis period and is a result of over-saturation. Step 3: The values of downstream arrival capacity obtained in the calculation process are used in this step, and the next step involves determining the feasibility and the capacity loss of the upstream capacity expansion treatments. The subject intersection is currently carrying 1,200 vehicles per hour toward its downstream approach. As long as the upstream departure volume after-treatment does not exceed the downstream arrival capacity (1,810 veh/h for underpass lane and 1,830 veh/h for regular lane), it would be possible for the treatment to provide the subject intersection with additional throughput and to improve the peak-period traffic conditions to some extent. Step 4: As shown in Table 1(b), the additional capacity is restricted to 610 veh/h for the underpass lane alternative and to 630 veh/h for the regular lane alternative as a result of the downstream queue effects, which means the underpass lane would only operate at less than half of its full capacity during the peak periods, and the remaining capacity is cut off due to queue spillback. Although the design capacity of the regular through lane is much lower than that of the underpass lane, the treatment of adding an at-grade lane can perform at its full capacity and it actually functions the same as the much more expensive underpass treatment.
Fig. 5 Layout of case study intersection
Step 2: Once the traffic and geographic information of the downstream intersection are identified, the before-treatment arrival volume at the downstream approach has to be determined in this step. The cumulative entry volume toward the WB downstream approach is 1,200 veh/h during the peak periods. A few driveways exist in the WB downstream segment, but their traffic generation is negligible. Calculation Process: The calculation process is introduced before conducting the last two steps of the evaluation process and is conducted by using the spreadsheet tool. For the underpass treatment, the downstream arrival type is assumed to be random. For the at-grade regular lane, Arrival type 4 (moderately dense platoon arriving during the green interval) is used in this process. As indicated in the calculation results summarized in Table 1(a), the growing vehicle queue in the left-turn lane group will first spill back into the upstream intersection once the
Table 1(a) Summary of case study calculation process results Upstream treatment Underpass lane
At-grade lane
Movements of downstream approach
Arrival type
Type of spillback
Determinant of arrival capacity
Left turn
3
Sustained
YES
Through/right turn
3
Cyclic
NO
Left turn
4
Sustained
YES
Through/right turn
4
Cyclic
NO
Downstream arrival capacity (veh/h) 1,810
1,830
Table 1(b) Summary of case study evaluation process results Upstream treatment
Downstream arrival capacity (veh/h)
Existing arrival volume (veh/h)
Maximal additional upstream departure volume
Design capacity of treatment facility (veh/h)
Capacity loss (veh/h)
Underpass lane
1,810
1,200
610
1,620
1,010
At-grade lane
1,830
1,200
630
600
0
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Therefore, it may be concluded from the analysis that both solutions are feasible for improving the subject intersection condition, but the adding lane alternative may be a better solution for the intersection. The underpass lane does not appear to be a cost-effective treatment if it is solely designed to address bottleneck intersection congestion and reduce peak hour delay, because more than half of its capacity is wasted due to the capacity constraint from downstream queues.
5
Urban Interchange Design and Operations Analysis, NCHRP Report 345, Transportation Research Board, 1991, 28–31. [5]
References
of Electrical and Electronics Engineers, 2003, 91(12): 2043–2067. [6] Simon P M, Nagel K. Simple Queueing Model Applied to the city of Portland, Los Alamos National Laboratory, Report LA-UR-98, 2-10 Jul. 1998. [7]
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[11] Gordon R L. Algorithm for controlling spillback from ramp meters. Journal Transportation Research Record 1554, Transportation Research Board, 1996, 162–171. [12]
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Conclusions
Adding capacity on one intersection in a group can worsen downstream traffic and generate longer back-of-queue size. Extended downstream queues, in turn, can reduce upstream capacity through spillback. This issue has been well recognized, but there is a lack of practical and systematic approaches available that analyze this problem. The main purpose of this research was to develop a quick and practical analysis method for identifying the potential queue spillback between signalized intersections and evaluating the interactive impacts of the downstream queues on the capacity expansion at a non-isolated intersection. This method provides an analytical and step-by-step process for assisting in decision making throughout the alternative selection and screening procedure and consists of a four-step evaluation process and a calculation process. The calculation process is programmed in a computational tool that automates the application of the calculation methodology. From the results of the analysis method, traffic engineers and planners will be able to select the most feasible and effective alternatives for an intersection capacity improvement project by minimizing the possibility of downstream queue spillback and maximizing the treatment performance.
[1]
[4] Messer C J, Bonneson J A, Anderson S D, et al. Single Point
[16]
Bonneson J A, Pratt M P, Vandehey M A. Predicting the
Officials. A Policy on Geometric Design of Highways and
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Report of NCHRP Project 3-79, D1-D42, Jan. 2008.
RESEARCH PAPER
Analysis of Downstream Queues on Upstream Capacity Expansion of Urban Signalized Intersection YU Xin1,*, SULIJOADIKUSUMO Goro2, PREVEDOUROS Panos1 1 Department of Civil and Environmental Engineering, University of Hawaii at Manoa, 2540 Dole Street, 383, Honolulu, HI 96822, USA 2 Hawaii Department of Transportation, 869 Punchbowl Street, Honolulu, HI 96813, USA
Abstract: Signalized intersection is a fundamental component of an urban transportation system and appropriate treatments for intersection related congestion and safety issues are increasingly growing in importance. The most direct and intuitive approach to alleviate the recurring congestion is to cope with the peak hour disparity between travel demand and supply at the bottleneck intersections by expanding intersection capacity. However, intersection treatments such as adding lanes, turning movement restrictions, and grade separation that were traditionally applied to improve intersection capacity may not realize the expected benefits of relieving congestion and reducing delay as the traffic conditions at the downstream intersections can be greatly deteriorated by increased upstream arrivals. Additionally, the extended queue generated from downstream intersections can spill back into the upstream intersection and diminish the performance of the upstream treatment. This phenomenon is frequently observed in large urban areas where the traffic volume is heavy, intersection spacing is short and cycle length is long. This study was conducted to provide traffic engineers with a simple, practical and step-by-step analysis method to identify the occurrence and the type of queue spillback (Cyclic and Sustained), to determine the effects of downstream queues on upstream capacity, and to select the best capacity expansion treatment. The theory and methods for measuring the consequence of downstream queue effects and quantifying the potential capacity cutoff are developed based on the updated queue size and intersection capacity estimation methodologies for signalized intersections in the Highway Capacity Manual 2010 (HCM 2010). A spreadsheet-based computational tool was developed to assist in the process of capacity constraint identification and calculation. A case study is presented to demonstrate the practical use of the analysis method. Key Words: urban traffic; signalized intersection; queue spillback; capacity expansion
1
Introduction
An intersection where traffic flows in different directions converge plays an essential role in the urban transportation network. Most of the signalized intersections are located in urbanized areas and allow for heavy traffic of motorized and non-motorized vehicles as well as that of pedestrians. A properly designed, timed, and maintained traffic signal can be expected to provide for the orderly and efficient movement of intersection users and to reduce the frequency and severity of certain types of conflicts. However, for a variety of reasons such as population, economic and auto ownership growth, increasing traffic demand can quickly exceed the capacity of urban intersections during peak periods. As a consequence, the traffic level of service deteriorates, and the safety risk
increases. Severe traffic congestion also causes unnecessary and excessive fuel consumption, emissions, and noise pollution. Furthermore, the sharply deteriorated traffic conditions are not only restricted at a single intersection. Queues can grow long at a saturated intersection and block driveways, access roads, and adjacent major intersections; so, the negative effects of intersection congestion can be both local and regional. Capacity expansion at a signalized intersection by adding lanes, channelizing, converting to grade-separated structures, restricting certain movements, or reducing signal phases are the most direct approaches that are used to alleviate the deteriorating traffic conditions. Additional capacity is expected to address the peak-period imbalance between travel
Received date: Jan 9, 2012; Revised date: Mar 7, 2012; Accepted date: Apr 4, 2012 *Corresponding author. E-mail: [email protected] Copyright © 2012, China Association for Science and Technology. Electronic version published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1570-6672(11)60206-7
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
demand and supply in a short term, but the congestion will reoccur over the long term due to latent demand. However, instead of investigating the cost effectiveness of intersection capacity expansion in the long term, this study is aimed at discussing how to determine and measure the immediate and interactive impacts between a signalized intersection capacity expansion and its downstream congestion. In reality, the benefits of capacity improvement in a non-isolated intersection can be significantly diminished by downstream queues. Since expanded upstream capacity will increase traffic demand and queue size at downstream intersections, the extended queue generated from downstream intersections can quickly use up the queue storage and overspread all the space between intersections, which results in queue spillback and lane blockage. When downstream queues spread back into upstream and prevent vehicles from entering the upstream intersection on green, the actual traffic-carrying capacity of the upstream intersection would be much lower than its design capacity.
The queue interaction between two paired intersections also creates many safety concerns, especially for grade-separated structures where hazardous rear-end collisions may occur when the exiting high-speed traffic suddenly comes across the stopped, queuing traffic. Sideswipe crashes may also be observed, as existing vehicles make an unexpected and unsafe lane changes in order to avoid hitting the back of the queue. A simplified example as indicated in Fig. 1 is used to demonstrate the queue interaction between two closely spaced intersections (Intersection A and B). The eastbound through the approach of Intersection A is carrying 2,000 peak-hour vehicles. The before-treatment condition through the capacity of Intersection A is 1,600 veh/h and that of its downstream intersection (Intersection B) is 1,200 veh/h. The back-of-queue size that aggregated on the upstream segments of both intersections would be 400 veh/h, if the midblock traffic generation and the contribution of left and right turns at Intersection A are minimal and ignorable.
Fig. 1 Demonstration of downstream queue effects on intersection capacity
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
Provided one through lane is added to Intersection A and the through capacity theoretically increased from 1,600 to 2,000 vehicles per hour, the back-of-queue on the eastbound through of Intersection A is expected to be eliminated, but the queue size at its downstream Intersection B would be increased to 800 veh/h, which is twice more than the before-treatment condition. However, if the link between two intersections can only process 600 queuing vehicles per hour, then the remaining 200 vehicles are unable to enter Intersection A and have to stay on its upstream segment, resulting in the operational capacity of Intersection A eastbound through being down to 1,800 vehicles per hour. The downstream queue spillback affects any upstream movement for which the intended destination is being blocked. However, the effects of queue interaction are restricted to the nearest downstream intersections. As shown in the example just cited, the volume exiting Intersection B toward further downstream (1,200 veh/h) remains unchanged after deploying the treatment used in Intersection A. The HCM methodology used in estimating signalized intersection delay and the level of service does not take into account the effect of queue spillback from a downstream signal and is unable to provide an accurate estimation if spillback is present[1]. Simulation models are recommended and also commonly accepted by traffic engineers for modeling intersection operations when the queue interaction between two closely spaced signalized intersections is suspected. Although simulation models can measure the interactions of individual vehicles, conducting a network-wide analysis of queue evolvement, and providing detailed and visual information on queue effects, traffic simulation are always a time- and resource-consuming and data-intensive endeavor. To address these deficiencies, this study is designed to provide a quick and practical analysis method by often using readily available data and standard engineering parameters that evaluate the interactions between downstream queues and upstream capacity. The method can be used to assist traffic engineers in examining the application of capacity expansion treatment at urban major intersections. Through measuring and comparing the potential capacity loss for different capacity expansion alternatives, the most beneficial and effective option can be identified, and whether significant additional resources should be utilized for a traffic simulation or further detailed analysis can also be determined.
2
Literature review
A large body of research exists highlighting the effects of queue interactions at closely spaced signalized intersections in an urban road network, especially the potential upstream capacity cutoff caused by downstream queue spillback. Kittelson & Associates‘s research found that queue spillback is one of the most common causes of flow restriction at
congested intersections[2]. The Traffic Timing Manual has recommended that the performance measures of intersection treatments should include queue lengths, and the objectives are to minimize the time period during which the queue spillback or spillover exists and to manage queue interactions between intersections during oversaturated conditions. According to the AASHTO Green Book[3], upgrading an existing at-grade intersection to interchange in an urbanized area may create a queue spillback problem and affect traffic on the interchange off ramp. NCHRP Report 345 exploited the design and operation of single-point urban interchange and indicated that queue spillback from the downstream intersection was found to have an adverse effect on the safety of the off-ramp maneuver and led to a significant reduction in the efficiency of the off-ramp movements[4]. Papageorgiou presented an overview of the approaches that optimize the use of the traffic signal for an urban road network and concluded that isolated intersection control strategies, especially increasing intersection capacity, can dissipate queues at a maximal flow rate so as to minimize the travel delay at an isolated intersection. However, as for an intersection group rather than an isolated intersection, over-saturation’s forward transfer cannot alleviate the global saturation degree; hence, the potential for an increase in the travel delay of an intersection group and the risk of capacity loss do exist[5]. Many researchers have also been devoted to the identification and evaluation of downstream queues interfering with capacity, delay, and level of service of its upstream intersection. The City of Portland, Oregon, presented a traffic micro-simulation model that simulates the upstream capacity affected by the downstream queue built-in and spillback. The model needs the EMME/2 type network data as input, plus the lane configuration of adjoining intersections[6]. A new series of the traffic analysis module was integrated with the recent versions of Trafficware’s Synchro Studio, which examine how queues can reduce capacity through spillback, and a new queue-delay factor was introduced to measure the additional delay incurred by the capacity loss[7]. Elefteriadou conducted a research on the method used for the operational analysis of the internal overflowing queue blockage of diamond interchange ramp terminals on at-grade intersections based on the results of simulations to predict different measures[8]. Another research project led by the Texas Tech University found that both the Synchro and Elefteriadou’s methods overestimate delay and queue effects under a certain condition. It introduced an open-source mathematical model based on the HCM 2000 delay model[9]. There is more research on the intersection capacity estimation by considering queue effects under various conditions. For example, a complex genetic algorithm (GA)-based program that is capable of capturing the dynamic interactions of spillback queues among lane groups and
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between neighboring intersections due to high demand, geometric constraints, or signal settings was described by Liu and Chang[10]. A simulation-based algorithms was developed by Gordo to control spillback from the ramp meters of upstream interchange of freeways for the high-amplitude limit cycle operation[11]. Ahmed and Abu-Lebdeh developed a macroscopic model for a hypothetical two-signal system to estimate the delay at signalized intersections caused by downstream congestion, using basic traffic flow properties and control parameters at neighboring intersections[12]. The Virginia Transportation Research Council reviewed a variety of computer programs that are capable of analyzing capacity at signalized intersections and recommended TRAF-NETSIM for capacity simulation analysis at non-isolated intersections where queuing and spillback are potential problems[13]. While reviewing these models, one can observe that most of these analytic approaches on queuing effects between intersections are either data intensive and require network-wide simulation models or compute intensive and need system-wide mathematical programming models. Network or system-wide simulation models are generated from a set of data, including traffic distributions, road system topographic maps, and characteristics of each link and node. It may be difficult and expensive to conduct a network- or system-wide investigation to gather the necessary information for applying these models, especially in the early stage of alternative screenings or for a minor/temporary intersection improvement project with a limited budget, such as signal optimization and temporary left-turn restriction. Therefore, a careful planning-level downstream effect analysis is essential to determine whether such effort should be expended and to develop a prioritized list of potential capacity expansion projects for major intersections. For example, in the primary
urban center of Honolulu with a population of approximately 500,000, about three dozen major intersections should be investigated. The method introduced in this article assists in determining whether significant additional resources should be expended for investigating a given site, so that most promising locations can be selected for subsequent analyses.
3
Methodology
The study described a systematic analysis method to determine whether queue spillback-related capacity cutoff will occur during the analysis period and to measure how the increased capacity at the subject (upstream) intersection deteriorates downstream traffic conditions. The full set of the analysis method shown in Fig. 2 consists of two interactive processes: evaluation process and calculation process. The evaluation process is used to identify the performance of the proposed treatments for the subject intersection. The calculation process focuses on the analysis of the traffic operation and the queuing condition at the downstream intersections and estimates the maximum rate of downstream traffic arrivals from the upstream intersection (i.e., the threshold of queue spillback). The threshold value is an essential input for the evaluation process in determining the feasibility and effectiveness of treatments. Although queue spillback may also occur due to oversaturation at unsignalized intersections and access points between major intersections, this study only considers the queue interactions between the paired signalized intersections, because the method described in this study is developed based on the HCM 2010 back-of-queue size and the capacity analysis procedures for signalized intersections.
Fig. 2 Flow chart of analysis method on downstream queue effects
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
3.1 Calculation process The methodology used in the calculation process is based on the queue accumulation and intersection capacity estimation methods introduced in the newly released HCM 2010. The queuing calculation in HCM 2010 is derived from Akcelik’s research[14] on the estimation of the full-stop rate at signalized intersections for uniform arrivals. Akcelik’s method was extended by Olszewski[15] for the platooned arrival type and the Texas Transportation Institute[16] for the coordinated actuated signal system. HCM 2010 further refined the estimation technique of back-of-queue size by eliminating slowing and partially stopped vehicles. An acceleration-deceleration delay da term is used to distinguish between a fully and a partially stopped vehicle[1]. da =
1.47(Sa − Ss )2 1 1 ( + ) 2Sa ra rd
where, Sa=average speed in the intersection approach (mi/h); it can be estimated by a posted speed limit Spl with the equation Sa=0.90(25.6+0.47 Spl); Ss=threshold speed defined for a stopped vehicle=5.0 (mi/h); ra=acceleration rate = 3.5 (ft/s2); rd=deceleration rate = 4.0 (ft/s2). The idea behind the derivation of the methodology in the calculation process is to investigate the capacity constraint of downstream queues by reversing and integrating the HCM procedures of intersection capacity and queue size estimation. According to HCM 2010[1], the queue size in any lane of a certain lane group can be estimated by accounting for the queue caused by the signal cycling through its phase sequence and the effect of random and cycle-by-cycle fluctuations in over-capacity demand. The provided signal timings and the queue storage capacity at two adjacent signalized intersections are known, through solving the inverse function of the arrival rate element in HCM queue size and intersection capacity estimation models, the downstream arrivals, subject to avoidance of queue spillback, for a certain lane group of the downstream intersection can be calculated by the equation given next: gQs ⎧ ⎪ qi = C ((Q − d s ) P − gs ( P − 1)) ⎪ a ⎨ g ( P − 1)(CQ + 450 gs ) ⎪q = ⎪⎩ i C 2 (d a P + g ( P − 1)) + 450Cg ( P − 1)
with
Q=
(Q < s (d a
P + g )) P −1
(Q ≥ s (d a
P + g )) P −1
(1)
D + Lv Lv
where, qi=traffic flow rate from the subject intersection to a lane group in its signalized downstream approach (veh/s/ln); Q=maximal back-of-queue size limited by the storage capacity of the road linking the two intersections, that is, the
maximum backward distance in vehicles over which the queue extends from the stop line of downstream intersections during a typical cycle (veh); s=adjusted saturation flow per second per lane in the lane group in the downstream approach (veh/s/ln). Note that the saturation flow of shared and exclusive lanes varies and should be estimated by using the methods defined in HCM 2010; g=effective green time for the lane group in the downstream approach (s); C=cycle length of the downstream intersection (s); D=specified distance between the exit of the subject intersection and the stop line of its downstream intersection. It approximates the intersection spacing if both are at-grade intersections (ft); Lv=average spacing between vehicles in a stopped queue, assumed to be 25 ft[16]; P=proportion of the vehicles arriving on green. Equation (1) is applicable for an individual lane; the arrival rate and saturation flow for the lane group have to be converted into individual lane values before applying this equation. The unequal lane utilization in a lane group is not reflected in the calculation, and no initial queue at the start of each analysis period is assumed. The inequalities in the parentheses of Equation (1) are used to determine the type of queue spillback (cyclic or sustained) by measuring whether the lane group in the downstream approach operates under capacity. Based on the definition in Chapter 17 of HCM 2010[1], if the intersection spacing and effective green time allow the downstream approach operating under this capacity, then queue spillback occurs. This spillback can be classified as cyclic spillback and may result from the long downstream cycle length and/or the poor quality of signal progression between intersections. If there is oversaturation at the downstream intersection, then the sustained spillback occurs. The impedance of sustained spillback could not be mitigated until either the downstream capacity is increased or the upstream demand is reduced. The proportion of all vehicles arriving during green (i.e., Parameter “P” in Eq. (1)) is recommended to be observed in the field, because it has a significant impact on the estimation of queue backup and capacity constraint. It can also be estimated by arrival type and platoon ratio at the downstream approach according to HCM (i.e., P=Rp g/C, in which “Rp” is platoon ratio and the default value of “Rp” can be computed by Rp=Arrival Type/3) (1). Downstream arrival type depends on the type of capacity expansion treatments deployed in the upstream intersection. If full or partial grade-separation treatment is applied, then downstream traffic arrivals can be assumed to have a random and uniform arrival flow profile. If adding lane or other at-grade capacity improvement treatments are used, then a dispersed and moderately dense platooned
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
arrival type may be more appropriate. Arrival Type 4 (Rp=1.33) is commonly used to establish signal progression for the peak period or travel direction if signals at the paired intersections are properly coordinated. Other arrival types, such as type 1 (Rp=0.33) and 2 (Rp=0.67), can be used if traffic engineers presume a poor coordinated signalization. The progression for the off-peak hours or uninterrupted flow is usually characterized as Arrival Type 3 (Rp=1.00). Therefore, if the arrivals are effectively random, then the proportion of vehicles arriving on green equals the green/cycle ratio (i.e., P=g/C), and Eq. (1) can be rewritten as given next: gs (C − d a − g ) Qs ⎧ (Q < ) (2) ⎪qi = (C − d a − g ) s + Q ⎪ ⎨ (C − g )(CQ + 450 gs ) ⎪q = ⎪⎩ i C (C 2 − C (d a + g − 450) − 450 g )
C−g
gs (C − d a − g ) (Q ≥ ) C−g
The downstream arrival rate calculated by Eq. (1) (for platooned arrivals) or Eq.(2) (for uniform arrivals) is only the proportion of total approaching traffic and contributes to the longest queue found in one of the lane groups in the downstream approach. It has to be repeated for each lane group in order to determine the global maximal downstream arrival rate under the constraint of queue storage capacity, intersection configuration, and signalization. Once the arrival rate for each lane group in the downstream approach is computed, then the maximal downstream arrival rate that can be accommodated by the downstream approach and queuing space is calculated by using the equation given next: qmax=min(qiNi/Pi) (3) where, qmax=maximum arrivals at the downstream approach so as to avoid the queue generated from any downstream lane group from spilling back into the subject intersection (veh/s); Ni=number of lanes in a lane group of the downstream approach; Pi=proportion of lane group volume in the entire approaching volume. At any higher downstream arrival rate than the maximal rate (qmax) during an average signal cycle, the longest spillback queue generated in a certain downstream lane group will prevent upstream vehicles which are approaching that lane group from entering the intersection. Therefore, the downstream arrival capacity (Cda) can be computed with Eq. (4): Cda=3600qmax (4) The upstream departure volume, plus the traffic gained or lost at midblock access points (if not negligible), should not exceed the downstream arrival capacity in order to avoid queue spillback. The restriction of upstream departure volume imposes a constraint on the traffic-carrying capacity of the upstream intersection. The capacity constraint estimated by Eqs. (3) and (4) is derived from the longest queue at the downstream approach and is a conservative estimate. When the queue spillback
occurs and blocks some lanes or movements at the upstream intersection, then some other lanes or lane groups may still have space to receive the oncoming traffic. However, in order to minimize the potential of queue spillback and related traffic operations and safety concerns, it could be more scientific and reasonable to determine the subject intersection capacity constraint by considering the longest downstream queue, because there will always be a certain amount of weaving and lane changing between the entrance and the exit, and the different movements may interfere with each other so that the queue in one lane may spread across the other lanes and eventually block all the traffic. Due to the complexity involved in the formulation of the calculation process and in order to reduce the chances of error, if attempting to calculate by hand, an interactive spreadsheet tool is developed by using Microsoft Excel 2007 to quickly execute the calculation process. The spreadsheet user is taken through this computerized tool where traffic and geographic information at the downstream intersection is collected, and the calculation is automatically processed. As shown in Fig. 3, the spreadsheet tool is a one-page worksheet containing three sections: Inputs, Summary, and Output. The user is required to select the lane group and enter data, including the downstream intersection geographic and signal timing information, in the green boxes of the input section. The summary section includes the intermediary outputs during the calculation process, such as the acceleration/deceleration delay, the types of queue spillback, and the order of spillback occurrence. These values provide a handy review and assist in understanding the final output. Especially, this section specifies “the determinant lane group,” which would most likely generate the longest queue and be the first one that creates queue spillback and lane blockage at the upstream intersection. The value of the downstream arrival capacity presented in the output section of the worksheet is used as a crucial input for the evaluation process to justify the feasibility of a capacity expansion treatment and, if justified, to determine the potential loss in capacity during the analysis period. 3.2
Evaluation process
As shown in Fig. 2, a four-step evaluation procedure that was proposed to examine the performance of upstream capacity expansion treatment and to determine the capacity loss resulting from downstream queues is described in the next few paragraphs. Identify the treatment and its downstream intersections affected by the proposed treatment. During this step, the downstream intersections that will experience higher traffic demand after treatment should be identified. It depends on the approach where the treatment will be deployed. For example, adding through lanes on westbound at an upstream intersection may only affect its westbound downstream
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
Downstream capacity constraint calculation worksheet
Downstream Intersection
Test Example
Analyzed by:
Xin Yu
Test Example
Project:
Test Example
Agency or Organization:
23-Feb-12
Date and Time:
Location:
University of Hawaii
Inputs A. Downstream intersection condition
Units
Posted Speed Limit
mi/hr
25
Distance to Upstream Int (D)
ft
900
Estimated Cycle Length (C)
sec
120
Select Lane Group (LG)
-
TH+RT
TH
RT
No. of Lanes
-
1
2
1
veh/s/ln
0.25
0.48
0.45
-
0.25
0.65
0.1
sec
25
25
25
-
3
3
3
mi/hr
34
sec
10
ft
25
veh
37
B. Lane configuration and signal timing
Saturation flow % LG Vol in Total Approaching Vol (Pi) Effective Green (g) Arrival Type
NA
Summary Avg. Approach Speed (Sa) Acc/Dec Delay (da) Veh Spacing in Queue (Lv) Max Back-of-Queue Size (Q )
-
TH+RT
TH
RT
% Veh Arriving on Green (P)
Lane Group (LG)
-
0.21
0.21
0.21
Cyclic or Sustained Spillback
-
Sustained
Sustained
Sustained
veh/s/ln
0.11
0.15
0.14
Max. Arrival Rate to LG (qi) Order of Spillback Occurrence
-
1
2
3
Determinant Lane Group
-
YES
NO
NO
Output Downstream Arrival Capacity (Rounded to the nearest 5)
veh/h
NA
1560
Fig. 3 Example calculation process using spreadsheet tool
intersection, and conversion to a four-way interchange may affect all the approaches and their associated downstream intersections. (ii) Identify Before-Treatment Downstream Arrival Volume. As depicted in Fig. 4, the before-treatment volume of each entry movement toward the downstream segment needs to be obtained. It can measure data in the field or forecasted volume for future years. The traffic entering and exiting from the driveways and access points between the two intersections may be assumed to be nonexistent or negligible if no midblock volume data are available or are in the preliminary planning stage. However, if the number of vehicles generated from the driveways, stop-controlled intersections, and access points within the downstream segment are available or suspected to be significant, then the amount should be
included in the estimation of total arrival volume. (iii) Determine the feasibility of capacity expansion at the subject intersection. This step is designed to examine whether the existing intersections condition and the queue storage capacity of link segments can accommodate an upstream capacity expansion. The determination of the downstream queuing condition in the calculation process (i.e., the determination of the determinant lane group and the downstream arrival capacity) should be done before conducting this step. If downstream arrival volume under the no-build condition computed in the previous step has already been higher or equal to the downstream arrival capacity, then queue spillback from the downstream intersection may already occur at the base condition. In this case, an upstream capacity improvement project cannot be justified, because the
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
Subject intersection
Downstream intersection
-Entry movements -Downstream segment
Fig. 4 Entry movements and downstream segment between two signalized intersections
implementation of a capacity expansion treatment would be counter-productive and have a negative effect on the traffic operations and safety at both subject and downstream congestions. (iV) If potentially feasible, determine the possible capacity cutoff. If the downstream arrival capacity has not been reached under the no-build condition, then the additional capacity at the upstream intersection may be possible. However, due to a potential increase in downstream arrivals, the extended downstream queues still have the possibility of restricting the upstream departure volume. Regardless of the treatment types, if the downstream arrival capacity is not more than the sum of the base downstream arrival volume and the capacity increment obtained from the treatment (i.e., the design capacity of the treatment facility), then the difference between the downstream arrival capacity and the sum would be the potential capacity loss. A positive capacity loss means the treatment may be unable to operate at a full capacity during the analysis period.
4
Case study
A case study is described in this part that illustrates the practical application of the analysis method. The subject intersection used in the case study is on the urban arterials Vineyard Boulevard and Punchbowl Street in downtown Honolulu, Hawaii. The eastbound (EB) and westbound (WB) of the subject intersection have been experiencing heavy congestion during peak periods. A partial grade-separation treatment by using one underpass though lanes and an at-grade treatment by adding one regular through lanes are proposed to be implemented in congested approaches to expand the intersection capacity. Since the grade-separated underpass lane theoretically obtains 100% green time at a signalized intersection and allows for uninterrupted through movement, in the urban condition, one underpass lane is anticipated to provide 1,620 veh/h additional through capacity for each of
the approaches (=default 1800 veh/h×0.9 area type factor). Considering the alternative adding lane treatment, given the through movement green-cycle ratio (0.37) at the subject intersection, the estimated additional capacity per regular through lanes is 600 veh/h, only about 2/5 of the underpass lane capacity. However, the expected capacity of the treatments added to the subject intersection may be negated by the downstream queues. The four-step evaluation process is applied to assess the capacity expansion treatments for this intersection. Step 1: In the first step, the downstream intersections that are suspected to be directly affected by the increased traffic arrivals from the subject intersection should be identified. As shown in Fig. 5, the subject intersection immediately connects to a signalized intersection: Vineyeard Boulevard and Queen Emma Street (V-Q Intersection) on its west end and the signal spacing is approximately 635 ft. Since the EB downstream approach connects a freeway on-ramp (midblock Miller Street is a right in/right out stop-controlled access point), no queue spillback effects on the subject intersection from the downstream freeway on-ramp is assumed. Note that a heavy congested freeway could also generate a queue on its access points, and the queue spillback may occur and affect adjacent intersections along the freeway on and off ramps. However, this study only accounts for the effects between signalized intersections and the queue spillback from freeway ramps, which is beyond the scope of this research. The WB approach of V-Q Intersection (i.e. the WB downstream approach of the subject intersection) has two through lanes, one exclusive left turn lane and one shared right/through lane. The posted speed limit is 30 mi/h. The percentage of left turns in the total WB approaching volume is averagely 18% for peak periods. The V-Q intersection signal timing plan during the peak periods is 160 s cycle length, 22 seconds green for the WB left turn, and 80 s for the WB through and right turn. The signalization of intersections is assumed to be properly coordinated.
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
downstream arrival rate exceeds its arrival capacity; so, the left-turn lane group of the V-Q intersection is the determinant lane group, and the queues in this lane group constrain the capacity of the upstream intersection.
N
The queue spillback at the left-turn lane group can be classified as sustained spillback, and the through/right-turn lane group generates cyclic spillback during the analysis period. According to HCM 2010 (1), the queue at the through/right-turn lane group is only growing during the red indication and will begin to dissipate once the green light presents. However, the sustained spillback at the left -urn lane occurs at some point during the analysis period and is a result of over-saturation. Step 3: The values of downstream arrival capacity obtained in the calculation process are used in this step, and the next step involves determining the feasibility and the capacity loss of the upstream capacity expansion treatments. The subject intersection is currently carrying 1,200 vehicles per hour toward its downstream approach. As long as the upstream departure volume after-treatment does not exceed the downstream arrival capacity (1,810 veh/h for underpass lane and 1,830 veh/h for regular lane), it would be possible for the treatment to provide the subject intersection with additional throughput and to improve the peak-period traffic conditions to some extent. Step 4: As shown in Table 1(b), the additional capacity is restricted to 610 veh/h for the underpass lane alternative and to 630 veh/h for the regular lane alternative as a result of the downstream queue effects, which means the underpass lane would only operate at less than half of its full capacity during the peak periods, and the remaining capacity is cut off due to queue spillback. Although the design capacity of the regular through lane is much lower than that of the underpass lane, the treatment of adding an at-grade lane can perform at its full capacity and it actually functions the same as the much more expensive underpass treatment.
Fig. 5 Layout of case study intersection
Step 2: Once the traffic and geographic information of the downstream intersection are identified, the before-treatment arrival volume at the downstream approach has to be determined in this step. The cumulative entry volume toward the WB downstream approach is 1,200 veh/h during the peak periods. A few driveways exist in the WB downstream segment, but their traffic generation is negligible. Calculation Process: The calculation process is introduced before conducting the last two steps of the evaluation process and is conducted by using the spreadsheet tool. For the underpass treatment, the downstream arrival type is assumed to be random. For the at-grade regular lane, Arrival type 4 (moderately dense platoon arriving during the green interval) is used in this process. As indicated in the calculation results summarized in Table 1(a), the growing vehicle queue in the left-turn lane group will first spill back into the upstream intersection once the
Table 1(a) Summary of case study calculation process results Upstream treatment Underpass lane
At-grade lane
Movements of downstream approach
Arrival type
Type of spillback
Determinant of arrival capacity
Left turn
3
Sustained
YES
Through/right turn
3
Cyclic
NO
Left turn
4
Sustained
YES
Through/right turn
4
Cyclic
NO
Downstream arrival capacity (veh/h) 1,810
1,830
Table 1(b) Summary of case study evaluation process results Upstream treatment
Downstream arrival capacity (veh/h)
Existing arrival volume (veh/h)
Maximal additional upstream departure volume
Design capacity of treatment facility (veh/h)
Capacity loss (veh/h)
Underpass lane
1,810
1,200
610
1,620
1,010
At-grade lane
1,830
1,200
630
600
0
YU Xin et al. / J Transpn Sys Eng & IT, 2012, 12(3), 98−108
Therefore, it may be concluded from the analysis that both solutions are feasible for improving the subject intersection condition, but the adding lane alternative may be a better solution for the intersection. The underpass lane does not appear to be a cost-effective treatment if it is solely designed to address bottleneck intersection congestion and reduce peak hour delay, because more than half of its capacity is wasted due to the capacity constraint from downstream queues.
5
Urban Interchange Design and Operations Analysis, NCHRP Report 345, Transportation Research Board, 1991, 28–31. [5]
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Conclusions
Adding capacity on one intersection in a group can worsen downstream traffic and generate longer back-of-queue size. Extended downstream queues, in turn, can reduce upstream capacity through spillback. This issue has been well recognized, but there is a lack of practical and systematic approaches available that analyze this problem. The main purpose of this research was to develop a quick and practical analysis method for identifying the potential queue spillback between signalized intersections and evaluating the interactive impacts of the downstream queues on the capacity expansion at a non-isolated intersection. This method provides an analytical and step-by-step process for assisting in decision making throughout the alternative selection and screening procedure and consists of a four-step evaluation process and a calculation process. The calculation process is programmed in a computational tool that automates the application of the calculation methodology. From the results of the analysis method, traffic engineers and planners will be able to select the most feasible and effective alternatives for an intersection capacity improvement project by minimizing the possibility of downstream queue spillback and maximizing the treatment performance.
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