Roundabout Level of Service Rahmi Akçelik Director Akcelik & Associates Pty Ltd email: rahmi.akcelik@sidrasolutions.com web: www.sidrasolutions.com 8 January 2009 Contents 1. Introduction... 1 2. Fundamental Aspects of Methodology... 2 3. Level of Service Thresholds... 3 4. Level of Service Using Delay and Degree of Saturation... 7 5. Acceptable Level of Service Targets... 9 1. Introduction This paper discusses the issue of Level of Service definitions appropriate for roundabouts. It presents comments related to the following documents: HCM 2010 Draft Chapter 21 (Roundabouts) dated 19 December 2008 Roundabout Threshold dated 15 October 2008 Roundabout Procedure White Paper dated 21 December 2008 Unsignalized F Definition dated 21 December 2008 In summary, this paper is critical of the Level of Service method proposed in HCM 2010 Draft Chapter 21 to use the same thresholds for roundabouts and stop-sign control, and its justification. Separate thresholds are proposed for roundabouts, and a method that incorporates the v/c ratio into definition for all intersection types considering both the capacity condition (v/c > 1) and the practical capacity condition (v/c > 0.85).
Akçelik - Roundabout Level of Service 2 2. Fundamental Aspects of Methodology The methodology recommended for roundabout has general implications for determining for other intersections. Consistency of methodology given in various chapters of the HCM is of great concern. This is not about the different thresholds used, but problem becomes more serious when combined with the use of different thresholds. HCM2010Rou Exhibit 21-1 states that "The criteria apply to the critical lane on a given approach. is not calculated for non-critical lanes, the approach, or for the intersection as a whole. " This brings an interesting dimension to determining. Potentially, could be determined for any of the following elements of an intersection using measures such as delay and degree of saturation (v/c ratio): per lane per movement per lane group per approach per intersection In representing of a higher (more aggregate) level element, the following choices are available (not all inclusive). Approach : approach represented by the worst approach lane considering the value of the selected measure: highest delay for any lane and/or highest v/c ratio for any lane; approach represented by the worst approach movement considering the value of the selected measure: highest delay for any movement and/or highest v/c ratio for any movement; approach represented by the average approach value of the selected measure: average delay considering all lanes or all movements is possible (and will be lower than the worst lane or worst movement value) but an average v/c ratio would not be sensible; Intersection (similar to approach, but worth repeating!): intersection represented by the worst intersection lane considering the value of the selected measure: highest delay for any lane and/or highest v/c ratio for any lane; intersection represented by the worst intersection movement considering the value of the selected measure: highest delay for any movement and/or highest v/c ratio for any movement; intersection represented by the average intersection value of the selected measure: average delay considering all lanes or all movements is possible (and will be lower than the worst lane or worst movement value) but an average v/c ratio would not be sensible; With shared lanes on a multi-lane approach, the values per lane, per movement and per lane group can be different, partly depending on how they are calculated. HCM uses different methodology for determining delay in different chapters, which introduces a problem. A consistent method is not possible since delay can be determined per lane for roundabouts in Chapter 21. Essentially a lane-by-lane methodology is now used but not for stop control and signals which determine delay per movement. The difference in methodologies is the first factor resulting in an inconsistent method to compare alternative intersection treatments. Considering approach, when roundabouts are assessed according to the worst lane delay, against signals assessed according to the average approach delay (considering all lanes or all movements, which is generally lower than the worst lane delay), and with a more strict thresholds for a roundabout to produce the same, is this a fair treatment? The difference in the selection of the average or worst values of the selected measure is the second factor resulting in an inconsistent method to compare alternative intersection treatments.
Akçelik - Roundabout Level of Service 3 Similar considerations apply to the intersection. HCM does not define an intersection for sign control, and now for roundabouts, and removing the intersection based on average delay for signals would improve consistency but does that solve the problem? If is not defined for the intersection, then the traffic analyst (practitioner) will look at the more detailed level, i.e. approach. If is not defined for the approach (as in the new roundabout chapter), the worst lane will be the defacto representative of the approach, and since it is not defined for the intersection, the worst lane will be the defacto representative of the intersection. This would be fine if the worst lane (or worst movement) method were used for all intersection types in a consistent way. Therefore careful decisions should be made regarding consistent method at this fundamental level. This relates to one the most frequently asked questions by software users. 3. Level of Service Thresholds The document titled Roundabout Threshold discusses the issue of appropriate thresholds for roundabouts vs signals. Are more pessimistic thresholds justified for roundabouts, and does this introduce a bias against roundabouts in the context of evaluation of alternative intersection treatments? The document seems to have justified the use of lower thresholds for roundabouts that are the same as sign control, essentially on the basis adopted in Chapter 21 as expressed by text above Exhibit 21-1: "The criteria have different threshold values than for signalized intersections, 1. primarily because it is assumed that drivers expect different levels of performance from different types of system elements; 2. in addition, the control delay at capacity for a roundabout is approximately 50 seconds, rather than the 80 seconds that would be suggested if using the signalized intersection thresholds." These two points are discussed below. Point 1 The first point may lead to various philosophical discussions. However, it invites an obvious question: Is using the same set of thresholds for roundabouts and sign-control justified in terms of driver perception, i.e. do drivers expect the same levels of performance from roundabouts and sign-control? In answering this question, it should be considered that roundabouts display a good safety record as reflected by low gap-acceptance (driver behavior) parameters. Drivers negotiating roundabouts do so relatively easily essentially due to the low speed of conflicting vehicles and a single conflicting (circulating) stream. This cannot be matched by critical movements at two-way sign control (e.g. left turn out of the minor road), as reflected by very large gap-acceptance parameters which are associated with higher speeds of conflicting movements and the larger number of conflicting movements. It is therefore considered that separate thresholds are justified for roundabouts. Table 1 shows the proposed thresholds for roundabouts which are between those used for signals and two-way sign control. The new thresholds for roundabouts are proposed in order to reduce the bias in assessing signals and roundabouts as alternative intersection treatments. If the acceptable target is D, then the thresholds proposed in Table 1 mean that up to 50 s delay is acceptable at roundabouts as opposed to 35 s at two-way sign control. For the A, B and C ranges in Table 1, the same thresholds are used for roundabouts and signals since roundabouts perform with shorter queues in this range of conditions, and drivers are likely to find negotiating a roundabout easy under these conditions.
Akçelik - Roundabout Level of Service 4 Table 1 - Level of Service thresholds including new thresholds proposed for roundabout Level of Service Control delay per vehicle in seconds (d) Signals Roundabouts Stop Control A d 10 d 10 d 10 B 10 < d 20 10 < d 20 10 < d 15 C 20 < d 35 20 < d 35 15 < d 25 D 35 < d 55 30 < d 50 25 < d 35 E 55 < d 80 50 < d 70 35 < d 50 F 80 < d 70 < d 50 < d Table 2 - Roundabout delay at capacity and its components (single-lane roundabout) Circulating flow rate (pcu/h) Capacity, Q Prop. of time with available gaps, u First-term delay, d 1 = 3600 / Q Second-term delay at capacity, d 2 Delay at capacity, d = d 1 + d 2 + 5 (HCM Unsig) (Proposed in Table 1) 0 1130 1.00 3.2 38.0 46.0 E D 300 837 0.74 4.3 44.0 53.3 F E 600 620 0.55 5.8 51.1 61.9 F E 900 459 0.41 7.8 59.4 72.2 F F 1100 376 0.33 9.6 65.6 80.2 F F 1200 340 0.30 10.6 69.0 84.6 F F 1400 279 0.25 12.9 76.2 94.2 F F Point 2 The second point made in Chapter 21 Exhibit 21-1 (based on the document titled Roundabout Threshold) is a very weak and biased one (not factual) as it is discussed below. The Roundabout Threshold document presents a figure which gives delay curves for a single-lane roundabout compared with 80 s delay as the F threshold for signals. The curve which represents the highest roundabout delay is for a circulating flow of 900 veh/h (pcu/h). In Table 2, capacities and delays calculated using the Chapter 21 equations for a single-lane roundabout are shown. The delay for a circulating flow of 900 pcu/h is shown to be 72.2 s whereas the figure presented in the Roundabout Threshold document is close to 60 s (this should be checked for accuracy). This type of analysis should also be applied to critical movements at two-way sign control to see that this approach makes sense in relation to the same thresholds proposed in HCM 2010 Chapter 21 for roundabouts and two-way sign control. The Unsignalized F Definition document describes various scenarios for two-way stop control which could be explained in the same way as the explanation given for roundabout cases.
Akçelik - Roundabout Level of Service 5 The use of circulating flow rates above 900 pcu/h in Table 2 needs discussion. The document titled Roundabout Procedure White Paper justifies the equation selected for the critical lane of a twolane roundabout by stating that it gives higher capacities above a circulating flow rate of 824 pcu/h, and shows capacity curves for circulating flow rates up to above 2000 pcu/h. Single lane data in the NCHRP 572 report show observed capacities of up to around 1400 veh/h. This indicates potential for this level of flow rate to enter the circulating road from one approach alone. In Table 2, circulating flow rates of 1100 (close to the maximum capacity of 1130 for a single-lane roundabout), 1200 and 1400 are also considered. These higher values of circulating flow should not be dismissed on the basis that they are not in the NCHRP 572 single roundabout data. If they are to be dismissed, then the single-lane model should be restricted to certain circulating flow rates, say 1200 as in HCM 2000. The following discussion is presented to explain the main mechanism which is at work here, which would be hidden when using circulating flows which are not high enough. This is rather fundamental, and needs to be discussed in order to demonstrate the bias in the Roundabout Threshold document. Two main contributors to delay (ignoring geometric or acceleration & deceleration delays) are: red time at signals and similarly lack of gaps (blocked time) at roundabouts (2-way sign control is similar), and v/c ratio representing the congestion (overflow) effects. In the HCM delay equation (d = d 1 + d 2 ), the first term (d 1 = 3600 / Q) represents the effect of lack of gaps, and the second term represents the congestion effects. At low degrees of saturation, the first term is the more important component of delay since capacity is high enough to absorb variations in arrival flow rates without causing overflows. At high degrees of saturation, the second term is the more important component of delay due to high levels of overflows. The first-term delay is related to the proportion of green time at signals and proportion of time when gaps are available at roundabouts (parameter u). Capacity is given by Q = (3600 / h s ) u where h s is the saturation headway at signals or follow-up headway at roundabouts. The highest capacity is obtained when u = 1.0 at zero circulating flow, Q o = 3600 / h s. Thus, Q = Q o u and the proportion of time when gaps are available at a roundabout can be determined from u = Q / Q o. Essentially, the decrease in capacity with increasing circulating flow rate is due to the decreasing proportion of time when gaps are available in the circulating stream (decreasing value of u). In Table 2, values of capacity, proportion of time when gaps are available, first term delay, secondterm delay at capacity (v/c = 1) and overall delay at capacity (v/c = 1) are given for various circulating flow rates using the HCM 2010 delay equation for single-lane roundabouts (Q o = 1130, T = 0.25 h, and 5 s added as the third-term value at capacity). It is seen that at high circulating flow rates, the proportion of time when gaps are available becomes very low, and the delay reaches levels above the signalized intersection threshold of 80 s. The situation is similar to minor road movements at signals, which receive relatively shorter green times, resulting in low green time ratios and high first-term delays even when the v/c ratio is not high. Contrary to statements such as "delays can be balanced at signals", both actuated signal control and pretimed control methods will allocate low green time ratios to minor movements. The latter method uses the equal degree of saturation method for critical movements, therefore minor movements get allocated short green times. It is also possible that the HCM unsignalised delay equation (3600 / Q) underestimates the firstterm delay, as it uses an equation based on simple queuing theory. The last table in the Roundabout Threshold document is also misleading since it presents values for varying green time ratios for signals but gives only one set of results for roundabouts for an unknown capacity condition.
Akçelik - Roundabout Level of Service 6 Table 3 gives assessments for roundabouts with different ratios of time when gaps are available corresponding to low, medium and high circulating flow rates of 300, 600 and 1100 (shown in Table 2). The delay values are calculated using the HCM 2010 Chapter 21 equation. values in accordance with the thresholds given in the HCM 2010 Chapter 21 and those proposed here for roundabouts (in Table 1) are given for comparison. The values for signals are as in the Roundabout Threshold document (unchecked). It is seen that the new thresholds proposed for roundabouts in Table 1 match the signal values for comparable conditions as indicated by the values of parameter u. At capacity (v/c = 1.0) both Chapter 21 and the proposed Table 1 values are less favorable to roundabouts compared with signals. Table 3 - values for roundabouts and signals v/c ratio Del. (s) Roundabout Signals Circulating flow rate (pcu/h) Cycle time (s) 1100 600 300 90 90 90 Capacity (veh/h) Capacity (veh/h) Draft Ch 21 376 620 837??? Proportion of time when gaps are available, u Green time ratio, u 0.33 u = 0.55 u = 0.74 0.30 0.40 0.50 Proposed Tab. 1 Del. (s) Draft Ch 21 Proposed Tab. 1 Del. (s) Draft Ch 21 Proposed Tab. 1 0.50 21 C C 14 B B 11 B B C C B 0.70 33 D C 22 C C 17 C B C C C 0.85 49 D D 34 D C 28 D C D C C 0.92 62 F E 45 E D 37 E D E D D 1.00 80 F F 62 F E 53 F E E D D Proposed thresholds for roundabouts are given in Table 1. values for Signals are those given in the Roundabout Threshold document. HCM HCM HCM
Akçelik - Roundabout Level of Service 7 4. Level of Service Using Delay and Degree of Saturation The Unsignalized F Definition document proposes consideration of redefining unsignalized intersection as control delay 50 s or v/c 1.0, and seems to be in favor of this. It is recommended that the above condition is stated as " control delay > 50 s or v/c > 1.0" to be consistent with current HCM threshold tables. When assessing intersection performance it is a very good practice to pay attention to both delay and v/c ratio (degree of saturation). Trying to devise a method for definitions to give an indication of oversaturated conditions is fine as long as this is done in a consistent way for all intersection types. It is most important that such a redefinition is applied to all intersection types, and not just to unsignalized intersections. This is also related to the fundamental issues discussed in Section 2, i.e. consistent use of the worst lane, worst movement, and so on. There should be an additional consideration to this. Should the consideration of v/c ratio be limited to the capacity condition (v/c> 1.0), or should there also be a consideration of the practical capacity limit? It is an accepted practice to use v/c = 0.85 as the practical degree of saturation for roundabouts (0.90 for signals, and 0.80 for sign control) in designing intersections. Should this be incorporated into definitions, e.g. consider conditions 0.85 < v/c 1.0 separately. The use of the capacity condition (v/c 1.0) alone could introduce some sudden jumps in allocation whereas introduction of practical capacity condition (0.85 < v/c < 1.0 for roundabouts) along with this would lead to smoother allocation of values. The use of a practical capacity (or practical v/c ratio) limit reflects the objective of avoiding conditions when delay (and queue length) increases at an increasingly higher rate, and the variability of delay times increases due to increased overflows (cycle failures) above such a v/c ratio value. This also reflects the fact that, for example, v/c = 0.98 is as almost as bad as v/c = 1.0 in practice. A method that uses both delay and v/c ratio exists for signalized intersections. This method was proposed by Prof. Berry in 1980s, and is implemented in SIDRA INTERSECTION as a option. The method is shown in Table 4. Table 4 - Level-of-service definitions for VEHICLES based on both vehicle delay and degree of saturation (SIDRA INTERSECTION option) Level of Service Control delay per vehicle in seconds (d) Signals and Roundabouts Stop and Give-Way / Yield Signs Degree of saturation (v/c ratio) (x) A d 10 d 10 0 < x 0.90 B 10 < d 20 10 < d 15 0 < x 0.90 C 20 < d 35 0 < d 35 D 35 < d 55 0 < d 55 E 55 < d 80 0 < d 80 15 < d 25 0 < d 25 25 < d 35 0 < d 35 35 < d 50 0 < d 50 0 < x 0.90 0.90 < x 0.93 0 < x 0.93 0.93 < x 0.95 0 < x 0.95 0.95 < x 1.00 F 80 < d 50 < d 1.00 < x method based on: BERRY, D.S. (1987). Using the volume-to-capacity ratios to supplement delay as criteria for levels of service at traffic signals. Transportation Research Record 1112, pp 23-28.
Akçelik - Roundabout Level of Service 8 The method shown in Table 4 uses an "or" condition, e.g. F is allocated if the specified delay limit (80 or 50 sec) is exceeded or x > 1.0 (not 1). Thus this method will always give F for oversaturated conditions regardless of the delay. Similarly, D will result if the v/c ratio is in the range 0.93 to 0.95 and delay does not exceed 55 s for signals whatever the value of delay subject to this condition. The method shown in Table 4 could be simplified and modified for the incorporation of the practical capacity condition in a general way to avoid complications of using separate v/c thresholds for different intersection types. The system shown in Table 5 is a possible method where the v/c ratio limits could apply to all intersection types reasonably well. According to the method in Table 5, the effect of the v/c ratio on would be as follows: If x > 1, = F whatever the delay value is; If 0.95 < x 0.85, = E whatever the delay value is in the range 80 s / 70 s / 50 s or less; If 0.85 < x 0.95, = D whatever the delay value is in the range 55 s / 50 s / 35 s or less; If x 0.85, = A, B or C according to the value of delay only. For these values, same thresholds are used for roundabouts and signals since roundabouts perform with shorter queues in this range of conditions, and drivers are likely to find negotiating a roundabout easy under these conditions. Table 5 - Level-of-service definitions for VEHICLES based on both vehicle delay and degree of saturation (a possible general method) Level of Service Control delay per vehicle in seconds (d) Signals Roundabouts Stop and Give-Way / Yield Signs Degree of saturation (v/c ratio) (x) A d 10 d 10 d 10 0 < x 0.85 B 10 < d 20 10 < d 20 10 < d 15 0 < x 0.85 C 20 < d 35 20 < d 35 15 < d 25 0 < x 0.85 D 35 < d 55 0 < d 55 30 < d 50 0 < d 50 25 < d 35 0 < d 35 0 < x 0.85 0.85 < x 0.95 E 55 < d 80 0 < d 80 50 < d 70 0 < d 70 35 < d 50 0 < d 50 0 < x 0.95 0.95 < x 1.00 F 80 < d 70 < d 50 < d 1.00 < x
Akçelik - Roundabout Level of Service 9 5. Acceptable Level of Service Targets HCM does not specify what an acceptable target is. The Design Analysis section in Chapter 21 ( page 21) states "The operational analysis described earlier in this chapter can be used for design purposes by using a given set of traffic flow data to iteratively determine the number and configuration of lanes that would be required to produce a given level of service." The Unsignalized F Definition document acknowledges the issue: "The definition of has at least two key practical implications: how users perceive the quality of service, and how agencies use the resulting letter grades for decision making. Specifically on the latter point, how should agencies react to the presentation of F for an unsignalized intersection? Does a F condition require mitigation or not? The discussion presumes the typical policy determination that E is acceptable for unsignalized intersections, although some agencies use D or other measures. While the HCM is silent on what is acceptable or not, AASHTO and other agencies do provide guidelines and/or standards that rely on HCM measures." In practice, it is necessary to choose acceptable targets for intersection evaluation, for example in design life analysis based on. The targets can be different for different intersection types, especially if different thresholds are used. Without defining acceptable thresholds, the method appears to be incomplete. The new thresholds for roundabouts in Tables 1 and 5 are proposed in order to reduce the bias in assessing signals and roundabouts as alternative intersection treatments. For example, if the acceptable target is D, then the thresholds proposed in Tables 1 and 5 mean that up to 50 s delay is acceptable at roundabouts compared with 35 s at two-way sign control if the HCM 2010 Chapter 21 thresholds are adopted. It is recommended that E is used as the acceptable target for roundabouts if the HCM 2010 Chapter 21 thresholds for sign control are adopted for roundabouts.