Right-turn Bypass Lanes at Roundabouts : Geometric Schemes and Functional Analysis

Right-turn bypass lanes can be implemented in conventional and innovative roundabout intersections to increase the capacity and improve the global functional performances. The Right-turn bypass lanes (also called slip lanes) can be distinguished according to the planimetric layout and the entry control type (stop, yield slip or Free Flow acceleration lane). This paper presents a closed-form model for the estimation of capacity, delays and level of service of roundabout equipped with Right-turn bypass lanes, considering the effect of geometric slip lane schemes, control type, vehicular and pedestrian flow. In order to examine the traffic conditions which can benefit from slip lane roundabouts in terms of capacity and delays, compared to traditional schemes which have no additional lanes, a great number of analyses have been carried out by considering different O/D matrices and vehicle and pedestrian flow vectors. Such comparisons have been made by considering the control delays in function of different O/D matrices. Such O/D matrices describe the most significant situations of traffic demand which can be of interest for the road intersections under study.


Introduction
It is known that in case of heavy right-turn flows, slip lanes can be implemented to increase the compact and mini single-lane roundabout capacity (NCHRP Report 672, 2010) (see Figure 1a).The additional right-turn slip lanes are also used to configure turbo roundabouts (Turborotondes -CROW, 2008;Fortuijn, 2009) and flower roundabouts (Tollazzi et al., 2011;Al-Ghandour et al., 2012) (see Figures 1b and 1c).In flower roundabouts actually the geometry and performance are characterized by slip lanes at each leg (Tollazzi et al., 2011).In urban and sub-urban areas, with bicycle and pedestrian activity, a right-turn bypass lane should be implemented only where needed because the entries and exits of bypass lanes can increase conflicts with pedestrians, bicyclists and with merging on the downstream leg.However, in locations with low pedestrian and bicycle activity, slip lanes can be used to improve capacity when heavy right-turning traffic exists (NCHRP Report 672, 2010;FHWA, 2004).
There are various right-turn slip lane types.They can be distinguished according to the planimetric layout, the position respect to the ring lane, the merging modes with the roundabout entry leg and the entry control type into the roundabout exit leg.As for the control type, there are stop and yield slip lanes (Figure 2), different from those with an acceleration lane (Figure 4).The guidelines for design the geometric elements of slip lanes have been provided by kinematic considerations and by taking into account the waiting phenomena in the end sections.For details on the different slip lanes configurations, see NCHRP Report 672 and HCM 2010, as examples.In this paper we are examined the geometric schemes of slip lanes shown in Figures 2 and 4. The slip lane type has effects on the global roundabout performance which can be also very different.A crucial role in bringing about these effects is played by the control type of exit flows from a slip lane.The capacity determination, the queue lengths and delays (measures of effectiveness, MOE) in right-turn slip lane roundabouts generally is carried out through traffic micro simulation (Al-Ghandour et al., 2012).This paper will show that, as a matter of fact, by considering the results developed as closed-form expressions through the queuing theory, it is possible to estimate if and which effects the slip lane geometry and control type (e.g.slip lane composition and length) can , any service time s and vehicle headways  for the flow Qu Tot distributed like a Gamma random variable with a parameter K (Mauro & Branco, 2012), according to P-K relationships (Pollaczek, 1930;Khinchine, 1932;Kleinlock, 1975), b = E[s] can be calculated as following: where: By means of (1) C E,R follows as: , The critical gap can be calculated by means of the following relation: where V is the vehicle speed on Qu Tot , a the acceleration by which Q E,R bypass vehicles enter into the flow Qu Tot ; is the safety time interval between the vehicles of this flow, equal to the Perception-Reaction Time  =1 s.V can be calculated through the procedure shown in NCHRP Report 672 in function of deflection radius of the vehicle trajectories passing through ring lane R 2 and coming from ring lane R 3 .For the dimensions of compact single-lane roundabouts considered in this paper, R

Right-turn Yield Slip Lanes
In this case the geometric layout is similar to that of stop-controlled slip lanes (Figure 2); the capacity formula is described in NCHRP Report 672: It is illustrated in Figure 3 along with the stop-controlled slip lane capacity. Figure 3 shows that the yield slip lane capacity is usually higher than that with a stop control.

Slip Lane with an Entry Lane (Free-flow Slip Lane)
This slip lane type is generally shown as in Figure 4.There are free-flow slip lane configurations which have an exit section as short as 30 m, for instance as provided for by Polish Road Intersections Design Guidelines -Part II, 2001.As in stop and yield-controlled slip lanes, the right-turn flow into the slip lane is denoted with Q bypass from the roundabout is indicated with Qu Tot (Figure 4).
The HCM 2010 Manual for free-flow slip lanes does not provide the capacity formulations but it qualitatively estimates capacity values higher than those obtained by Yeld-controlled slip lanes.The following relation ( 6) has been obtained from Tracz (Tracz, 2008;Tracz et al., 2011) for free-flow slip lanes at single-lane roundabouts: The relation ( 6) is illustrated in Figure 3.

Effect of Pedestrian Flow on Slip Lane Capacity
The presence of pedestrian crossings reduces entry and exit capacity of slip lanes (there are generally 2 pedestrian crossings at each slip lane: the former that lies adjacent to the entry to the roundabout, the latter at the exit leg).In order to take these entry effects into consideration, the analyses carried out in this paper have adopted Brilon's formula (Brilon et al., 1993): where: M E,R Entry = right-turn lane pedestrian capacity reduction factor;  • Section 1 (of length L1) with capacity C E,R ped-Entry , flow Q E,R bypass and saturation degree x 1 ; • Section 2 (of length L2) with capacity C E,R

ped-Exit
, flow Q' E,R bypass and saturation degree x 2 ; • Section 3 (of length L3) with capacity C E,R , flow Q'' E,R bypass and saturation degree x 3 ; Since the three sections are in sequence, the following conditions need to be verified: where C E,R is calculated by means of expressions ( 4), ( 5), ( 6) according to the slip lane control type.The degree of saturation in a slip lane (required for the estimation of the Total Entry Capacity) corresponds to the maximum value of x 1 , x 2 , x 3 : x E,R = max (x 1 , x 2 , x 3 ) (20) As an example, Figure 6 shows the values of saturation degrees (x1, x2, x3) of a yield-controlled slip lane under varying pedestrian flow intensity (Q ped Exit = 50 ÷ 850 ped/h) in the following traffic conditions: Q u Tot = 800 veh/h, Q ped Entry = 200 ped/h; Q E,R bypass = 600 veh/h.Section L3 (see Figure 5) has also been assumed to be 60 m long.
Figure 6.Values of the degree of saturation (bypass with yeld signal)

Capacity of the Merging Lane with the Ring Road
The entry lane capacity to the ring C E,TLT can be determined through the formulation provided for by the HCM 2010 for roundabouts with a single lane at entries and a single lane at the ring; by denoting the circulating flow with Qc it follows that: In order to take the pedestrian flow into consideration, Brilon's formula is used (Brilon et al., 1993):  The respective saturation degree of a lane is given by: , , , , (24)

Total Entry Capacity
After obtaining the entry lane capacity of a slip lane, by denoting the saturation degrees (entry flow/capacity ratio) with x, the entry capacity (C E ped ) can be estimated through the following relation (Mauro & Branco, 2010;Corriere & Guerrieri, 2012;Giuffrè et al., 2012) Where Q E,R , Q E,TLT , x E,R , x E,TLT are respectively flows and degree of saturation at the two lanes of the entry E.

Determination of Delays, Levels of Service and Length of the Queue
Once the capacity and saturation degrees of entry lanes have been obtained, it is possible to determine the delays and the levels of service for each lane and the entry itself.To this end, the following relations contemplated by the Manual HCM 2010 can be applied, suitably modified to take any pedestrian flow into consideration: , where D E,R ped , Q E,R , D E,TLT ped , Q E,TLT are respectively delays and flow rates at the two lanes of the entry E. T is the reference time (T = 1 for 1-hour analysis; T = 0.25 for 15-minute analysis).The levels of service referred to the delay values obtained by means of the previous relations ( 26), ( 27) and ( 28) are shown in Table 1 (HCM, 2010).
As an example, Figure 7 below indicates the value assumed by the mean control delay for an entry to the roundabout with a slip lane under varying saturation degrees in the following traffic conditions: Q c = 750 veh/h; Q ped Entry = 50 ped/h; Q ped Exit = 50 ped/h; Q u Tot = 500 veh/h.Whenever traffic changes, surfaces similar to those in Figure 7 are obtained.

Functio
In order to than conve matrices.I layout has The geome In order to For each l and (28).T For each traffic condition examined, the vehicle flows entering the roundabout have been increased from value 0 to the value which determines the reaching of the roundabout simple capacity with regard to the geometric design which, each time, offers the highest capacity.It is noted that roundabouts with slip lane allow a significant delay reduction in all the flow conditions compared to conventional roundabouts with a single lane at entries (layouts (1+1) and (1+2)).On the contrary, compared with multilane roundabouts (2+2) their performances are lower, up to 70% of the total right-turn flows.Once such a threshold is exceededand according to the pedestrian flow intensity, it can be more convenient to use slip lane roundabouts than all the other designs.Moreover, free-flow slip lanes prove to be more advantageous than those controlled by stop or yield signs; this is consistent with the results shown by Al-Ghandour (Al-Ghandour et al., 2012).The following figures elucidate the above points.More specifically, if right-turn percentage is lower than 70% (Figures 8,9,10 and 11), roundabouts with slip lanes cause intermediate delays between roundabouts with the geometric schemes (1+2) and (2+2).On the contrary, when the right-turn percentage is higher or equal to 70% of the total (see Figures 12 and 13), slip lane roundabouts can cause delays inferior to those observed in the other configurations examined.In case of moderate pedestrian flow (Qp3), only roundabouts with free-flow slip lanes can cause delays inferior to those with double lanes.If, on the contrary, the pedestrian flow is high (Qp2), the performances of roundabouts with right-turn bypass lanes are the best among all the configurations, regardless of their control type.As for the effects of the distribution of right-turn flows on vehicle delays, also the case in which Q E,R no-bypass  0 has been estimated.It follows that: It has been observed that if right-turn manoeuvres prevail (like, for instance, with matrix 6) and with high pedestrian flows (Qp2), the distribution of right-turn flows between slip lanes and entry lanes can result in a modest reduction of average intersection delays.For instance, for 6, Q4, Qp2, in case of ' = 0.6 there is a maximum benefit of 2 seconds, as shown in Table 2 (yield-controlled slip lane compared to the case in which ' = 1).Such a circumstance can be explained by the fact that when ' < 1, if on the one hand there is a delay reduction in slip lanes, on the other there is a delay increase in lanes entering the roundabout.

Conclusions
Right-turn slip lanes are employed to increase the capacity of roundabouts.Generally, the slip lane roundabout performances are evaluated through traffic simulations implemented with specialized software.This paper suggests a closed-form model for calculating the capacity and delays in slip lane roundabouts which takes into consideration a great number of geometric and traffic-regulating parameters, among which, slip lane dimensions, traffic control type (stop sign, yield sign, Free Flow), intensity and distribution of vehicle and pedestrian flows, saturation degrees of the lanes and so on.In order to examine the traffic conditions which can benefit from slip lane roundabouts in terms of capacity and delays, compared to traditional schemes which have no additional lanes, a great number of analyses pedestrian flow vectors.The results of the analyses show that roundabouts with right-turn bypass lane lead to a significant delay reduction in any flow condition compared to conventional roundabouts with one lane at entries ((1+1) or (1+2) layouts).Compared to multilane roundabouts (2 ring lanes + 2 entry lanes), slip lane roundabouts cause more serious delays, in the case of right-turn flows up to 70% of the total.When such a threshold is exceeded slip lane roundabouts appear to be more convenient than any other design, in that the average vehicle delays decrease in a more and more marked manner in the presence of the same traffic volume.Moreover, among the slip lane types, those with a free-flow lane are more advantageous than those with a stop or yield sign. Finally, we have observed that the distribution of right-turn flows between a slip lane and a lane entering the roundabout (' < 1) can cause a slight reduction in the average intersection delays; this exclusively happens when the right-turn percentage is higher than 70%.

Figure 3 .
Figure 3. Free Flow, Yeld and Stop slip lane capacity

Figure 4 .
Figure 4. Entry, circulating and exit flows at roundabout (free flow bypass lane) Figure 5. Flow entry leg, th ns, or free-flow g to the vehicu Vol. 7, No. 1 23) M E,TLT = through and left-turn lane pedestrian capacity reduction factor; C E,TLT ped = through and left-turn lane vehicle capacity, impact of pedestrians considered [veh/h]; C E,TLT = through and left-turn lane vehicle capacity (no pedestrians crossing, only vehicles) [veh/h]; Figure 7. Ent

Figure 8 .Figure 9 .
Figure 8. Roundabouts mean delay -Scenario: 1, Q1, Qp1 have been carried out by considering different O/D matrices and vehicle and

Table 1 .
Level of service

Table 2 .
Values of the intersection mean delay [s/veh] as function of '