**4. Real-time cooperative control**

Operation is the last pillar, following design and planning. The nature of public transport operations is stochastic, with disruptions occurring due to irregularities in travel times and variation in passenger demand. Thanks to the advances in Intelligent Transportation Systems (ITS), the performance of a transit network can be monitored in real time, and corrective actions can be applied to restore the targeted level of service. All different applications have widened the spectrum of real time control strategies that can be deployed [13]. Until now, C-ITS Driver Advisory Systems have exclusively focused on assisting vehicles traverse signalized intersections and reducing the number of TSP requests, disregarding the consequences of their control actions to the regularity of the transit line [27]. The regularization of a line is the main objective of many real time strategies for public transport, with holding to be one of the thoroughly investigated in literature and applied in practice [17, 36]. We investigate how C-ITS can complement holding strategy and achieve a synergy to address both the objectives of regularity and the mitigation of the number of stops at signalized intersections.

time for red *t*

where *t*

time at traffic light *t*

the red time *t*

**109**

*Red*,*remain* is estimated and added to the expected arrival time *t*

*exit*

In case of green, the vehicle should either accelerate to catch the current phase

*ijk* <sup>þ</sup> *<sup>t</sup>* Re *<sup>d</sup>*,*remain* (48)

*ijk* and one for the expected

*ijk* (49)

<sup>1</sup> is selected since vehicle accelerates

*arr*,*tl*

*exit*

*ijk* þ *tGreen*,*remain* þ *t* Re *<sup>d</sup>*

(50)

*<sup>k</sup>* <sup>¼</sup> *<sup>d</sup> <sup>j</sup>*,*tl t arr*,*tl ijk* � *t*

or wait for the next green phase. Therefore, two candidate speeds can be

arrival at the next green phase, given by Eqs. (45) and (46), respectively.

<sup>1</sup> <sup>¼</sup> *<sup>d</sup> <sup>j</sup>*,*tl t arr*,*tl ijk* � *t*

*exit*

In case of two candidate speeds, the one respecting the speed limits is selected. If

to arrive during current green phase. If both speeds are outside the speed limits, no speed advisory is given by the controller. In contrast, if there is no need to restore

R-GLODTA is the second hybrid controller, combining holding and GLODTA. In principle, holding and GLODTA are using the same control logic, by extending the time at stop to achieve their objectives to restore regularity and mitigate stops at traffic lights respectively. Therefore, with this controller, the prolongation of dwell time at stops aims to satisfy both objectives. After the vehicle arrives at the stop and completes dwell time, two candidate holding times are calculated to restore regularity. Then, the expected arrival time to the next signalized intersection is estimated using Eq. (43). If the expected arrival time is during green phase, then no GLODTA time is needed. In contrast, if the vehicle is expected to arrive during red, then the waiting

*ijk* is calculated by subtracting the current red time *t*

*wait*,*tl* <sup>¼</sup> *<sup>t</sup>* Re *<sup>d</sup>* � *<sup>t</sup>* Re *<sup>d</sup>*,*<sup>c</sup>* (51)

*Green* (52)

*GLODTA* with the duration of green phase

*Red* the red time of the cycle of the current traffic light.

*VRGLOSA*

*<sup>k</sup>* <sup>¼</sup> *<sup>d</sup> <sup>j</sup>*,*tl t arr*,*tl ijk* � *t*

*4.1.2 Reliability green light optimal dwell-time adaptation (R-GLODTA)*

the recommended speed is calculated using Eq. (44):

*Optimal Management of Electrified and Cooperative Bus Systems*

*DOI: http://dx.doi.org/10.5772/intechopen.93892*

*VRGLOSA*

recommended, one for the estimated arrival time *t*

*VRGLOSA*

both speeds are within the speed limits, *VRGLOSA*

regularity, the controller is treated as GLOSA.

*wait*,*tl*

*Red* as in Eq. (51):

time for the passengers. GLODTA time *t*

intersection without stopping (Eq. 52).

*t*

*t*

*GLODTA*, *t*

The waiting time at the traffic light corresponds to the GLODTA time *t*

define a time interval, within a vehicle will traverse the downstream signalized

The waiting time at traffic light is transferred at the bus stop and utilized as dwell

*GLODTA* <sup>þ</sup> *<sup>t</sup>*

The hybrid controller can work as holding or GLODTA alone depending on the current performance and needs of the system. If both candidate holding times (for

*arr*,*tl ijk* . Then

*Red*,*<sup>c</sup>* from

*GLODTA*.

We combine two DAS, namely GLOSA and GLODTA, with a rule-based holding criterion at stops prior to signalized intersections, to provide a pair of holding time and speed advisory or a holding time to achieve both objectives. The combined controllers are presented in the following sections, followed by the results obtained from a real-world case study.

#### **4.1 Regularity based driver advisory systems**

#### *4.1.1 Reliability green light optimal speed adaptation (R-GLOSA)*

The first regularity based advisory system is R-GLOSA. At the bus stops applied, it instructs a vehicle to be held to regulate the operation and depart with the speed needed to traverse the next green phase. After the arrival of a vehicle at a bus stop prior to a signalized intersection and the completion of dwell time, its position subject to the preceding and the succeeding vehicle is checked. If the headway from the preceding vehicle is short enough, then the vehicle will be held until the consecutive headways are even. We use the same rule-based holding criterion with [36], which regulates the departure time of a vehicle and limits the maximum allowed headway based on the planned headway.

After holding time is calculated, the departure time from the stop is updated and the expected arrival to the first downstream signalized intersection is estimated. The expected arrival time at the first signalized intersection downstream *t arr*,*tl ijk* is estimated by adding to the updated exit (departure) time *t exit ijk* , the time the bus needs between the stop and the intersection. The time corresponds to the expected running time derived by the ratio of the distance *dj*,*tl* between current bus stop *j* and the signalized intersection *tl* and *Vk* the average speed of vehicle *k* at the link downstream of stop *j*. The expected arrival time is expressed by Eq. (43):

$$\mathbf{t}\_{\rm ijk}^{\rm arr, tl} = \mathbf{t}\_{\rm ijk}^{\rm exit} + \frac{\mathbf{d}\_{\rm j, tl}}{\mathbf{V}\_{\rm k}} \tag{47}$$

After the expected arrival time is calculated, information of the signal timing and phasing are transmitted, to estimate if the vehicle will stop or not by the time of the arrival at the intersection. If the current indication is red then the remaining

time for red *t Red*,*remain* is estimated and added to the expected arrival time *t arr*,*tl ijk* . Then the recommended speed is calculated using Eq. (44):

$$V\_k^{\text{RGLOSA}} = \frac{d\_{\,j,tl}}{\left(t\_{ijk}^{arr,tl} - t\_{ijk}^{exit} + t^{\text{Red},remain}\right)}\tag{48}$$

In case of green, the vehicle should either accelerate to catch the current phase or wait for the next green phase. Therefore, two candidate speeds can be recommended, one for the estimated arrival time *t arr*,*tl ijk* and one for the expected arrival at the next green phase, given by Eqs. (45) and (46), respectively.

$$V\_1^{\text{RGLOSA}} = \frac{d\_{j,tl}}{\left(t\_{ijk}^{arr,tl} - t\_{ijk}^{exit}\right)}\tag{49}$$

$$V\_k^{\text{RGLOSA}} = \frac{d\_{j,tl}}{\left(t\_{ijk}^{arr,tl} - t\_{ijk}^{exit} + t^{Green,remain} + t^{Red}\right)}\tag{50}$$

where *t Red* the red time of the cycle of the current traffic light.

In case of two candidate speeds, the one respecting the speed limits is selected. If both speeds are within the speed limits, *VRGLOSA* <sup>1</sup> is selected since vehicle accelerates to arrive during current green phase. If both speeds are outside the speed limits, no speed advisory is given by the controller. In contrast, if there is no need to restore regularity, the controller is treated as GLOSA.

## *4.1.2 Reliability green light optimal dwell-time adaptation (R-GLODTA)*

R-GLODTA is the second hybrid controller, combining holding and GLODTA. In principle, holding and GLODTA are using the same control logic, by extending the time at stop to achieve their objectives to restore regularity and mitigate stops at traffic lights respectively. Therefore, with this controller, the prolongation of dwell time at stops aims to satisfy both objectives. After the vehicle arrives at the stop and completes dwell time, two candidate holding times are calculated to restore regularity. Then, the expected arrival time to the next signalized intersection is estimated using Eq. (43).

If the expected arrival time is during green phase, then no GLODTA time is needed. In contrast, if the vehicle is expected to arrive during red, then the waiting time at traffic light *t wait*,*tl ijk* is calculated by subtracting the current red time *t Red*,*<sup>c</sup>* from the red time *t Red* as in Eq. (51):

$$t^{\mu \text{out}, \text{tl}} = t^{\text{Re} \, d} - t^{\text{Re} \, d, \text{c}} \tag{51}$$

The waiting time at the traffic light corresponds to the GLODTA time *t GLODTA*. The waiting time at traffic light is transferred at the bus stop and utilized as dwell time for the passengers. GLODTA time *t GLODTA* with the duration of green phase define a time interval, within a vehicle will traverse the downstream signalized intersection without stopping (Eq. 52).

$$\left[t^{\text{GLOData}}, t^{\text{GLOData}} + t^{\text{Green}}\right] \tag{52}$$

The hybrid controller can work as holding or GLODTA alone depending on the current performance and needs of the system. If both candidate holding times (for regularity and GLODTA) meet the criteria, then the shorter time is selected. If with both holding times, the vehicle is expected to arrive during red, then the holding time with the less estimated remaining time at the traffic light is selected and the controller counts simply as a regularity controller:

$$t^{hold} = \min\left(t\_{ijk}^{exit} + t\_{ijk,1}^{hold} + \frac{d}{V\_k}, t\_{ijk}^{exit} + t\_{ijk,2}^{hold} + \frac{d}{V\_k}\right) \tag{53}$$

first level, referred as weak TSP, the scenario in which both green extend and green recall are up to 5 s. With strong TSP, green phase can be modified by 15 s In the R-GLODTA scenarios only strong TSP is tested. Lastly, in the R-GLODTA scenarios, the hybrid controller is combined with GLOSA and TSP.

*Optimal Management of Electrified and Cooperative Bus Systems*

*DOI: http://dx.doi.org/10.5772/intechopen.93892*

The main performance indicators used in this study are the adherence of headway of the line as well as the total trip time and its variability. Moreover, we will also analyze the delay at the signalized intersections and the times the vehicles managed to pass through a green phase. Finally, for the performance of the joint controller, the number of times requested is given and the share or each subcontroller are recorded. In summary, these are the performance indicators selected

• Regularity indicators: Coefficient of variation of headways; bunching;

• Link performance indicators: stop frequency and delay at traffic light, average

• Controller performance: share of control requests and of controller choice.

All regularity indicators are summarized in **Table 2**. It is clear from the results that the control schemes, the objective of which is to regulate the operation, dominate the regularity indicators. The coefficient of variation of headway and the level of bunching are chosen are regularity indicators. It should be noted that R-GLOSA has a minor difference from holding control since it is based on the same criterion to calculate holding time. The additional gaining comes from the speed recommendation given by the GLOSA part of the controller. Among strategies there are no significant differences in waiting time of passengers at stops. The independent application of the two DASs has no effect on system's regularity. Both have the same performance with the benchmark scenario. The regularity indicators remain unchanged regardless the TSP strength and similar to the do-nothing scenario. R-GLOSA manages to integrate the performance of holding strategy in terms of regularity and GLOSA in terms of cycle time. The cycle time with R-GLOSA is better than weak TSP and results to the least variable cycle time among all

> **In vehicle time [s]**

**Cycle time [s]**

**Cycle time deviation [s]**

• Passengers' cost indicators: in-vehicle time; waiting time at stops;

for the study:

*4.2.1 Results*

**Table 2.**

**111**

*Regularity performance indicators.*

speed and running time;

**CV Line** **Bunching Waiting time**

**[s]**

**NC** 0.599 0.372 302.98 204.74 4096.91 415.61 **HOLDING** 0.486 0.269 302.38 211.90 4042.55 415.61 **GLODTA** 0.628 0.382 302.40 212.49 4166.16 505.49 **GLOSA** 0.597 0.351 302.63 200.66 4050.49 480.16 **RGLOSA** 0.466 0.254 302.30 212.73 4042.09 394.56 **TSP5** 0.607 0.378 303.14 204.00 4060.26 472.07 **TSP10** 0.590 0.358 302.22 203.25 4013.18 472.07 **TSP15** 0.613 0.370 301.45 198.51 4012.75 490.94

In case of on time or late arrival, the vehicle will depart after *t GLODTA* in order to recover by saving time at traffic light, again if needed. This joint strategy, which we name R-GLODTA.

#### **4.2 Cooperative control in the City of Luxembourg**

The two hybrid controllers are tested for one of the busiest lines of the city of Luxembourg, AVL Line 16. Line 16 is the backbone of the bus network of the city of Luxembourg. As depicted in **Figure 7**, The line consists of 19 stops, among which there are stops in the city center, the central business district of Kirchberg and the new activity zone of Cloche d'Or at the south. Additionally, Line 16 connects the central railway station, the airport and the Kirchberg multimodal transport hub. The line is running in high frequency and double articulated busses are used. In addition, the busses run in dedicated lanes and are equipped with AVL technology. We assume that all traffic lights have the same signal program with cycle of 120 s (80 green and 40 red) with the red indication first at the simulation environment. No coordination has been considered between signals.

Two case studies, one for each of the newly introduced controller, were conducted. In both cases, a do-nothing scenario is used as a benchmark scenario. In addition, the hybrid controllers are compared with a holding strategy and the individual application of GLOSA and GLODTA. Moreover, different levels of TSP are put into test. For the R-GLOSA scenarios, three different levels are tested. The

**Figure 7.** *Line 16 in Luxembourg City.*
