1. Lecture 1 Traffic Signal Coordination

2. Lecture 1 Why? When the traffic signals are placed close enough, it is often seen that the cars waiting in a queue in the upstream signal looses green time at a downstream signal, only to arrive there as the signal turns red. Hence, coordination is needed to establish efficient network-wide signal systems. Coordination attempts to achieve some combination of the following objectives: Minimise fuel consumption Minimise pollution emission Minimise stops Minimise delay Maximise smooth flow Maximise capacity Minimise queue length Minimise arrival of platoons at red lights The signals less than 800m apart are coordinated as common practise. All but most complex coordination scheme requires same cycle length for all signals.

3. Lecture 1 Factors influencing coordination Benefits: 1.The conservation of energy and the preservation of environment. 2.Maintenance of preferred speed 3.More cost-effective transport system Factors lessening benefits: 1.Inadequate roadway capacity 2.Existence of parking, loading space etc. 3.Complicated intersections, involving multiphase control 4.Wide variability of traffic speeds 5.Very short signal phasing 6.Heavy turning volumes Exception: Some intersections with heavy traffic volume might not be included in the network-wide coordination scheme and might be designed for a different (mostly longer) cycle length. This type of intersections need special consideration while modelling.

4. Lecture 1 Terminology OFFSET Offset: the difference between the green initiation times at two adjacent intersections. Usually expressed as a positive number between zero and the cycle length. Sometimes convenient to think of it as a negative number, usually no more than one half a cycle length. Ideal offsets The ideal offset is a value such that the first vehicle of a platoon just arrives at the downstream signal, the downstream signal turns green. t(ideal) = L/S where, L = block length, S= vehicle speed BANDWIDTH The amount of green time used by a continuously moving platoon of vehicles through a group of intersections (time difference between the first and the last vehicle moving through the system without stopping)

5. Lecture 1 Terminology TIME-SPACE DIAGRAM Plot of signal indications as a function of time Trajectory: Path vehicle travels in time (X-axis) Signal Layout according to distance (Y-axis)

6. Lecture 1 Signal Progression in 1-way street Assuming no vehicles are queued at the signals, the ideal offsets can be determined assuming a desired platoon speed (say,60 fps)

7. Lecture 1 Signal Progression in 1-way street Time space diagram 1.The vertical should be scaled so as to accommodate the dimensions of the arterial, and the hori­zontal so as to accommodate at least three to four cycle lengths. 2.The beginning intersection should be scaled first, usually with MSG initiation at t = 0, followed by green and red phase (yellow may be shown for precision). See Point 1. 3.The MSG of the next downstream signal should be located next, relative to t = 0. With this point located (Point 2), fill in the periods of green, yellow, and red for this signal. 4.Repeat the procedure for all other intersections, working 1 at a time.

8. Lecture 1 Signal Progression in 1-way street Effects of vehicles queued The lost time is counted only at the first downstream intersection, at most: If the vehicle(s) from the preceding intersection were themselves stationary, their start-up causes a shift that automatically takes care of the start-up at later intersections. The ideal offset is calculated as, t ideal = L/S – (Q.h +Loss) where, Q = # veh queued per lane, h = discharge headway (~ 1.9 s), Loss = loss time associated with vehicles starting from rest at the first downstream signal (~2 s)

9. Lecture 1 The time-space diagram for the example, given queues of 2 vehicles per lane in all links. The arriving vehicle platoon has a smooth flow, and the lead vehicle has 60 fps travel speed. The visual image of the "green wave" or progression speed is much faster. The "green wave“ is travelling at varying speeds as it moves down the arterial. However, the window available for moving a platoon nonstop is much smaller.

10. Lecture 1 A note on queue estimation It is a difficult and expensive task to estimate the queue size from cycle to cycle. Sources of queued vehicles may include:  Vehicles turning in from upstream side streets during their green (which is the main-street red)  Vehicles leaving parking garages  Part of a previous platoon truncated by insufficient green

11. Lecture 1 Signal Progression in 2-way street Determining ideal offset on a 2-way street If any offset is changed to accommodate the southbound vehicle then the northbound movement will suffer. Hence, actual offsets in both directions are interrelated t NB,I + t SB,I = nC Actual offsets are ideal offsets + some error term.

12. Lecture 1 Signal Progression in 2-way street 1.Offsets in a two-way arterial are not independent. 2.A typical cycle yields the obvious conclusion that the offsets in two directions adds up to the cycle length. 3.However, for longer block lengths the offsets might add to two (or more) cycle lengths. Indeed, when queue clearances are taken into account, the offsets might add to zero cycle lengths. 4.In signal optimization programs the objective is to minimise the total discrepancies between actual and ideal offsets for all the designed links.

13. Lecture 1 Signal Progression in Grid The relative difficulty of finding progressions on a two-way street, compared to on a one-way street, might lead one to conclude that the best approach is to establish a system of one-way streets, to avoid the problem. A one-way street system has a number of advantages, not the least of which is elimination of right turns against opposing traffic. However, the total elimination of the constraints imposed by the "closure" of loops within the network or grid is not possible. In the figure: If the cycle length, splits, and three offsets are specified, the offset in the fourth link-denoted Link D in this Illustration is determined and cannot be independently specified. In a grid of multiple one-way streets, where the offsets in all the NS links are independently specified, then the specification of a single EW offset will lock all other EW offsets.

14. Lecture 1 Signal Progression in Grid This extends to a grid of one-way streets, in which all of the north-south streets are independently specified. The specification of one east-west street then "locks in" all other east-west offsets. Note that the key feature is that an open tree of one-way links can be completely independently set, and that it is the closing or "closure" of the open tree which presents constraints on some of the links.

15. Lecture 1 Signal Progression in Grid

16. Lecture 1 After reaching intersection 1, we are back at the starting point and now t=0 or a multiple of cycle length. And we can write, The g values should include the change and clearance intervals. Fundamental results: if you set the offsets in one direction on a 2-way street, then you also set them in the other direction. In a network, you can set any" open tree" of links, but links that close the tree already have their offsets specified".

17. Lecture 1 Signal Progression in Grid

18. Lecture 1 Signal Progression in Grid While it is sometimes necessary to consider networks in their entirety, it is common traffic engineering practice to decompose networks into non-interlocking arterials whenever possible.

19. Lecture 1 Bandwidth This concept is very popular as the windows of green are easy visual image for professionals and public perception and good solutions can be often obtained manually. But, when substantial internal queues exist, this solution can be misleading and erroneous. Efficiency of a bandwidth is defined as: Efficiency(seconds) = (bandwidth/cycle length) X 100% An efficiency of 40-55 % is considered as good. The bandwidth is limited by the min green in the direction of interest. Nonstop volume =[3600 (BW) (L)]/(h)(C) vph Where BW = measured or computed bandwidth (s); L = number of through lanes; h = headway (sec/veh), C = cycle length (s) Generally bandwidth in the two opposing dierctions are designed to be in the same ratio as the flows in the two directions.

20. Lecture 1 Bandwidth

21. Lecture 1 Signal Progression