Pre-time signal control
The pre-timed control, which has fixed cycle lengths and preset phase times, operates according to a predetermined time schedule. The pre-timed controllers are best suited for locations with stable volumes and traffic patterns such as downtown areas.
Timing plans are usually selected on a time-of-day/ day-of-week basis. Although pre-timed controllers have a degree of flexibility for daily traffic, they can cause excessive delay when the traffic signal controller uses timing plans determined from historical demands. The Webster method can be used to determine the optimum cycle lengths for minimal delay.
Webster (1958) [32] has shown that minimum intersection delay is obtained when
the cycle length is obtained by the equation
(2.11) where:
C = optimal cycle length (second);
L = total lost time per cycle (second);
yi = the critical lane group volume (i th phase, vph) / saturation flow (vph);
n = number of phases.
The total lost time is the time not used by any phase for discharging vehicles. Total lost time is given as
(2.12) where:
li = lost time for phase i, which is usually 4 seconds;
R = the total all-red time during the cycle.
The total effective green time, available per cycle, is given by
(2.13) To obtain minimum delay, the total effective green time should be distributed among the different phases in proportion to their y values to get the effective green time for each phase,
(2.14) The actual green time for each phase (not including yellow time) is obtained by
(2.15) Where is yellow time for phase i.
Actuated signal control
An actuated signal [33] operates with variable vehicular timing and phasing intervals that depend on traffic volumes. The signals are actuated by vehicular detectors placed in the roadways. The cycle lengths and green times of actuated control may vary from cycle to cycle in response to demands. Actuated controllers include semi-actuated, fully actuated, and density controllers.
In semi-actuated operation, the main street has a “green” indication at all times until a vehicle or vehicles have arrived on one or both of the minor approaches. The signal then provides a “green” phase for the side street that is retained until vehicles are served, or until a preset maximum side-street green is reached. Non-actuated phases may be coordinated with nearby signals on the same route, or they may function as an isolated control. Non-actuated phases usually operate with fixed minimum green times and may be extended by using green time that is not used by actuated phases with low demand. That is, the green duration will be extended beyond the minimum green time until a vehicle actuates the detector on the side street. At a semi-actuated controlled intersection, detectors installed on the side street collect information for timing the signal.
In fully actuated operations, all signal phases are controlled by detector actuations.
In general, each phase has a minimum green duration, but it also is shorter than the maximum green time. A phase in the cycle may be skipped entirely if no demand exits for that phase. The right of way does not return automatically to a specific phase under the fully actuated mode unless recalled by a special setting in the controller. That is, the controller shows green indication in the phase last served until conflicting demand appears.
In density operations, the controllers keep track of the number of arrivals and
reduce the allowable gap according to several rules as vehicles show up or as time progresses. The specifications allow gap reduction based only upon time waiting on the red. This type of controller also has a variable initial interval, thus allows a variable minimum green. Detectors are normally place farther back of the intersection stop line, particularly on high-speed approaches to the intersection of major streets.
The timing characteristics of actuated signal operation are introduced here. In an actuated phase, there are three timing parameters: the minimum green interval, the unit extension, and the maximum green interval. These intervals are a function of the type and configuration of the detectors installed at the intersection. These three intervals are shown in Figure 2.11. This figure shows a case that the phase terminates before it reaches the maximum green period because there is no vehicular actuation in the last unit extension period.
The unit extension is time by which a green phase could be increased during the extendable portion after an actuation on that phase. It depends on the average speed of the approaching vehicles and the distance between the detectors and the stop line.
Initial interval is the first portion of the green phase that is adequate to allow vehicles waiting between the stop line and the detector during the red phase to clear the intersection. This time depends on the number of vehicles waiting, the average headway, and the starting delay.
The minimum green interval is the shortest time that should be provide for a green interval during any traffic phase. In basic design of actuated phase intervals, the minimum green interval equals the sum of the initial interval and the unit extension.
Figure 2.11 Actuated phase intervals
The maximum green interval is the limit that a phase can hold green in the presence of conflicting demand. Normal range of maximum green is between 30 and 60 seconds depending on traffic volumes. Webster‟s model for pre-timed controllers can be used to compute the maximum green interval. The computed green intervals are multiplied by a factor ranging between 1.25 and 1.50 to obtain the maximum green.
Traffic-actuated controllers automatically determine cycle lengths and phase durations based on detection of traffic on the various approaches. The cycle lengths and green times are random variables, which depend on the real-time traffic demand.
Therefore, the capacities of approaches to an intersection are random variables.
Synchro software
Synchro [34] is a macroscopic and deterministic signal timing tool. Synchro has the following features: it is able to simultaneously optimize lead-lag phase ordering in addition to cycle lengths, phase lengths, and coordinated offsets, Percentile Delay estimation method, data input and comprehensive output options, capability of modeling RTOR, U-turns and six-legged intersections, capability of modeling signalized and signalized intersections and roundabouts and it allows exporting its files to CORSIM and HCS.
Synchro implements the HCM 2000 procedures for signalized intersections capacity and delay calculation. Also, it possesses percentile delay calculation method and intersection capacity utilization (ICU) 2003 methods. The basic premise of the percentile delay method is that traffic arrivals follow a Poisson distribution. The percentile delay method calculates vehicle delays for five different scenarios (i.e., 10th, 30th, 50th, 70th and 90th percentiles) and takes a volume weighted average of delays predicted for each scenario. The ICU method sums the amount of time required to serve all movements at saturation for a given cycle length. It is similar to taking sum of critical volume to saturation flow ratios (v/s), yet allows minimum timing to be considered. The ICU can tell how much reserve capacity is available or how much the intersection is overcapacity.
Synchro does not use the Genetic Algorithm for optimization of signal timings.
The optimization objective function available is minimizing the percentile delay. It optimizes the four signal timing parameters by evaluating a series of cycle lengths, applying a heuristic method for green splits, conducting an exhaustive search for
The best cycle length is found by calculating a performance index (PI).
The PI is calculated as follows.
(2.16) where
PI = Performance Index;
D = Percentile Signal Delay (s);
QP = Queue Penalty (vehicles affected);
ST = Vehicle Stops (vph);
D=
;
VD10 = 10th percentile Vehicle-Delay per hour;
v10 = 10th percentile volume rate (vph).
TRANSYT 7F
TRAffic Network StudY Tool (TRANSYT) is one of the most widely used signal timing programs. The original version of TRANSYT was developed by Dennis Robertson at the Transportation and Road Research Laboratory in UK in 1967. Though TRANSYT is most commonly used as an offline optimization tool, it may also be used in an online fashion to compute signal settings every few minutes and download these settings to the field. TRANSYT is a macroscopic, deterministic simulation and optimization model. The model requires the link flows and link turning proportions as inputs and assumes them to be constant for the entire simulation period. The program optimizes splits and offsets given a set cycle length and carries out a series of iterations between its traffic simulation module and the signal setting optimization
module. TRANSYT-7F (Traffic Network Study Tool, version 7, Federal) [35] was
“Americanized” for the Federal Highway Administration (FHWA) in 1981 by the University of Florida Transportation Research Center. TRANSYT-7F Release 10.1 introduced in January 2004 included the ability to optimize cycle length, phase sequence, green splits and offsets using a genetic algorithm (GA) and a traditional hill-climb technique. Recent versions of TRANSYT-7F introduced the CORSIM simulator in its optimization of cycle length, green splits and offset only. The direct-CORSIM optimization in T7F consists of the CORSIM simulator and the GA optimizer. It uses the CORSIM input file (*.trf) as an input so that T7F can directly import all information related to the network and signal timing plan from the CORSIM input file.
TRANSYT-7f includes detailed simulation of platoon dispersion, queue spillback, queue spillover, traffic-actuated control, and the flexibility to perform lane-by-lane analysis. Beside link wise simulation, TRANSYT-7F provides stepwise simulation which updates all links one time step at a time. With stepwise simulation, TRANSYT-7F can explicitly model queue spillback condition. TRANSYT-7F provides left-hand drive right-hand drive option and it can only simulate two-way stop-controlled (TWSC) intersections. HCS files can be loaded directly into T7F and timing plans can be exported from T7F to HCS. Many traffic principles embedded in TRANSYT-7F such as arrival type, delay calculation, level of service, capacity calculation and saturated flow calculation are based on HCM 2000 procedures. TRANSYT-7F includes measures of effectiveness (Throughput) for use in optimization of congested networks.
TRANSYT-7F has twelve distinct criteria. These criteria include functions designed to minimize delay, minimize a combination of delay and stops (the Disutility Index-DI),
The performance index (PI) may be defined as follow:
PI=
(2.17)
MAXBAND
In 1966, John D. C. Little and his research colleagues at MIT defined the new state of the art, called MAXBAND[36, 37, 38], ending with a set of algorithms to synchronize fixed-timed traffic lights for streets with two-way traffic. It is one of the representatives of the Fixed-Time Coordinated Control Strategies. By their nature, fixed-time strategies are only applicable to under-saturated traffic conditions.
MXBAND considers a two-way arterial with n signals from S1 to Sn (intersections) and specifies the corresponding offsets in order to maximize the number of vehicles traveling at given range of speed without stopping at any signal (green wave).
MAXBAND considers splits as given (in accordance with the secondary street demands); hence the problem consists in placing the known red durations of the arterial‟s signals to maximize the inbound and outbound bandwidths In_B and Out_B, respectively (See Figure 2.12). In order to make MAXBAND work for a network of arterials, Little (1966) extended the basic MAXBAND method by incorporation of some cycle constraints. MAXBAND used into several networks into North America and other countries.
Figure 2.12 A maximum band along an arterial [36].
The underlying optimization model in MAXBAND is a Mixed Integer Linear Programming (MILP) model. MAXBAND include its freedom to provide a range for the cycle time and speed and it can operate a traffic signal effectively through the interlocking control of neighboring intersections. Its disadvantages are the lack of incorporated bus flows, limited field tests and because it is based on off-line analysis, it is impossible for it to cope actively with irregularities in the traffic environment.
MAXBAND optimizes the signal by maximizing arterial progression bandwidth.
The output of the program includes cycle time, offsets, speeds and order of left turn phases to maximize the weighted combination of bandwidths. The program can automatically choose cycle time from a given range, allow the design speed to vary within given tolerances, select the best lead or lag pattern for left turn phases from a specified set, allow a queue clearance time for secondary flow accumulated during red, accept user-specified weights for the green bands in each direction and handle a simple
network in the form of a three artery triangular loop.
The limitation of Maximization existing bandwidth is that the progression bands do not correspond to the actual traffic flows on the arterial links. Therefore, bandwidth maximization will not always lead to optimal system performance in terms of stops, delay, and fuel consumption.
Near researches
The jammed traffic of closely spaced intersections is generally derived from poor progression, unstable demands and inefficient signal operation. Poor regression of the signals leads to queue spill-back from one intersection to upstream intersections. To solve the aforementioned problems, researches focused on oversaturated demand, closely spaced intersections, and traffic flow theories should be considered together.
Abu-Lebdeh and Benekohal [23] had developed a traffic control method and queue management procedures for oversaturated arterials. Chang and Sun [39] had optimized an oversaturated network by utilizing a bang-bang like model for the oversaturated intersections and TRANSYT-7F for the undersaturated intersections. Michalopoulos and Stephanopoulos brought the concept of shockwave theory to traffic signal control [29].
Tian, Urbanik and Gibby [40] had an application of diamond interchange control strategies on a site of six closely spaced intersections. Messer [41] had studied the traffic operations at oversaturated, closely spaced signalized intersection by NETSIM simulations. Liu and Chang [42] had an arterial signal optimization model to do with queue spill-back and lane blockage. Existing researches usually paid attention to through traffics of the arterial; however, they seldom focused on the crooked traffics of the adjacent minor approaches. As the traffic demand on minor approaches grows, progression on those approaches should also be introduced. Despite the contribution of those researches, most of such models have not addressed such progression issue.
Existing full-actuated signal scheme can only be applied to arterials; not much it can do while facing a path-based progression situation. Zheng and Chu [43] and Skabardonis [31] suggest methods to dynamically adjust maximal green for full-actuated control under oversaturated traffic. With adjustable maximal green, full-actuated control scheme have the potential to adaptive to oversaturated demands.
However, full-actuated schemes are focused on approach or arterial; they never focused on path-based progression. Therefore, they should be modified to suit the specific path-based situation.
III. Research methodology
In this chapter, some essential concepts of the critical path signal control of closely spaced intersections are discussed. Begin with the introduction to Radar vehicle detection algorithm, the brief introduction to three new traffic parameters is addressed in section 3.2. Section 3.3 shows the shockwave detection at intersection. The estimation for upstream flow and speed by shockwave concept is illustrated in section 3.4. A critical path signal control algorithm is introduced, in section 3.5.