Model petri net of adaptive traffic lights and its collaboration with a special event

Traffic lights have an important role as the system control of vehicles flow on the urban network. Commonly, most countries still using fixed time strategy. Our research proposes the adaptive traffic lights model to response the traffic demand. It uses basic Petri net as a general modeling framework. Foractuating method of minimum and maximum green signal time interval, the green traffic lights have three-time extension units. Next, we collaborate on a case of the existence of railways that crosses on the southern arm of an intersection. We introduce both of collaboration model design of traffic lights and the railway's gate which always closes while a train passing. Verification and validation of the model are based on the simulation result of vehicles queue. The collaboration model design of traffic lights has excellent performance, and it can resolve the congestion problem better than conventional schedule.


1Introduction
The primary role of the traffic lights is to improve the capacity and performance of junctions/ intersections in urban network area [1]. Traffic lights are installed to reduce congestion and travel delays, to make the main road crossable, to establish the time sharing fairly, to improve the safety of traffic vehicles and pedestrians, and so efficiency [2], [3].
Based on the time strategy, traffic lights are classified into two main categories, i.e., Fixed time strategy and traffic responsive strategy. The setting of the first strategy assumes that the traffic demand is constant. The second strategy is traffic lights that have the real-time control signal measurement [4]. It uses detectors to respond the fluctuation of traffic demand or special events [3].
The standard traffic lights have the sequence of green, yellow, and red signals that turn on in the specific time interval [5]. This paper's aim proposes modeling approach of adaptive traffic lights. This model is very beneficial to adjust to fluctuations in vehicles volume that passes on the road. Primarily in connection with the existence of a railway crossing. Of course, the number of railway's gate closures in the day will increase significantly during the beginning of double track of Railways era. It uses Petri Net (PN) to model traffic light behavior because they offer representation of conflict, sharing, synchronous and asynchronous, and priority [5]. Petri Net (PN) consisting of a four-tuple elements, i.e., places, transitions, arcs and tokens [6], [7].
The Marking places in a Petri Netcontaining a discrete number of tokens that the distribution represents a reachability of the net. An enabled transition of a Petri net may fire states while there are sufficient tokens in all of its input places. The firing of a transition consumes the required input tokens and deposits tokens in its output places [5].
A place may be refined into a subnet with many places and transitions resulting an expanded Petri Net [8]. That becomes the controller of the time interval of traffic lights. T = {t1, t2, t3,.... tm} is a transitions finite set, T ≠ Ø, mN+. Transitions are illustrated by bars. The task of enabled transitions is as the trigger tools for signals, or events change. These are given the term fire.
Pre: (P x T) → N+ is an input function that defines directed arcs from places to transitions.
Post: (T x P) → N+ is an output function that defines directed arcs from transitions to places. N+ is the set of nonnegative integers. M0 is the initial marking.
Based on the reason that the model design must correct, the Petri Net (PN) desires some properties [5], [6], i.e., Reachability, Reversibility, Boundedness, Safeness [9], Liveness or deadlock free [5].A Marking M is to be reachable from the initial if there exists a sequence of transitions firing which transform a marking from the initial. The Marking must able to return to the initial marking, It is called as reversible. Boundedness is a control strategy to prevent overflow in the model. A place p is said to be k-bounded if the number of tokens in p is always less than or equal to k(k ∈N+) for every marking M that reachable from the initial marking. It is safe if it is 1-bounded.

Green minimum and Maximum Time Interval
To reduce the top-down Petri net model complexity, the traffic lights design must be performed in a modular way. It may be presented in parts of the system, the subsystems, and a part of the subsystems.
The modularity can be specified and taken into account separately.
P_Green Thistype of adaptive traffic light system has a simple algorithm.Manysystems implement complex algorithms and require new technologywhich is often an error. This minimum and maximum systems are easy to implement and durable [5].

Signals Invariant of Two Phases Traffic Lights
Signal invariants indicate set of signal places which they guarantee the number of tokens remains unchanged in all reachable markings. All entries of signal place invariants are either 0 or 1. A signal turn on while a token exists in the signal place and the marking equal to 1. It will be off when it is empty and the marking equal to 0.
The invariant (1) presents that can be a token available in one of three signal places GSN, YSN, and RSN only of south-north traffic lights. It is similar for signal Places invariant (2). The signal place invariant (5) uses intermediation places S1 and S2. These are the artificial signal places. While a token exists in places S1 or S2, the traffic lights turn on red signal for all phases.

Method
The method for actuating minimum and maximum green signal time interval applies three-time extension units. The analysis and verification of traffic lights model use invariants, occurrence graphs, and Petri Net Simulator 2.0 for simulation [13]. At last, the performance test is also presented.

A Case Study
Acase is shown in Figure 2

Design Model of The Railway's Gate and Its Collaboration
Model of railway's gate in Fig. 3

. has two places, namely Idle (when it open) or Busy (while closed). The place busy includes circumstances of the preparation for closing the railway's gate that must be longer than or equal to the time interval of YSN. Based on the reason of model simplification, it is not shown. Transition tRC (ready to come) and tRC1 represent that the train ready to come and the railway's gate ready to close. The transition can be enabled if there are tokens in all its input signal places. The enabled transition can fire a token of the previous signal places to the next signal places. Transition tRC (ready to come) enabled if the train arrives while the Green South-North signal turns on. Otherwise, transition tRC1 enabled if the railway's gate ready to close while red South-North signal turns on. It bases on the information of the train detectors. Transition tC (completed) informs that the train had crossed completely and the railway's gate ready to reopen.
The train is the priority. The signal model design in Fig. 3. has GSN minimum and maximum time interval. For the road users safety reason, It must have unlimited time interval connecting to the time interval of railway's gate closure. Sometimes while the train ready to come, it forces the green signal to turn yellow and then red, and it maintains the red signal until the train passes completely.

Analysis and Verification of Petri Net Model Design
While the train is passing and the railway's gate is closing, this means that the busy state is going on. Conversely, while the railway's latch is not closing, it means in the Idle state. In this state applies invariant (6), (7), and (8).

Places invariant (6) presents that the railway's gate state are either Busy or Idle. Places invariant (7) means that the south-north traffic lights may not turn on green signal while the railway's gate is busy. Places invariant (8) notes that while the railway's gate closes the eastwest traffic lights must turn on green signal only.
Occurrence Graph (OG) shows that there is no possibility of a deadlock in the model. It is not presented here.

Simulation Results and Discussion
The Fig. 4

. is the result of the verification and validation of the east arm vehicles flow. It uses "Passenger Car Equivalence" (PCE) to measure the traffic flow volume [14].
While the traffic flows is low, the frequency of minimum green time interval on the east arm is high. Very low traffic occurs in the midnightcausing traffic lights to always be lit with minimum interval time.
When medium traffic time interval in the early morning, the green time interval can be on additional time ext 1, ext 2, or maximum. The time ext 1 (28 seconds) is 21 times, time ext 2 (32 seconds) is 25 times, and the maximum green time interval (36 seconds) is five times.
On the peak hours, it can be ext 2 or the maximum green time interval. While the heavy traffic and a congestion after the railway's gate reopened again, the traffic lights are always lit at the maximum green interval time.
Basedon the reason the system algorithm is simple, the system is easily repaired when a little damage occurs.Thefour-second extension on the green time interval proved precisely to the actual demand of traffic on each arm.    There has been a railway's gate closure for 135 seconds during the peak hours. The time interval is longer than a     10. shows the queue pattern implementing collaboration. At the beginning of the railway's gate closure, the queue of vehicles increase in accordance with the direction of the arrow. After the train has finished passing, the railway's gate reopened. The graph moves to left back. This means that the queue of vehicles decreased toward normal circumstances. It has a beautiful pattern. This illustrates the flow of vehicles in real situations that remain controlled. The bottlenecks are resolved in four cycles. It is two cycles faster when compared to the uncollaborated schedule.
The traffic lights setting applies collaboration able to reduce queues of vehicles coming from the east arm. The reopening of the railway's gate connected to the initial of the green signal for the north-south arm. The setting in this way is more efficient to ensure safety for all road users. The south-north traffic tends become impatient waiting after a long stop. Fig. 10. is a visualization of the performance of the schedule of the collaboration of traffic lights to railway's gate. It looked better results to tackle congestion after an interruption. Whenthe railway's gate reopens, and peak hour, the traffic light applies the maximum green signal time.
The patterns while a low traffic flows has a similar shape, but smaller. The response of minimum and the maximum time interval of the traffic light are not visible, this due to traffic volume fluctuations that impossible occurred in a short period.

Conclusion
It has introduced an adaptive traffic lights model design with Petri net. This study also introduced a traffic light model that applies an interruption. This model is a collaboration between traffic lights and railway's gate closure. The simulation results show that this model has a better performance when compared to ordinary traffic light model to overcome the bottleneck after the closure of the railway's gate.