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Performance measure against which our proposed policy to be tested is green time utilization. This performance measure is estimated by measuring the green time during which vehicles are served for an instance of a given phase and then dividing by the total length of the green time instance (i.e. minimum and maximum green time)
The supporting data for green time utilization are as follows: * Allocated minimum and maximum green time * vehicle departure times * Saturation headway

These data can be retrieved from the Signal control data and stop line detector. Our objective is to maintain ideal state as long as possible if control system deviates from this ideal state to (over-utilization) or (under-utilization) then by using adaptive control strategy system will take actions by changing existing policy.
Objective:
max.8≤Ugfk<1
Subject to constraints: g minfk≤gfk≤g maxfk (1) f=AFgfk≤C (2)
Here,
Ugf= Average time taken by vehiclesAvailable time
Ugf=number of departures in phase f× hsat{gmin, gmax}
Ugminf= number of departures in phase f× hsat{gmin}, Ugmaxf= number of departures in phase f× hsat{gmax}
So, theoretically the green time utilization should follow following condition to be remain in ideal state (i.e. state),
Ugmaxf<1≤Ugminf
So far in literature for traffic control systems are designed with three detection systems 1. Upstream detection for arrival rate 2. Downstream detection for occupancy detection 3. Both upstream and downstream detection
For most of developed country are following these systems, generally these control system works in order to respond the traffic demand which is estimated or predicted based on arrival rate (or headway).With this demand and departure rate (if known) one can find expected queued vehicles waiting for green signal.
But for heterogeneous traffic (mixed traffic) both 1 and 3 detection systems are not suitable. Using 2nd system of detection, number of departures and departure headway can be measured. In our problem also we are having inputs from stop line detectors only, so we are relying on departure rate only. To find expected number of queued vehicles at each link at end of fth phase of kth cycle, the computations are carried out by weighted average method where most recent cycle having more weight.
For model proposed here assumptions made are as follows, 1. Arrival rate does not exceeds capacity of intersection 2. One major assumption is that service rate = arrival rate 3. Even though data is available for all links, from each group of link only critical link data is considered for setting parameters. 4. Each vehicle is considered as one unit irrespective of its size and length
When control system monitors the flow at intersection phase by phase the resulting states of the phases are one of the / / . These states at end of each phase trigger the control action. In order to find better policy controller changes the signal parameters which would serve the estimated traffic demand.

Control strategy The objective of the controller system is to maintain the phase as long as possible on control horizon.
Case 1. If last phase was in state * Increase gmin and gmax or * Reduce threshold headway value (hthr)
Case 2. If last phase was in state * Reduce gmin and gmax or * Increase threshold headway value (hthr) So, to take these actions in terms of increase or decrease the control parameters requires approximate number of vehicles that may be queued-up at link in next phase.

One fundamental component of any traffic adaptive signal control system is the prediction of queue lengths at signalized intersection approaches. How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The because cumulative vehicle count for arrival traffic is not available here for our model instead of counting arrival traffic flow in the current signal cycle, we solve the problem of measuring intersection queue length by exploiting the queue discharge process in the immediate past cycle. Using traffic signal data, and applying simple forecasting model we are able to identify traffic state changes that distinguish queue discharge flow from upstream arrival traffic. Therefore, our approach can estimate time-dependent queue length even when the signal links are congested with long queues our model are evaluated by comparing the estimated maximum queue length with the ground truth data observed from the field. Evaluation results demonstrate that the proposed models can estimate long queues with satisfactory accuracy. It’s difficult to predict the flow rate or queued vehicles in next time interval (red time) based on number of departures in last time interval (green time). Here I used time interval term because red and green interval are the two time intervals which are taking place alternatively for each group of links. It is obvious that the number of queued vehicles at links of active phase is depending on the green time given to other active phase in same cycle.

The intersection controlled by traffic lights pertaining to cycle of common length C, this cycle involves the phases which are responsible to clear the traffic from set of links. i= Index for links {i=1, 2,…, I} f= Index for phase {f=A, B,…, F} k=Index for cycle {k=1, 2,…, K} l= Index for vehicle {l=1, 2,…., L} gi, minfk=Minimum green time required for fth phase of kth cycle gi, maxfk=Maximum green time required for fth phase of kth cycle gifk= Green time taken by fth phase of kth cycle hthrfk= Threshold departure headway (Maximum allowable headway) value for fth phase of kth cycle (Set at the beginning of kth cycle) hlf= Departure headway value for lth vehicle of fth phase
P (k) = Policy for kth cycle {gi, minfk,gi, maxfk, hthrfk}, ∀f difk-1 = Number of departures from link i at end of fth phase of (k-1)th cycle qifk= Expected number of queued vehicles at link i at end of fth phase of (k-1)th cycle
Li= Distance between upstream entry detector and stop line detector of link i
Vi= Average speed of vehicles on link i τi = Travelling time in link i =LiVi
Sifk= Signal status
Sifk=1 if phase f is active in kthcycle 0 O.w
We want to predict the queued vehicles at links of inactive phase. As queued vehicles during inactive phase is function of green time given to active phase (or red time of inactive phase) qifk=0 if iϵfgfk.(1/3)j=13dicF/fk-jgF/fk-j, if i∉fgfk.(1/3)j=02dicF/fk-jgF/fk-j, if i∉f and f=B ∀ i,f
Control parameters
Expected queue service time for next phases of kth cycle is, gF/fk=qicfk. hsat+startup lost time,
If fth phase is last phase then, expected queue service time required, gF/fk+1=qicfk. hsat+startup lost time
The condition for revision of green time bounds is arises if at end of fth phase of kth cycle corresponding critical link’s status is or , 1) - State (Over-utilization of green phase):
Whatever green time allocated to particular phase is not sufficient to serve the demand of traffic from set of links included in that phase.
Therefore for setting green time limits on phases in next cycle we use averaged demand over last 3 cycles, gminF/fk=max⁡{gmaxF/fk-1, gF/fk} gmaxF/fk= 1.15.gF/fk
(Here, we assumed 15% more green time for maximum allowable green time) 2) - State (Under-utilization of green phase):
Whatever green time allocated to particular phase is much more than that of required to serve the demand of traffic from set of links included in that phase.
If at end of fth phase of kth cycle corresponding critical link’s status is then, similarly for setting green time limits on phases in next cycle we use averaged demand over last 3 cycles, gminF/fk=min{gminF/fk-1, gF/fk} gmaxF/fk= min{1.15.gF/fk, gmaxF/fk-1}

Example: If intersection is having four links i= {1, 2, 3, 4} designed with two phases {A, B} and Set of critical link is ic= {1, 2}
The main objective is to predict the queue length
Here,
f Active phase

For above intersection,
If f=A, in kth cycle
Then the link group belongs to phase A does not have any queued vehicle at end of phase A of kth cycle, q1Ak=0, q3Ak=0
This gives the prediction for queued vehicles at link 1 and 3 at end of phase ‘A’ in kth cycle.
Whereas, for link group of inactive phase, q2Ak=gAk.(1/3)j=13d2Bk-jgBk-j ,
This gives the prediction for queued vehicles at link 2 at end of phase ‘A’ in kth cycle. q4Ak=gAk.(1/3)j=13d4Bk-jgBk-j
This gives the prediction for queued vehicles at link 4 at end of phase ‘A’ in kth cycle.
Control parameter
For above problem, expected queue service time for phase B of kth cycle is, gBk=q2Ak. hsat+startup lost time,
If f=B, in kth cycle
Then the link group belongs to phase A does not have any queued vehicle at end of phase A of kth cycle, q2Bk=0, q4Bk=0
This gives the prediction for queued vehicles at link 2 and 4 at end of phase ‘B’ in kth cycle.
Whereas, for link group of inactive phase, q1Bk=gBk.(1/3)j=02d1Ak-jgAk-j ,
This gives the prediction for queued vehicles at link 1 at end of phase ‘B’ in kth cycle. q3Bk=gBk.(1/3)j=02d3Ak-jgAk-j
This gives the prediction for queued vehicles at link 3 at end of phase ‘B’ in kth cycle.
Control Parameter
If fth phase is last phase then, expected queue service time required, gAk+1=q1Bk. hsat+startup lost time

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