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| Notations | Definitions |
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| The average delays of buses |
| The average delays of nontransit vehicles |
| The average delays of all vehicles (both buses and nontransit vehicles are included) |
| The green duration of the phase in the cycle after optimization |
| The green duration of the phase in the cycle before optimization |
| The minimum green duration requirement of the phase |
| The minimum cycle length requirement |
| The length of the cycle after optimization |
| The length of the cycle before optimization |
| The maximum cycle length requirement |
| The saturation flow rate of the leg |
| The arrival rate of the leg |
| The duration of the control horizon |
| The detected moment from the start of the control horizon |
| The buffer time duration. Usually set as the sum of all red duration and yellow duration |
| The outcome of dwell time for bus detected at the cycle in the leg |
| The probability of the bus dwells at the station for second(s) |
| The moment when the bus arrives at the stop line if the bus dwells at the station for second(s) |
| The start moment of the nearest unfinished green stage for leg at cycle |
| The delays of the bus if the bus dwells at the station for second(s) |
| The moment when the queue is cleared in cycle in leg in scenario |
| The maximum allowed degree of saturation in leg |
| The phase that grants right-of-way to cars in leg |
| The design operation speed for buses in leg |
| The end time of the phase in cycle after optimization |
| The end time of the phase in cycle before optimization |
| A binary variable indicating whether the end moment of the phase in the cycle is changeable |
| A large enough positive number |
| The mathematical expectation of the random variable |
| The delays of nontransit vehicles in leg , cycle , and under the scenario |
| The delays of nontransit vehicles in leg and cycle |
| An indication of whether the condition is true |
| The distance between the station and the stop line in leg |
| The distance between the detector and the stop line in leg |
| The number of residual nontransit vehicles in cycle , leg , and under the scenario |
| The number of residual nontransit vehicles in cycle and leg |
| The number of phases in the intersection |
| The number of nontransit vehicles appears in the intersection during the control horizon |
| The number of buses appears in the intersection during the control horizon |
| The number of cycles included in the control horizon |
| The number of legs in the intersection |
| The number of the outcomes of bus dwell time in the leg |
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