The blocking problem naturally arises in transportation systems as multiple vehicles with different itineraries share available resources. In this paper, we investigate the impact of the blocking problem to the waiting time at the intersections of transportation systems. We assume that different vehicles, depending on their Internet connection capabilities, may communicate their intentions (e.g., whether they will turn left or right or continue straight) to intersections (specifically to devices attached to traffic lights). We consider that information collected by these devices are transmitted to and processed in a cloud-based traffic control system. Thus, a cloud-based system, based on the intention information, can calculate average waiting times at intersections. We consider this problem as a queuing model, and we characterize average waiting times by taking into account (i) blocking probability, and (ii) vehicles' ability to communicate their intentions. Then, by using average waiting times at intersection, we develop a shortest delay algorithm that calculates the routes with shortest delays between two points in a transportation network. Our simulation results confirm our analysis, and demonstrate that our shortest delay algorithm significantly improves over baselines that are unaware of the blocking problem.
Analyzing waiting times and modeling transportation systems using queueing theory have a long history (more than 50 years) @cite_0 . @cite_23 , @cite_15 , @cite_12 considered one-lane queues and calculated the expected queue length and arrivals using probability generation functions. These models focus on fixed-cycle traffic signals, and they calculate the steady-state delays and queue lengths under the assumption that the arriving process does not change over time @cite_1 . Time-dependent arrivals have also been considered in @cite_2 , @cite_16 , @cite_9 , @cite_25 , @cite_18 , @cite_14 , @cite_7 , @cite_21 , @cite_5 , @cite_4 . Different modeling strategies are also studied; such as the queuing network model @cite_8 , cell transmission model @cite_17 , store-and-forward @cite_24 , and petri-nets @cite_26 . As compared to this line of work, our work considers (i) that some vehicles can communicate their intentions, which affects the delay analysis, and (ii) blocking problem.
@cite_2 @cite_5 @cite_15 @cite_18 @cite_4 @cite_8 @cite_21 @cite_23 @cite_17 @cite_26 @cite_7 @cite_16 @cite_25 @cite_12 @cite_14 @cite_9 @cite_1 @cite_0 @cite_24
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Most existing discussions regarding the time-dependent distribution of queue length was undertaken in the context of isolated intersections. However, computing queue length distributions for a signalized network with generic topology is very challenging because such process involves convolution and nonlinear transformation of random variables, which is analytically intractable. To address such issue, this study proposes a stochastic queue model considering the strong interdependence relations between adjacent intersections using the probability generating function as a mathematical tool. Various traffic flow phenomena, including queue formation and dissipation, platoon dispersion, flow merging and diverging, queue spillover, and downstream blockage, are formulated as stochastic events, and their distributions are iteratively computed through a stochastic network loading procedure. Both theoretical derivation and numerical investigations are presented to demonstrate the effectiveness of the proposed approach in analyzing the delay and queues of signalized networks under different congestion levels. Optimization Policies for Adaptive Control (OPAC) is a computational strategy for real-time demand-responsive traffic signal control. It has the following features: (a) It provides performance results that approach the theoretical optimum, (b) it requires on-line data that can be readily obtained from upstream link detectors, (c) it is suitable for implementation on existing microprocessors, and (d) it forms a building block for demand-responsive decentralized control in a network. Studies undertaken in the development of this strategy and the testing of its performance via the NETSIM simulation model are described. The paper presents the design approach, the objectives, the development, the advantages, and some application results of the traffic-responsive urban control (TUC) strategy. Based on a store-and-forward modelling of the urban network traffic and using the linear-quadratic regulator theory, the design of TUC leads to a multivariable regulator for traffic-responsive co-ordinated network-wide signal control that is particularly suitable also for saturated traffic conditions. Simulation investigations demonstrate the efficiency of the proposed approach. Results of TUC's first field implementation and evaluation are also presented. Finally, summarising conclusions are drawn and future work is outlined. This paper proposes a delay model for signalized intersections that is suitable for variable demand conditions. The model is applicable to the entire range of expected operations, including highly oversaturated conditions with initial queues at the start of the analysis period. The proposed model clarifies several issues related to the determination of the peak flow period, as well as the periods immediately preceding and following the peak. Separate formulas are provided for estimating delay in each of the designated flow periods as well as in the total flow period. Formulas are also provided to estimate the duration of the oversaturation period where applicable. The strength of the model lies in the use of simple rules for determining flow rates within and outside the peak, using the peak flow factor, a generalization of the well-known peak hour factor parameter. Simple rules are also provided for the identification of the location and duration of the peak flow period from observations of the demand profile. Such information is considered vital from an intersection design and evaluation viewpoint. Application of the model to a variety of operating conditions indicates that the estimated delay for vehicles arriving in the peak flow period is an acceptable predictor of the average delay incurred during the total flow period, even when oversaturation persists beyond the total flow period. On the other hand, the use of the average degree of saturation with no consideration of peaking can lead to significant underestimation of delay, particularly when operating at or near capacity conditions. These findings were confirmed by comparing the model results with other models found in the literature. The significant contribution of this work is not simply in the development of improved delay estimates, but, more important, in providing an integrated framework for an estimation process that incorporates (a) the peaking characteristics in the demand flow pattern, (b) the designation of flow-specific periods within the total flow period in accordance with the observed peaking and (c) the estimation of performance parameters associated within each flow period and in combination with other periods. A revised delay formula for the U.S. Highway Capacity Manual (HCM) is proposed. The revised formula has no constraints on the peak flow period degree of saturation, unlike the current HCM formula. It is also recommended that a simple formula for estimating the duration of oversaturation be used in conjunction with the revised delay formula. The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods.