Walking-distance introduced queueing model for pedestrian queueing system: Theoretical analysis and experimental verification

We have introduced the effect of delay in walking from the head of a queue to the service windows in the queueing model and obtain a suitable type of queueing system under various conditions by both computational simulation and theoretical analysis. When there are multiple service windows, the queueing theory indicates that mean waiting time in a fork-type queueing system (Fork), which collects pedestrians into a single queue, is smaller than that in a parallel-type queueing system (Parallel), i.e., queues for each service window. However, in our walking-distance introduced queueing model, we have examined that mean waiting time in Parallel becomes smaller when both the arrival probability of pedestrians and the effect of walking distance are large. Moreover, enhanced Forks, which shorten waiting time by reducing the effect of walking distance, are considered, and parts of our results are also verified by real queueing experiments.     

Simulations of pollutant dispersion at toll plazas using three-dimensional CFD models

Toll plazas are particularly susceptible to build-ups of vehicle-emitted pollutants because vehicles pass through in low gear. To look at this, three-dimensional computational fluid dynamics simulations of pollutant dispersion are used on the standard k − ε turbulence model. The effects of wind speed, wind direction and topography on pollutant dispersion were discussed. The Wuzhuang toll plaza on the Hefei-Nanjing expressway is considered, and the effects of the retaining walls along both sides of the plaza on pollutant dispersion is analysed. There are greater pollutant concentrations near the tollbooths as the angle between the direction of the wind and traffic increases implying that retaining walls impede dispersion. The slope of the walls has little influence on the variations in pollutant concentration.     

Real-time queue length estimation for congested signalized intersections

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 traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic is not available once the detector is occupied by the queue. In this paper, 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 high-resolution “event-based” traffic signal data, and applying Lighthill–Whitham–Richards (LWR) shockwave theory, 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. Variations of the queue length estimation model are also presented when “event-based” data is not available. Our models 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. Limitations of the proposed model are also discussed in the paper.     

Time-dependent queueing at road junctions: Observation and prediction

Measurements of queue lengths and vehicle delays have been used to test the predictions of time-dependent queueing models. Observations were made at eight public road sites for a number of peak periods at each site. In all, sixty-eight peaks were studied. The model predictions of the time-dependent trials-average queues and delays agreed with the observations within the limits set by day-to-day variability for seven of the sites, but for the eighth there was consistent overprediction.     

Point queue models: A unified approach

In transportation and other types of facilities, various queues arise when the demands of service are higher than the supplies, and many point and fluid queue models have been proposed to study such queueing systems. However, there has been no unified approach to deriving such models, analyzing their relationships and properties, and extending them for networks. In this paper, we derive point queue models as limits of two link-based queueing model: the link transmission model and a link queue model. With two definitions for demand and supply of a point queue, we present four point queue models, four approximate models, and their discrete versions. We discuss the properties of these models, including equivalence, well-definedness, smoothness, and queue spillback, both analytically and with numerical examples. We then analytically solve Vickrey’s point queue model and stationary states in various models. We demonstrate that all existing point and fluid queue models in the literature are special cases of those derived from the link-based queueing models. Such a unified approach leads to systematic methods for studying the queueing process at a point facility and will also be helpful for studies on stochastic queues as well as networks of queues.     

Delay processes at unsignalised junctions: The interrelation between geometric and queueing delay

The interrelation between geometric delay—the delay caused by the need for isolated vehicles to slow down to negotiate a junction—and the queueing delay due to vehicle-vehicle interactions is considered. The delay elements present in measurements of geometric delay are identified, and some overlap is seen with those normally included in the service mechanisms in queueing models. The total delay per vehicle is not, therefore, the sum of the measured geometric delay and the queueing delay. Although the geometric delay can be redefined so as to eliminate the overlap, it is not then measurable. A framework is developed in which the relationships between the “pure” and measured geometric delay and the queueing delay are expressed for the population mean values. Approximate expressions are developed for the elements of delay. The framework is extended to allow queueing delays to be represented by time-dependent functions allowing approximately for non-randomness in arrival and departure patterns and service time differences between queueing and non-queueing vehicles. Numerically, geometric delay elements constitute a significant proportion of total delay except at traffic intensities approaching unity. In this region time-dependent effects dominate the queueing process.     

How a fast lane may replace a congestion toll

This paper considers a congested bottleneck. A fast lane reserves a more than proportional share of capacity to a designated group of travelers. Travelers are otherwise identical and other travelers can use the reserved capacity when it would otherwise be idle. The paper shows that such a fast lane is always Pareto improving under Nash equilibrium in arrival times at the bottleneck and inelastic demand. It can replicate the arrival schedule and queueing outcomes of a toll that optimally charges a constant toll during part of the demand peak. Within some bounds, the fast lane scheme is still welfare improving when demand is elastic.     

A model for optimizing electronic toll collection systems

This paper examines the deployment of electronic toll collection (ETC) and develops a model to maximize social welfare associated with a toll plaza. A payment choice model estimates the share of traffic using ETC as a function of delay, price, and a fixed cost of acquiring the in-vehicle transponder. Delay in turn depends on the relative number of ETC and manual collection lanes. Price depends on the discount given to users of the ETC lanes. The fixed cost of acquiring the transponder (not simply a monetary cost, but also the effort involved in signing up for the program) is a key factor in the model. Once a traveler acquires the transponder, the cost of choosing ETC in the future declines significantly. Welfare depends on the market share of ETC, and includes delay and gasoline consumption, toll collection costs, and social costs such as air pollution. This work examines the best combination of ETC lanes and toll discount to maximize welfare. Too many ETC lanes cause excessive delay to non-equipped users. Too high a discount costs the highway agency revenue needed to operate the facility. The model is applied to California’s Carquinez Bridge, and recommendations are made concerning the number of dedicated ETC lanes and the appropriate ETC discount.     

Real-time congestion pricing strategies for toll facilities

This paper analyzes the dynamic traffic assignment problem on a two-alternative network with one alternative subject to a dynamic pricing that responds to real-time arrivals in a system optimal way. Analytical expressions for the assignment, revenue and total delay in each alternative are derived as a function of the pricing strategy. It is found that minimum total system delay can be achieved with many different pricing strategies. This gives flexibility to operators to allocate congestion to either alternative according to their specific objective while maintaining the same minimum total system delay. Given a specific objective, the optimal pricing strategy can be determined by finding a single parameter value in the case of HOT lanes. Maximum revenue is achieved by keeping the toll facility at capacity with no queues for as long as possible. Guidelines for implementation are discussed.     

Modeling and simulation of vehicle projection arrival–discharge process in adaptive traffic signal controls

Real‐time signal control operates as a function of the vehicular arrival and discharge process to satisfy a pre‐specified operational performance. This process is often predicted based on loop detectors placed upstream of the signal. In our newly developed signal control for diamond interchanges, a microscopic model is proposed to estimate traffic flows at the stop‐line. The model considers the traffic dynamics of vehicular detection, arrivals, and departures, by taking into account varying speeds, length of queues, and signal control. As the signal control is optimized over a rolling horizon that is divided into intervals, the vehicular detection for and projection into the corresponding horizon intervals are also modeled. The signal control algorithm is based on dynamic programming and the optimization of signal policy is performed using a certain performance measure involving delays, queue lengths, and queue storage ratios. The arrival–discharge model is embedded in the optimization algorithm and both are programmed into AIMSUN, a microscopic stochastic simulation program. AIMSUN is then used to simulate the traffic flow and implement the optimal signal control by accessing internal data including detected traffic demand and vehicle speeds. Sensitivity analysis is conducted to study the effect of selecting different optimization criteria on the signal control performance. It is concluded that the queue length and queue storage ratio are the most appropriate performance measures in real‐time signal control of interchanges. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of transient bulk queues with general vehicle dispatching strategies

Relatively simple iterative procedures are developed for simulating the queue length distribution for transient bulk arrival, bulk service queues. The method allows the study of holding strategies where the length of time a vehicle is held can depend on both the length ofthe queue and how long the vehicle has been held. The system is modeled in discrete time, and a series of numerical experiments are presented that examine the errors introduced by this discretization.     

Dynamic network loading: A stochastic differentiable model that derives link state distributions

We present a dynamic network loading model that yields queue length distributions, accounts for spillbacks, and maintains a differentiable mapping from the dynamic demand on the dynamic queue lengths. The model also captures the spatial correlation of all queues adjacent to a node, and derives their joint distribution. The approach builds upon an existing stationary queueing network model that is based on finite capacity queueing theory. The original model is specified in terms of a set of differentiable equations, which in the new model are carried over to a set of equally smooth difference equations. The physical correctness of the new model is experimentally confirmed in several congestion regimes. A comparison with results predicted by the kinematic wave model (KWM) shows that the new model correctly represents the dynamic build-up, spillback and dissipation of queues. It goes beyond the KWM in that it captures queue lengths and spillbacks probabilistically, which allows for a richer analysis than the deterministic predictions of the KWM. The new model also generates a plausible fundamental diagram, which demonstrates that it captures well the stationary flow/density relationships in both congested and uncongested conditions.     

Network traffic flow optimization under performance constraints

In this paper, a model-based perimeter control policy for large-scale urban vehicular networks is proposed. Assuming a homogeneously loaded vehicle network and the existence of a well-posed Network Fundamental Diagram (NFD), we describe a protected network throughout its aggregated dynamics including nonlinear exit flow characteristics. Within this framework of constrained optimal boundary flow gating, two main performance metrics are considered: (a) first, connected to the NFD, the concept of average network travel time and delay as a performance metric is defined; (b) second, at boundaries, we take into account additional external network queue dynamics governed by uncontrolled inflow demands. External queue capacities in terms of finite-link lengths are used as the second performance metric. Hence, the corresponding performance requirement is an upper bound of external queues. While external queues represent vehicles waiting to enter the protected network, internal queue describes the protected network’s aggregated behavior.By controlling the number of vehicles joining the internal queue from the external ones, herewith a network traffic flow maximization solution subject to the internal and external dynamics and their performance constraints is developed. The originally non-convex optimization problem is transformed to a numerically efficiently convex one by relaxing the performance constraints into time-dependent state boundaries. The control solution can be interpreted as a mechanism which transforms the unknown arrival process governing the number of vehicles entering the network to a regulated process, such that prescribed performance requirements on travel time in the network and upper bound on the external queue are satisfied. Comparative numerical simulation studies on a microscopic traffic simulator are carried out to show the benefits of the proposed method.     

Metamodels for estimating waterway delays through series of queues

A numerical method has been developed for estimating delays on congested waterways. Analytic and numerical results are presented for series of G/G/1 queues, i.e. with generally distributed arrivals and service times and single chambers at each lock. One or two-way traffic operations are modelled. A metamodelling approach which develops simple formulas to approximate the results of simulation models is presented. The structure of the metamodels is developed from queueing theory while their coefficients are statistically estimated from simulation results. The numerical method consists of three modules: (1) delays, (2) arrivals and (3) departures. The first estimates the average waiting time for each lock when the arrival and service time distributions at this lock are known. The second identifies the relations between the arrival distributions at one lock and the departure distributions from the upstream and downstream locks. The third estimates the mean and variance of inter-departure times when the inter-arrival and service time distributions are known. The method can be applied to systems with two-way traffic through common bi-directional servers as well as to one-way traffic systems. Algorithms for both cases are presented. This numerical method is shown to produce results that are close to the simulation results. The metamodels developed for estimating delays and variances of inter-departure times may be applied to waterways and other series of G/G/1 queues. These metamodels for G/G/1 queues may provide key components of algorithms for analyzing networks of queues.     

Dynamic vehicular delay comparison between a police-controlled roundabout and a traffic signal

Effects of queues on motorists during rush hours are severe at intersections controlled by roundabouts. Traffic police are frequently used in order to optimize the traffic flow and to control queue length at such intersections. However, the question as to how efficient such system is, compared with traffic signal, is not clear from the dynamic delay point of view. In this study a criterion is being developed based on vehicular delays as the motorist join the queues and cross the stop-line. The adopted method avoids oversimplification of reality and prevents unrealistic assumptions. The data required for the study were mainly collected through video filming technique. The results, for a given set of geometric and traffic characteristics, indicate that both a police-controlled roundabout and a traffic signal act in a similar manner in terms of vehicular delay at a certain critical value. This critical value is considered to be the point of intersection between the curves representing traffic signal and roundabout on a delay–space diagram for the vehicles as they join the tail end of the queue until they cross the stop-line. Beyond the critical value, the effect of delays and buildup of queues at roundabouts will be excessive, compared to traffic signals. Before the critical value the delays at traffic signals are quite high compared to roundabouts. The study will assist the concerned authorities to operate the existing conditions, particularly the roundabouts, more efficiently. It will also be beneficial for the traffic planners and policy makers in making judicious decisions regarding control type at intersections.     

Modeling probability distribution of delay at signalized intersections

Accurate estimation of vehicle delay is difficult because of the randomness of traffic flow and large number of factors affecting intersection capacity. Existing delay models simplify the real traffic conditions and provide only approximate point estimates of average delay, whereas its variability should also be of interest. A stochastic model was used to study the changing probability distribution of delay. The model is based on sequential calculation of queue length probabilities with any type of arrival process. Delay probability distribution was investigated for different degrees of saturation, arrival types and control conditions. The variance of delay increases rapidly with degree of saturation and is inversely proportional to the approach capacity. Other parameters such as cycle time and saturation flow do not have a significant effect on delay distribution. Both the mean and variance of delay are sensitive to arrival process characteristics and increase with the variance of arrivals.     

A block queueing system for slow moving traffic

A common cause of pollution and waste in urban areas is facilities which provide a continuous slow service for motor vehicles. As demand approaches supply, queues can develop and large numbers of engines can often be idling. Typical examples are car park entrances and drive through fast food outlets. This paper proposes a block queueing system to alleviate the problem without using excessive road space and with a minimum of extra infrastructure. The queue is divided into an active section at the front (with engines running) and a passive section at the rear (where drivers switch their engines off). Periodically, as the active queue becomes depleted, the passive queue is momentarily activated and a block of vehicles advances into the active queue. A visual cue can be provided to the drivers using a vehicle actuated traffic signal. It is readily apparent that drivers in the passive queue have to switch their engines on and off at regular intervals. Since this operation has an inherent cost in itself, this argues in favour of a large block size. However, large blocks mean more engines idling in the active queue. A compromise must be therefore reached for the likely range of queue lengths which the system under consideration exhibits. An expression is derived for the optimum block size in steady state conditions. It is shown that the potential benefits of the regime are considerable.     

Approximate queueing models for analyzing harbor terminal operations

The purpose of this paper is to present approximate queueing models to help assess the impacts of tug services on congested harbor terminals. The models are intended for harbors in which tug shortages are rare. A congested harbor terminal is modelled as a queueing system with m identical tugs (servers) and n identical berths (customers), and with general probability distributions of tug service time and berth cargo-handling time. The distribution of the number of berths in the system, a basic element to analyze the system performance, was established for two cases. For large m, the distribution was approximated by a binomial model and the respective accuracy tested. For small m, an approximate model for this distribution was developed. Particular emphasis was given to developing explicitly the probability of having one berth in queue and establishing the remaining probabilities of the distribution approximately. The model for small m was validated by means of simulation for various cases of harbor terminal operations exhibiting different ranges of the coefficient of variation of tug service time. The models were found to be reasonably accurate within a certain range covering situations in which tug shortages are in the order of 10% of the time or less.     

Real time queue length estimation for signalized intersections using travel times from mobile sensors

We study how to estimate real time queue lengths at signalized intersections using intersection travel times collected from mobile traffic sensors. The estimation is based on the observation that critical pattern changes of intersection travel times or delays, such as the discontinuities (i.e., sudden and dramatic increases in travel times) and non-smoothness (i.e., changes of slopes of travel times), indicate signal timing or queue length changes. By detecting these critical points in intersection travel times or delays, the real time queue length can be re-constructed. We first introduce the concept of Queue Rear No-delay Arrival Time which is related to the non-smoothness of queuing delay patterns and queue length changes. We then show how measured intersection travel times from mobile sensors can be processed to generate sample vehicle queuing delays. Under the uniform arrival assumption, the queuing delays reduce linearly within a cycle. The delay pattern can be estimated by a linear fitting method using sample queuing delays. Queue Rear No-delay Arrival Time can then be obtained from the delay pattern, and be used to estimate the maximum and minimum queue lengths of a cycle, based on which the real-time queue length curve can also be constructed. The model and algorithm are tested in a field experiment and in simulation.     

The impact of signal control on land-side traffic patterns at the Dallas/Fort worth airport

The Parkway Corridor is the primary ground facility at the Dallas/Fort Worth (D/FW) International Airport. It consists of an expressway for passengers to-and-from terminals and a service road mainly for employees of airline-associated agencies to access the service areas. As the Parkway Corridor is a natural short cut in the region, it has attracted more and more through commuters who usually choose to use the service road so as to circumvent the toll plazas on the expressway. The dramatic increase in both the volume and speed of through commuting traffic in recent years not only impedes service activities, but also raises safety concerns. The D/FW Airport Board is considering the installation of a series of traffic signals to regulate the cruise speed and thereby discourage use of the service road by commuters. This research is conducted to evaluate its effectiveness and potential impact on traffic patterns along the Parkway Corridor. A systematic approach, integrating queueing theories (G/M/m), discrete models, and traffic assignment, is proposed in this research, which allows the user to project the traffic distribution on each route with only the information obtained by traffic counts. Numerical results of alternate control strategies and a sensitivity analysis with respect to key parameters, such as the toll and cycle length of traffic signals are also reported.