Dynamic estimation of queue behaviour in urban traffic (original) (raw)

MODELING OVERFLOW QUEUES ON URBAN SIGNALIZED INTERSECTIONS

Much effort has been spent in developing more efficient control systems for signalized intersections to adapt the capacity of the network to the variability of the demand. This variability is partly due to time-dependent factors but also to the stochastic nature of the demand itself. The available formulae can still be successfully adopted in undersaturated conditions, where the stochastic effects fade into one green phase, or in highly oversaturated cases, where the queues aren't comparable with their portions caused by these uncertainties. In cases where the value of the degree of saturation is close to one the stochastic effect plays a relevant role. This paper provides a novel heuristic formula able to model the transition phase when the study involves a variable demand. It particularly solves the queuing behavior of an oversaturated period on the successive undersaturated ones. The delay experienced by the users is modeled using a Markov Chain process. Based on this data the novel model is calibrated. The new model for queues is further applied in two case studies. The first involves a two arms intersection where users of the two OD pairs can only choose between different times of departure. The second involves one OD pair and two parallel routes, one faster but ending with a traffic light while the other is unsignalised. The paper discusses the change in users' decisions with respect to the travel times and the delays they perceive at signalized intersections both from the route choice and the departure time choice point of view. In this sense a Dynamic Traffic Assignment problem in an extended network can be applied and solved. From this research we gained a deeper knowledge of the relevant role played by the random nature of the queue evolution in time for the delay experienced by the users. By acquiring this knowledge a timedependent queue function has been provided. It is now possible to model the queue as a continuous function with more accurate results than the ones provided by the simple deterministic method.

Discrete-time point processes in urban traffic queue estimation

IEEE Transactions on Automatic Control, 1979

He has studied the behavior of perturbations of traffic assignments, energy consumption in traffic networks with multiple vehicle t y p e s , improved methods for calculation of user-equilibrium traffic flows, and related areas in transportation. He has investigated routing optimization in networks of machine tools and the effects of hmited buffer storage space. Dr. Gershwin is a member of the IEEE Control Systems Society, Tau Beta Pi, the American Association for the Advancement of Science, and an associate member of ORSA.

Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue

Communications in Statistics - Theory and Methods, 2013

In this paper, maximum likelihood estimator (MLE) as well as Bayes estimator of traffic intensity (ρ) in an M/M/1/∞ queueing model in equilibrium based on number of customers present in the queue at successive departure epochs have been worked out. Estimates of some functions of ρ which provide measures of effectiveness of the queue have also been derived. A comprehensive simulation study starting with the transition probability matrix has been carried out in the last section.

Transient Behaviour of Queueing Systems with Correlated Traffic

Performance Evaluation, 1996

In this paper, we present the time-dependent solutions of various stochastic processes associated with a finite Quasi-Birth-Death queueing system. These include the transient queueing solutions, the transient departure and loss intensity processes and certain transient cumulative measures associated with the queueing system. The focus of our study is the effect of the arrival process correlation on the queueing system before it reaches steady-state. With the aid of numerous examples, we investigate the strong relationship between the time scales of variation of the arrival process and those of the transient queueing, loss and departure processes. These time-dependent solutions require the computation of the exponential of the stochastic generator matrix G which may be of very large order. This precludes the use of known techniques to solve the matrix exponential such as the eigenvalue decomposition of G. We present a numerical technique based on the computation of the Laplace Transform of the matrix exponential which may then be numerically inverted to obtain the time-dependent solutions. In this paper, we also propose new QoS metrics based on transient measures and efficient techniques for their computation.

Analytical Models Based Discrete-Time Queueing for the Congested Network

International Journal of Modeling, Simulation, and Scientific Computing, 2012

Congestion is one of the well-studied problems in computer networks, which occurs when the request for network resources exceeds the buffer capacity. Many active queue management techniques such as BLUE and RED have been proposed in the literature to control congestions in early stages. In this paper, we propose two discrete-time queueing network analytical models to drop the arrival packets in preliminary stages when the network becomes congested. The first model is based on Lambda Decreasing and it drops packets from a probability value to another higher value according to the buffer length. Whereas the second proposed model drops packets linearly based on the current queue length. We compare the performance of both our models with the original BLUE in order to decide which of these methods offers better quality of service. The comparison is done in terms of packet dropping probability, average queue length, throughput ratio, average queueing delay, and packet loss rate.

Simple, generalized method for analysis of traffic queue upstream of a bottleneck

1998

An approach is generalized for enhancing a standard input-output diagram to represent graphically the time and distance that vehicles spend in a queue upstream of a bottleneck. The approach requires the construction of a curve depicting the cumulative number of vehicles to have reached the back of the queue as a function of time. The original technique, described in a previous paper, is reviewed for bottlenecks with constant capacity and for those where capacity changes once.

A queueing based traffic flow model

Transportation Research Part D: Transport and Environment, 2000

The assessment of uninterrupted traffic flow is traditionally based on empirical methods. We develop some analytic queueing models based on traffic counts and we model the behavior of traffic flows as a function of some of the most relevant determinants. These analytic models allow for parameterized experiments, which pave the way towards our research objectives:

M/g/c/c State Dependent Queueing Model for Road Traffic Simulation

Applied Mathematics & Information Sciences, 2017

In this paper, we present a stochastic queuing model for the road traffic, which captures the stationary density-flow relationships in both uncongested and congestion conditions. The proposed model is based on the M/g/c/c state dependent queuing model of Jain and Smith, and is inspired from the deterministic Godunov scheme for the road traffic simulation. We first propose a reformulation of the M/g/c/c state dependent model that works with density-flow fundamental diagrams rather than density-speed relationships. We then extend this model in order to consider upstream traffic demand as well as downstream traffic supply. Finally, we calculate the speed and travel time distributions for the M/g/c/c state dependent queuing model and for the proposed model, and derive stationary performance measures (expected number of cars, blocking probability, expected travel time, and throughput). A comparison with results predicted by the M/g/c/c state dependent queuing model shows that the proposed model correctly represents the dynamics of traffic and gives good performances measures. The results illustrate the good accuracy of the proposed model.

A procedure for generating time-dependent arrivals for queueing simulations

Naval Research Logistics Quarterly, 1977

This paper presents a method for modeling cyclic inputs to a congested system in a discrete event digital simulation. Specifically, we express the mean of the interarrival time conditional on the last arrival as II linear combination of harmonic components whose coefficients can be determined by stepwise regression. We also assume that the conditional interarrival time normalized by its corresponding mean follows a distribution that is independent of time. The result can, in turn, be used to generate the desired input for a simulation, An example based on a set of actual data is used to illustrate the process of parameter estimation for the model.