Simulation of queue with cyclic service in signalized intersection system

The simulation was implemented by modeling the queue with cyclic service in the signalized intersection system. The service policies used in this study were exhaustive and gated, the model was the M/M/1 queue, the arrival rate used was Poisson distribution and the services rate used was Exponential distribution. In the gated service policy, the server served only vehicles that came before the green signal appears at an intersection. Considered that there were 2 types of exhaustive policy in the signalized intersection system, namely normal exhaustive (vehicles only served during the green signal was still active), and exhaustive (there was the green signal duration addition at the intersection, when the green signal duration at an intersection finished). The results of this queueing simulation program were to obtain characteristics and performance of the system, i.e. average number of vehicles and waiting time of vehicles in the intersection and in the system, as well as system utilities. Then from these values, it would be known which of the cyclic service policies (normal exhaustive, exhaustive and gated) was the most suitable when applied to a signalized intersection syste

Heavy-traffic analysis of k-limited polling systems

In this paper we study a two-queue polling model with zero switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$, $i=1,2$) in each queue. The arrival processes at the two queues are Poisson, and the service times are exponentially distributed. By increasing the arrival intensities until one of the queues becomes critically loaded, we derive exact heavy-traffic limits for the joint queue-length distribution using a singular-perturbation technique. It turns out that the number of customers in the stable queue has the same distribution as the number of customers in a vacation system with Erlang-$k_2$ distributed vacations. The queue-length distribution of the critically loaded queue, after applying an appropriate scaling, is exponentially distributed. Finally, we show that the two queue-length processes are independent in heavy traffic

Simulation of queue with cyclic service in signalized intersection system

The simulation was implemented by modeling the queue with cyclic service in the signalized intersection system. The service policies used in this study were exhaustive and gated, the model was the M/M/1 queue, the arrival rate used was Poisson distribution and the services rate used was Exponential distribution. In the gated service policy, the server served only vehicles that came before the green signal appears at an intersection. Considered that there were 2 types of exhaustive policy in the signalized intersection system, namely normal exhaustive (vehicles only served during the green signal was still active), and exhaustive (there was the green signal duration addition at the intersection, when the green signal duration at an intersection finished). The results of this queueing simulation program were to obtain characteristics and performance of the system, i.e. average number of vehicles and waiting time of vehicles in the intersection and in the system, as well as system utilities. Then from these values, it would be known which of the cyclic service policies (normal exhaustive, exhaustive and gated) was the most suitable when applied to a signalized intersection syste

Delays at signalised intersections with exhaustive traffic control

In this paper we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting distributions of the delays under Heavy Traffic (HT) conditions, using theory on polling models. Furthermore, we derive the Light Traffic (LT) limit of the mean delays for intersections with Poisson arrivals, and develop a heuristic adaptation of this limit to capture the LT behaviour for other interarrival-time distributions. We combine the LT and HT results to develop closed-form approximations for the mean delays of vehicles in each lane. These closed-form approximations are quite accurate, very insightful and simple to implement

Delays at signalised intersections with exhaustive traffic control

In this paper, we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting distributions of the delays under heavy traffic (HT) conditions. Furthermore, we derive the light traffic (LT) limit of the mean delays for intersections with Poisson arrivals, and develop a heuristic adaptation of this limit to capture the LT behavior for other interarrival-time distributions. We combine the LT and HT results to develop closed-form approximations for the mean delays of vehicles in each lane. These closed-form approximations are quite accurate, very insightful, and simple to implement

Delays at signalised intersections with exhaustive traffic control

In this paper, we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting distributions of the delays under heavy traffic (HT) conditions. Furthermore, we derive the light traffic (LT) limit of the mean delays for intersections with Poisson arrivals, and develop a heuristic adaptation of this limit to capture the LT behavior for other interarrival-time distributions. We combine the LT and HT results to develop closed-form approximations for the mean delays of vehicles in each lane. These closed-form approximations are quite accurate, very insightful, and simple to implement

Performance Analysis of Isolated Intersection Traffic Signals

This dissertation analyzes two unsolved problems to fulfill the gap in the literature: (1). What is the vehicle delay and intersection capacity considering left-turn traffic at a pre-timed signal? (2). What are the mean and variance of delay to vehicles at a vehicle-actuated signal? The first part of this research evaluates the intersection performance in terms of capacity and delay at an isolated pre-timed signal intersection. Despite of a large body of literature on pre-timed signals, few work has examined the interactions be- tween left-turn and through vehicles. Usually a protected left-turn signal phase, before (leading) or after (lagging) through signal, is applied to a signalized inter- section when the traffic demand is relatively high. A common problem for leading left-turn operation is the blockage to left-turn vehicles by through traffic, particularly at an intersection with a short left-turn bay. During the peak hour, some vehicles on the through lane might not be able to depart at the end of a cycle, resulting in an increased probability of left-turn blockage. In turn, the blocked left-turn vehicles may also delay the through traffic to enter the intersection during the following cycle. Those problems may not exist for a lagging left-turn operation, since left-turn vehicles intend to spill out of the bay under heavy traffic. In this case, the through capacity is reduced, leading to an increase of total delay. All of these factors contribute to the difficulties of estimating the delay and capacity for an isolated intersection. In order to examine this missing part of study on the signalized intersection, two probabilistic models are proposed to deal with the left-turn bay blockage and queue spillback in a heuristic manner. Numerical case studies are also provided to test the proposed models. The second part of this research studies an isolated intersection with vehicle-actuated signal. Typically an advanced detector is located at a distance prior to the intersection such that an arriving vehicle triggers a green time extension in or- der to pass through without any stop. This extended time period actuated by the vehicle is called unit extension in this study. If no vehicle actuation occurs during a unit extension, the green phase would terminate in order to clear queues in other approaches. In this way, the actuated system dynamically allocates the green time among multiple approaches according to vehicle arrivals. And the unit extension is the only control parameter in this case. We develop a model to study the vehicle delay under a general arrival distribution with a given unit extension. Our model allows optimizing the intersection performance over the unit extension. The third part of this research applies graphical methods and diffusion approximations to the traffic signal problems. We reinterpret a graphical method which is originally proposed by Newell in order to directly measure the variance of the time for the queue clearance at a signalized intersection, which remains yet to be carefully examined in practice and would be rather challenging if only using the conventional queuing techniques. Our results demonstrate that graphical method explicitly presents both the deterministic and stochastic delay. We also illustrate that the theoretical background for the graphical methods in this particular application is inherently the diffusion approximation. Furthermore, we investigate the problems of disruptions occurred during a pre-timed traffic signal cycle. By diffusion approximation, we provide quantitative estimation on the duration that the effects of disruptions would dissipate