Downstream Queue Research Articles

Managing oversaturated signalized arterials: A maximum flow based approach

Under oversaturated traffic conditions, signal timings need to be adjusted accordingly in order to alleviate the detrimental impacts caused by oversaturation. In this research, our focus is to mitigate two types of detrimental effects, signal phase failure with residual queue and downstream queue spillover. Building upon our previous work on the oversaturation severity indices, a maximum-flow based approach to manage oversaturated intersections is developed. The proposed model maximizes the discharging capacity along oversaturated routes, while satisfying the constraints on available green times. We show that a simple Forward–Backward Procedure (FBP) can be used to obtain the optimal solution to the maximum flow model. The forward process aims to increase green time to mitigate oversaturation, therefore improve the throughput for the oversaturated approach; and the backward process aims to gate the traffic at some intersections to prevent residual queues and downstream queue spill-back when the available green time is insufficient. The algorithm is tested using a microscopic traffic simulation model for an arterial network in the City of Pasadena, CA. The results indicate the model can effectively and efficiently reduce oversaturation and improve system performance.

Standards-Compliant EPON Sleep Control for Energy Efficiency: Design and Analysis

Owing to environmental concerns, reducing energy consumption of optical access networks has become an important problem for network designers. This paper focuses on reducing energy consumption of optical network units (ONUs) in an Ethernet passive optical network (EPON). In an EPON, the optical line terminal (OLT) located at the central office broadcasts the downstream traffic to all ONUs, each of which checks all arriving downstream packets so as to obtain the downstream packets destined to itself. Thus, receivers at ONUs always have to stay in the awake status and consume a large amount of energy. To address the downstream challenge, we propose a novel sleep control scheme that can efficiently put ONU receivers into sleep without modifying the standardized EPON media access control protocol. The proposed scheme contains two main parts: downstream traffic scheduling rules at the OLT and sleep control schemes at ONUs. By letting ONUs be aware of the downstream traffic scheduling rules, ONUs can infer their own downstream queue status and switch into the sleep status properly; by letting the OLT know the sleep control scheme implemented at ONUs, the OLT can accurately infer the sleep status of ONUs and buffer traffic of asleep ONUs accordingly. We also theoretically analyze the impacts of different parameters in the sleep control scheme on the delay and energy-saving performances by using semi-Markov chains. It is shown that, with proper settings of sleep control parameters, the proposed scheme can save as much as 50% of the ONU receiver energy.

Calculation of Additional Lost Green Time at Closely Spaced Intersections

At closely spaced signalized intersections or interchanges, additional lost green time can occur at upstream intersections when there is a queue spillback. For an accurate estimation of capacities and delays at closely spaced intersections, it is necessary to account such additional lost time. The Highway Capacity Manual (HCM) 2010 provides a model for the estimation of the additional lost time due to the presence of a downstream queue. However, case studies indicate that the HCM model does not provide a very accurate estimation when the distance to the downstream queue is short. In this paper, a new model is developed for the estimation of additional lost time considering queue discharge patterns and traffic flow patterns. Simulation results show that the proposed model provides a more accurate estimation of additional lost time compared with the HCM model when the distance to the downstream queue is limited.

Estimating the waiting time of multi-priority emergency patients with downstream blocking

To characterize the coupling effect between patient flow to access the emergency department (ED) and that to access the inpatient unit (IU), we develop a model with two connected queues: one upstream queue for the patient flow to access the ED and one downstream queue for the patient flow to access the IU. Building on this patient flow model, we employ queueing theory to estimate the average waiting time across patients. Using priority specific wait time targets, we further estimate the necessary number of ED and IU resources. Finally, we investigate how an alternative way of accessing ED (Fast Track) impacts the average waiting time of patients as well as the necessary number of ED/IU resources. This model as well as the analysis on patient flow can help the designer or manager of a hospital make decisions on the allocation of ED/IU resources in a hospital.

Transient analysis of Lévy-driven tandem queues

This short communication considers a tandem queue fed by Lévy input. The main result concerns expressions for the Laplace transform of the transient workload in the downstream queue, under the condition that the system starts off empty. This expression greatly simplifies if the driving Lévy process is spectrally one-sided; in that situation the transform is given explicitly in terms of the Laplace exponent of the Lévy input.

Time-Variant Travel Time Prediction Model and Its Application in a Cooperative Traffic Control System

This paper presents a travel time prediction model and an application of this model to vehicle cooperative control systems. The travel time prediction model considers vehicle delay because of downstream queue formation and traffic signal operation. For estimation of traffic signal–induced delay, this model uses a time-variant nonlinear probability function that maps the vehicle arrival time at a downstream stop line to the probability that it will receive a green signal on arrival. The probability function is determined iteratively. The travel time prediction model can be applied to any phase-based traffic controller. The road vehicle cooperative control system is developed on the basis of vehicle-to-infrastructure communication. The control system optimizes signal timing according to data transmitted in real time and sends speed adjustment recommendations to selected vehicles on the road. Results from numerical tests validate the accuracy of the travel time prediction model and demonstrate the benefits of the cooperative control system.

Estimation of Delay Induced by Downstream Operations at Signalized Intersections over Extended Control Time

Analytical macroscopic models are presented to quantify delay at signalized intersections for extended control periods (multiple cycles) attributable to downstream time-variable congestion. Each of the models consists of an upstream demand estimation algorithm, a downstream queue build-up prediction algorithm, a shockwave propagation and dissipation tracking algorithm, and an algorithm that carries traffic aftereffect of a cycle’s control into the following cycle. Model inputs are basic traffic flow properties, signal control parameters, and link geometry. The models are modular and can be incorporated into any size system for one or multiple cycles. The models were tested on a hypothetical system of closely spaced intersections and under different traffic flow, control, and geometric conditions. Results show that delay induced by downstream traffic operations on an upstream intersection can be significant and that it may change with time and reach steadiness once traffic flow, downstream queues, and signal control measures stabilize and start replicating over time. Green ratios of neighboring intersections exert a significant influence on delay. For certain green ratios and geometric combinations, offsets can exert appreciable influence as well. The delay values and their temporal variation compared well with those from a microscopic simulation model.

Analysis of Downstream Queues on Upstream Capacity Expansion of Urban Signalized Intersection

AbstractSignalized intersection is a fundamental component of an urban transportation system and appropriate treatments for intersection related congestion and safety issues are increasingly growing in importance. The most direct and intuitive approach to alleviate the recurring congestion is to cope with the peak hour disparity between travel demand and supply at the bottleneck intersections by expanding intersection capacity. However, intersection treatments such as adding lanes, turning movement restrictions, and grade separation that were traditionally applied to improve intersection capacity may not realize the expected benefits of relieving congestion and reducing delay as the traffic conditions at the downstream intersections can be greatly deteriorated by increased upstream arrivals. Additionally, the extended queue generated from downstream intersections can spill back into the upstream intersection and diminish the performance of the upstream treatment. This phenomenon is frequently observed in large urban areas where the traffic volume is heavy, intersection spacing is short and cycle length is long. This study was conducted to provide traffic engineers with a simple, practical and step-by-step analysis method to identify the occurrence and the type of queue spillback (Cyclic and Sustained), to determine the effects of downstream queues on upstream capacity, and to select the best capacity expansion treatment. The theory and methods for measuring the consequence of downstream queue effects and quantifying the potential capacity cutoff are developed based on the updated queue size and intersection capacity estimation methodologies for signalized intersections in the Highway Capacity Manual 2010 (HCM 2010). A spreadsheet-based computational tool was developed to assist in the process of capacity constraint identification and calculation. A case study is presented to demonstrate the practical use of the analysis method.

Dynamic production control in parallel processing systems under process queue time constraints

This research examines the production control problems in two-station serial production systems under process queue time (PQT) constraints. In these serial production systems, all jobs must be processed at a fixed order in the upstream and downstream stations. There are multiple machines in both stations, and all machines are subject to random machine failures. In the downstream queue, the sum of waiting and processing time for each job is limited by an upper bound. This upper bound of time is called the PQT constraint. Violation of the PQT constraint causes high rework or scrap costs.In this research, a Multi-machine Admission Control (MMAC) model is formulated using Markov decision processes (MDPs). Machine failures are major causes of PQT constraint violation; hence, MMAC model explicitly considers real time machine reliability status. Because real time reliability status of all machines is explicitly considered, computational efficiency of MMAC model suffers from the well-know “curse of dimensionality” of dynamic programming. To overcome the computational complexity issue, we prove the existence of optimal exhaustive production control policy. Based on the existence of optimal exhaustive control policy, an efficient algorithm is designed to significantly reduce computational complexity. In numerical study, we compare the performance of MMAC with other control policies in literature. Our numerical results indicate that MMAC can reduce production costs and scrap counts by at least 14.88% in average.

Stochastic control of computer networks

Although transmission control protocol (TCP) is a proven protocol in networks with congestion-dominated packet losses, it is a poor match for mobile networks with bit-error-dominated packet losses. This article considers a control theoretic approach for more effective flow control in reliable network transmissions. An extended Kalman filter is developed to estimate two key network state indicators: individual queue sizes and packet arrival rates to each queue. A source node estimates these parameters for each of the downstream queues currently servicing packet streams originating from itself. These estimates can be used by an linear quadratic Gaussian (LQG) ‘steady-state’ linear perturbation proportional-plus-integral (PI) controller to regulate the size of downstream queues by altering the packet rate sent towards a particular downstream queue. Although this work demonstrates the effects of a single controller, it is anticipated that a network wide deployment could achieve significant throughput and stability benefits. The primary contributions of this work include: (a) development of the necessary Kalman filter theory, (b) design of a network state estimator using a transient queue behaviour model, (c) equations for the LQG synthesis of a steady-state linear perturbation PI controller and (d) demonstration of the resulting controller performance, which shows significant improvement over traditional TCP implementations.

State-dependent importance sampling for a slowdown tandem queue

In this paper we investigate an advanced variant of the classical (Jackson) tandem queue, viz. a two-node system with server slowdown. By this mechanism, the service speed of the upstream queue is reduced as soon as the number of jobs in the downstream queue reaches some pre-specified threshold. We focus on the estimation of the probability of overflow in the downstream queue before the system becomes empty, starting from any given state in the state space. The principal contribution of this paper is that we construct importance sampling schemes to estimate these probabilities in case they are small; in particular: (1)We use powerful heuristics to identify the exponential decay rate of the probability under consideration, and verify this result by applying sample-path large deviations techniques. (2) Based on these heuristics we develop a change of measure to be used in importance sampling. (3) We prove that this scheme is asymptotically efficient, using a shorter and more straightforward method than usually provided in the literature. Unfortunately, this scheme is difficult to use in practice, therefore (4) we propose an algorithm that offers considerable computational advantage over the first scheme. For this scheme we provide a proof of asymptotic efficiency for certain parameter settings, as well as numerical results showing that the scheme works well for all parameters.

State-dependent importance sampling for a Jackson tandem network

This article considers importance sampling as a tool for rare-event simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jacksonian two-node tandem queue; it is known that in this setting “traditional” state-independent importance-sampling distributions perform poorly. We therefore concentrate on developing a state-dependent change of measure, that we prove to be asymptotically efficient. More specific contributions are the following. (i) We concentrate on the probability of the second queue exceeding a certain predefined threshold before the system empties. Importantly, we identify an asymptotically efficient importance-sampling distribution for any initial state of the system. (ii) The choice of the importance-sampling distribution is backed up by appealing heuristics that are rooted in large-deviations theory. (iii) The method for proving asymptotic efficiency relies on probabilistic arguments only. The article is concluded by simulation experiments that show a considerable speedup.

Dynamic production control in a serial line with process queue time constraint

This research examines the production control problem in two-station tandem queueing systems under time constraints. In these two-station tandem queueing systems, jobs must first be processed at the upstream station and then the downstream station. For each job, the sum of the waiting and processing time in the downstream queue is limited by an upper bound. This time constraint is called the process queue time constraint. When the process queue time constraint is violated, a significant scrap cost will be accrued. In this research, we develop a Markov decision model to study the production control problem under process queue time constraints. The objective is to minimise the sum of the expected long-run average inventory holding costs and scrap costs. According to the Markov decision model, an interesting exhaustive structure of the optimal production control policy is found. Based on this exhaustive structure, an efficient algorithm is developed to solve the production control problem numerically. The performance of the proposed algorithm is verified by a simulation study. Compared with other heuristics in the literature, the proposed algorithm can significantly reduce production costs while improving system throughput and utilisation.

Asymptotic analysis of Lévy-driven tandem queues

We analyze tail asymptotics of a two-node tandem queue with spectrally-positive Levy input. A first focus lies in the tail probabilities of the type ?(Q 1>? x,Q 2>(1??)x), for ??(0,1) and x large, and Q i denoting the steady-state workload in the ith queue. In case of light-tailed input, our analysis heavily uses the joint Laplace transform of the stationary buffer contents of the first and second queue; the logarithmic asymptotics can be expressed as the solution to a convex programming problem. In case of heavy-tailed input we rely on sample-path methods to derive the exact asymptotics. Then we specialize in the tail asymptotics of the downstream queue, again in case of both light-tailed and heavy-tailed Levy inputs. It is also indicated how the results can be extended to tandem queues with more than two nodes.

Large deviations and importance sampling for a tandem network with slow-down

We consider a variant of the two-node tandem Jackson network where the upstream server reduces its service rate when the downstream queue exceeds some prespecified threshold. The rare event of interest is the overflow of the downstream queue. Based on a game/subsolution approach, we rigorously identify the exponential decay rate of the rare event probabilities and construct asymptotically optimal importance sampling schemes.

Efficient Simulation of a Tandem Queue with Server Slow-down

Tandem Jackson networks and more sophisticated variants have found widespread application in various domains. One such variant is the tandem queue with server slow-down, in which the server of the upstream queue reduces its service speed as soon as the downstream queue eXceeds some prespecified threshold, to provide the downstream queue some sort of `protection'. This paper focuses on the overflow probabilities in the downstream queue. Owing to the Markov structure these can be solved numerically, but the resulting system of linear equations is usually large. An attractive alternative could be to resort to simulation, but this approach is cumbersome due to the rarity of the event under consideration. A powerful remedy is to use importance sampling, i.e. simulation under an alternative measure, where unbiasedness of the estimator is retrieved by weighing the observations by appropriate likelihood ratios. To find a good alternative measure, we first identify the most likely path to overflow. For the standard tandem queue (i.e. no slow-down) this path was known, but we develop an appealing novel heuristic which can also be applied to the model with slow-down. The knowledge of the most likely path is then used to devise importance sampling algorithms, both for the standard tandem system and for the system with slow-down. Our eXperiments indicate that the corresponding new measure is sometimes asymptotically optimal, and sometimes not. We systematically analyze the cases that may occur.

An approximate compositional approach to the analysis of fluid queue networks

Fluid models have for some time been used to approximate stochastic networks with discrete state. These range from traditional ‘heavy traffic’ approximations to the recent advances in bio-chemical system models. Here we present a simple approximate compositional method for analysing a network of fluid queues with Markov-modulated input processes at equilibrium. The idea is to approximate the on/off process at the output of a queue by an n -state Markov chain that modulates its rate. This chain is parameterised by matching the moments of the resulting process with those of the busy period distribution of the queue. This process is then used, in turn, as a separate Markov-modulated on/off process that feeds downstream queue(s). The moments of the busy period are derived from an exact analytical model. Approximation using two- and three-state intermediate Markov processes are validated with respect to an exact model of a tandem pair of fluid queues — a generalisation of the single queue model. The analytical models used are rather simpler and more accessible, albeit less general, than previously published models, and are also included. The approximation method is applied to various fluid queue networks and the results are validated with respect to simulation. The results show the three-state model to yield excellent approximations for mean fluid levels, even under high load.

Departure process of a single server queueing system with Markov renewal input and general service time distribution

The independence of processes in queueing systems is generally assumed when developing queueing models. However, real systems often involve several process dependencies, and failure to take these into consideration can lead to serious underestimation of the performance measures. We consider herein a single server queueing system with a Markov renewal process (MRP) for its arrival process and a general service time distribution, and derive the distribution function and correlation coefficient of the departure process. Since the departure process also often corresponds to an arrival process in downstream queues, the results obtained here can be used to derive a better approximation of the performance measures of a non-product form general queueing network.

The Network Kinematic Waves Model: A Simplified Approach to Network Traffic

Flow of traffic on freeways and limited access highways can be represented as a series of kinemetic waves. Solutions to these systems of equations become problematic under congested traffic flow conditions, and under complicated (real-world) networks. A simplified theory of kinematics waves (KWaves) was previously proposed. Simplifying elements includes translation of the problem to moving coordinate system, adoption of triangular speed-density relationships, and adoption of restrictive constraints at the on- and off-ramps. However, these simplifying assumptions preclude application of this technique to most practical situations. By directly addressing the limitations of the original theory, this article proposes a simplified Kwaves model for network traffic (N-KWaves). Several key constraints of the original theory are relaxed. For example, the original merge model, which gives full priority to on-ramp traffic, is relaxed and replaced with a capacity-based weighted queuing (CBWFQ) merge model. The original diverge model, which blocks upstream traffic as a whole when a downstream queue exceeds the diverge, is also relaxed and replaced with a contribution-based weighted splitting (CBWS) diverge model. Based on the above, the original theory is reformulated and extended to address network traffic. Central to the N-KWaves model is a five-step computational procedure based on a generic building block. It is assumed that a freeway network can be represented by the combination of some special cases of the generic building block. An empirical field study showed satisfactory results. The N-KWaves model is best suited for modeling traffic operation in a regional freeway network and has a strong connection to Intelligent Transportation Systems (ITS).

Network decomposition: theory and practice

We show that significant simplicities can be obtained for the analysis of a network when link capacities are large enough to carry many flows. We develop a network decomposition approach in which network analysis can be greatly simplified. We prove that the queue length at the downstream queue converges to that of a single queue obtained by removing the upstream queue, as the capacity and the number of flows at the upstream queue increase. The precise modes of convergence vary depending on the type of input traffic, i.e., from regulated traffic arrivals to point process inputs. Our results thus help simplify network analysis by decomposing the original network into a simplified network in which all the nodes with large capacity have been eliminated. By means of extensive numerical investigation under various network scenarios, we demonstrate different aspects and implications of our network decomposition approach. Some of our findings are that our techniques perform well especially for the cases when: i) many flows are multiplexed as they enter the queue and/or ii) departing flows are routed to different downstream nodes, i.e., no single flow dominates at any node.