Fluid Traffic Model Research Articles

Equilibrium Manifolds in 2D Fluid Traffic Models

The main goal of this paper is to analytically find a steady-state in a large-scale urban traffic network with known and constant demand and supply on its boundaries. Traffic dynamics are given by a continuous two-dimensional macroscopic model, where state corresponds to the vehicle density evolving in a 2D plane. Thereby, the flux magnitude is given by the space-dependent fundamental diagram and the flux direction depends on the underlying network topology. In order to find a steady-state, we use the coordinate transformation such that the 2D equation can be rewritten as a parametrized set of 1D equations. This technique allows us to obtain the curves along which the traffic flow evolves, which are essentially the integral curves of the flux field constructed from the network geometry. The results are validated by comparing the obtained steady-state with the one estimated by using a microsimulator.

Research and Improvement of the Keep-Right-Except-to-Pass Rule

In order to deal with the impact on traffic flow of the rule, we compare the influence factors of traffic flow (passing, etc.) into viscous resistance of fluid mechanics, and establish a traffic model based on fluid mechanics. First, in heavy and light traffic, we respectively use this model to simulate the actual segment of the road and find that when the traffic is heavy, the rule hinder the further increase in traffic. For this reason, we make further improvements to the model to obtain a fluid traffic model based on no passing and find that the improved model makes traffic flow increase significantly. Then, the improved model is applied to the light traffic, we find there are no significant changes in traffic flow .In this regard we propose a new rule: when the traffic is light, passing is allowed, but when the traffic is heavy, passing is not allowed.

Available bandwidth estimation for the network paths with multiple tight links and bursty traffic

Available bandwidth (ABW) estimation is useful for various applications such as network management, traffic engineering, and rate-based multimedia streaming. Most of the ABW estimation methods are based on the fluid cross-traffic model. Inevitably, their estimation accuracy is limited in the network environments with bursty cross-traffic. In this paper, we apply packet trains (a series of probing packets) and a modified Ping to probe the ABW of a network path. Our proposed probing method can identify several tight links along a path and can infer their individual ABWs. The ABW estimation algorithm developed in this study, GNAPP, is also based on the fluid traffic model, but it can effectively filter out probing noise incurred in networks that carry bursty traffic. The algorithm employs not only the gaps of any two consecutive probing packets but also those of nonadjacent probing packets for ABW estimation. Thus, the number of samples for ABW estimation increases significantly without resorting to sending more probing packets and the estimation efficiency and accuracy are improved. In addition, two-stage filtering and moving averages are used in GNAPP for reducing estimation errors. Numerical results demonstrate that the estimation scheme based on GNAPP can achieve good accuracy even when the traffic is bursty and there are multiple tight links on the path being observed. Thus, it outperforms other well-known ABW estimation tools.

Data assimilation and inverse problem for fluid traffic flow models and algorithms

AbstractThis article deals with traffic data assimilation and algorithms that are able to predict the traffic flow on a road section. The traffic flow is modellized by the Aw–Rascle hyperbolic system. We have to minimize a functional whose optimization variables are initial condition. We use the Roe method to compute the solution to the traffic flow modelling system. Then we compute the gradient of the functional by an adjoint method. This gradient will be used to optimize the functional. Copyright © 2008 John Wiley & Sons, Ltd.

JitterPath: Probing Noise Resilient One-Way Delay Jitter-Based Available Bandwidth Estimation

Measurement of end-to-end available bandwidth has received considerable attention due to its potential use in improving QoS. Available bandwidth enables the sending rate to adapt to network conditions, so that packet loss, caused by congestion, can be significantly reduced before error control mechanisms are finally employed. To this end, we propose a probing noise resilient available bandwidth estimation scheme, called JitterPath, which is adaptive to both the fluid and bursty traffic models. Two key factors, one-way delay jitter and accumulated queuing delay, are both exploited to predict the type of queuing region for each packet pair. Then, the bottleneck utilization information included in the joint queuing regions is estimated and used to quantify the captured traffic ratio, which indicates the relationship between the probing rate and available bandwidth. The contributions of our method are as follows: 1) JitterPath can work without being restricted to fluid traffic models; 2) since JitterPath does not directly use the bottleneck link capacity to calculate the available bandwidth, it is feasible for use in a multihop environment with a single bottleneck; and 3) JitterPath inherently reduces the impact of probing noises under the bursty cross traffic model. Extensive simulations, Internet experiments, and comparisons with other methods were conducted to verify the effectiveness of our method under both single-hop and multihop environments

Packet delay in optical circuit-switched networks

A framework is provided for evaluation of packet delay distribution in an optical circuit-switched network. The framework is based on a fluid traffic model, packet queueing at edge routers, and circuit-switched transmission between edge routers. Packets are assigned to buffers according to their destination, delay constraint, physical route and wavelength. At every decision epoch, a subset of buffers is allocated to end-to-end circuits for transmission, where circuit holding times are based on limited and exhaustive circuit allocation policies. To ensure computational tractability, the framework approximates the evolution of each buffer independently. Slack variables are introduced to decouple amongst buffers in a way that the evolution of each buffer remains consistent with all other buffers in the network. The delay distribution is derived for a single buffer and an approximation is given for a network of buffers. The approximation entails finding a fixed point for the functional relation between the slack variables and a specific circuit allocation policy. An analysis of a specific policy, in which circuits are probabilistically allocated based on buffer size, is given as an illustrative example. The framework is shown to be in good agreement with a discrete event simulation model.

On fluid queueing systems with strict priority

We consider priority fluid queueing systems where high-priority class has strict priority access to service. Sample path analysis tools, such as Poisson counter driven stochastic differential equation, are employed to study system queueing behavior in steady state. We are able to obtain various analytical results for different fluid traffic models and system configurations. Those results can be used as a general rule of thumb in buffer dimensioning and other traffic engineering issues.

On the distribution of calls in a wireless network driven by fluid traffic

This note develops a modelling approach for wireless networks driven by fluid traffic models. Introducing traffic sets that follow movement of subscribers, the wireless network with time-varying rates is transformed into a stationary network at these traffic sets, which yields that the distribution of calls over the cells of the network depends on the call length distribution only through its mean. The result is extended to a network of infinite server queues with time-varying arrival rates.

Design and Modeling of an Interval-based ABR Flow Control Protocol

A novel flow control protocol is presented for Availability Bit Rate (ABR) service in Asynchronous Transfer Mode (ATM) networks. This scheme features periodic explicit rate feedback that enables precise allocation of link bandwidth and buffer space on a hop-by-hop basis to guarantee maximum throughput, minimum cell loss, and high resource efficiency. With the inclusion of resource management cell synchronization and consolidation algorithms, this protocol is capable of controlling point-to-multipoint ABR services within a unified framework. The authors illustrate the modeling of single ABR connection, the interaction between multiple ABR connections, and the constraints applicable to flow control decisions. A loss-free flow control mechanism is presented for high-speed ABR connections using a fluid traffic model. Supporting algorithms and ATM signaling procedures are specified, in company with linear system modeling, numerical analysis, and simulation results, which demonstrate its performance and cost benefits in high-speed backbone networking scenarios.

On the relevance of long-range dependence in network traffic

There is much experimental evidence that network traffic processes exhibit ubiquitous properties of self-similarity and long-range dependence, i.e., of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much previous modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process. We introduce and evaluate a model in which these parameters can be controlled. Specifically, our model is a modulated fluid traffic model in which the correlation function of the fluid rate matches that of an asymptotically second-order self-similar process with given Hurst parameter up to an arbitrary cutoff time lag, then drops to zero. We develop a very efficient numerical procedure to evaluate the performance of a single-server queue fed with the above fluid input process. We use this procedure to examine the fluid loss rate for a wide range of marginal distributions, Hurst (1950) parameters, cutoff lags, and buffer sizes. Our main results are as follows. First, we find that the amount of correlation that needs to be taken into account for performance evaluation depends not only on the correlation structure of the source traffic, but also on time scales specific to the system under study. For example, the time scale associated with a queueing system is a function of the maximum buffer size. Thus, for finite buffer queues, we find that the impact on loss of the correlation in the arrival process becomes nil beyond a time scale we refer to as the correlation horizon. This means, in particular, that for performance-modeling purposes, we may choose any model among the panoply of available models (including Markovian and self-similar models) as long as the chosen model captures the correlation structure of the source traffic up to the correlation horizon. Second, we find that loss can depend in a crucial way on the marginal distribution of the fluid rate process. Third, our results suggest that reducing loss by buffering is hard for traffic with correlation over many time scales. We advocate the use of source traffic control and statistical multiplexing instead.

On the relevance of long-range dependence in network traffic

There is mounting experimental evidence that network traffic processes exhibit ubiquitous properties of self-similarity and long range dependence (LRD), i.e. of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process.We introduce and evaluate a model in which these parameters can be easily controlled. Specifically, our model is a modulated fluid traffic model in which the correlation function of the fluid rate is asymptotically second-order self-similar with given Hurst parameter, then drops to zero at a cutoff time lag. We develop a very efficient numerical procedure to evaluate the performance of the single server queue fed with the above fluid input process. We use this procedure to examine the fluid loss rate for a wide range of marginal distributions, Hurst parameters, cutoff lags, and buffer sizes.Our main results are as follows. First, we find that the amount of correlation that needs to be taken into account for performance evaluation depends not only on the correlation structure of the source traffic, but also on time scales specific to the system under study. For example, the time scale associated to a queueing system is a function of the maximum buffer size. Thus for finite buffer queues, we find that the impact on loss of the correlation in the arrival process becomes nil beyond a time scale we refer to as the correlation horizon. Second, we find that loss depends in a crucial way on the marginal distribution of the fluid rate process. Third, our results suggest that reducing loss by buffering is hard. We advocate the use of source traffic control and statistical multiplexing instead.

Push forward link-level scheduling for network-wide performance

A virtual circuit network with arbitrary topology is considered. The traffic streams follow prespecified routes, different in general for each stream, to reach their destination. A fluid traffic model is adopted and a processor sharing service discipline is considered. A policy is proposed for setting adaptively the fractions of the transmission capacity, which is allocated to the different traffic streams in the processor sharing discipline at each link. The amount of traffic arrived at the originating node of each link is measured for each stream. The fraction of the link capacity allocated to each stream is set to be proportional to the measured traffic. The traffic is measured continuously and the fractions are updated regularly based on the most recent traffic measurements. It is shown that eventually, the transmission capacity allocated to each stream converges to a quantity proportional to the average rate of the stream. Hence, if the capacity condition is satisfied, sufficient fractions of the capacity are allocated at each link for each stream. End-to-end performance guarantees are provided, if the traffic is regulated. The policy is distributed since each link adjusts the service fractions based on observations of the traffic arriving at its originating node only. Furthermore, it is adaptive since no information on the traffic characteristics is needed for the application of the policy.