Traffic Limit Research Articles

Whittle index approach to the multi-class queueing systems with convex holding costs and IHR service times

AbstractWe consider the dynamic scheduling problem in a single-server multi-class queueing system, where the accumulated holding costs of a customer is a convexly increasing function of the time that the customer spends in the system. This problem was already addressed by van Mieghem in his seminal paper (Ann Appl Probab 5:808–833, 1995). He launched the so-called generalized $$c\mu $$ c μ rule and proved its asymptotic optimality in the heavy traffic limit. The optimal scheduling problem with convex holding costs have also been studied in many other papers. However, the holding costs in these papers are typically count-convex, i.e., the aggregate holding cost rate related to a class of customers increases convexly as a function of the current number of customers in this class, which is clearly different from the time-convex holding costs introduced in van Mieghem (Ann Appl Probab 5:808–833, 1995) and studied also in the present paper. We utilize the Whittle index approach to develop a novel heuristic policy for the dynamic scheduling problem with time-convex holding costs. Instead of the original open version of the continuous-time scheduling problem, we apply the Whittle index approach to the corresponding discrete-time closed version of the problem. As the main theoretical contribution, we prove that, for IHR service times, the discounted discrete-time problem is indexable and also give an explicit expression for the Whittle index itself. A special challenge in our model is the two-dimensional state space with an infinite number of possible states. By utilizing the discrete-time results, we develop a novel index policy for the original continuous-time problem and demonstrate, by numerical simulations, that this Whittle index policy outperforms the generalized $$c\mu $$ c μ rule. Thus, while the generalized $$c\mu $$ c μ rule is asymptotically optimal in the heavy traffic limit, it can still be improved in normal traffic conditions.

Traffic intensity and vegetation management affect flower‐visiting insects and their response to resources in road verges

Abstract Road verges can support high densities of flowers and could therefore provide new opportunities for the conservation of flower‐visiting insects. One way of optimizing road verges for vascular plant diversity is to adjust mowing regimes, but to date it is unclear how this affects flower‐visiting insects. Furthermore, for mobile organisms like wild bees and butterflies, there is a risk that the benefit of increased habitat quality in road verges is limited by the proximity to traffic, but this is poorly studied. In a crossed study design, we separated mowing time and frequency (early summer and autumn, or only late summer) from road verge habitat classification (valuable for biodiversity according to transport authority, or regular). We did so along a gradient of traffic intensity, to investigate if a mowing regime designed to enhance plant diversity can also benefit wild bees and butterflies, and if traffic limits the conservation potential of road verges. Road verges that were mown only in late summer had higher flower densities, and there was a positive relationship between flower density and wild bee abundance and species richness. Butterfly abundance and species richness only benefitted from a late summer mowing in valuable but not in regular road verges. Traffic intensity had a substantial negative impact on abundance and species richness of wild bees and butterflies. Higher traffic intensities limited the positive relationship between plant and butterfly species richness that we observed at lower traffic intensities. Increasing width of the road verges buffered negative effects of the traffic on wild bee as well as butterfly abundances, and on wild bee species richness. Synthesis and applications. Road verges can play a valuable role for the conservation of wild bees and butterflies, but there is a need to consider both traffic intensity and resource availability when implementing management strategies. To support wild bee and butterfly diversity, we recommend actions to enhance plant species richness and flower resource availability, and to focus these conservation efforts on roads with low traffic intensity, or on wide road verges.

Exploring the effect of perceived safety in first/last mile mode choices

AbstractMicro-mobility transport modes like e-bikes and e-scooters promise higher flexibility when covering the first/last mile trip from/to the public transport stop/station to the destination point and vice-versa. However, safety concerns about riding a micro vehicle in mixed traffic limit the flexibility of shared mobility modes and make conventional ones still more attractive, e.g., private car and walking. This study investigates the effect of perceived safety in first/last mile mode choice by conducting an image-based double stated preference experiment targeted at potential micro-mobility users and developing ordinal and mixed logistic regression models. The Value-of-Safety (VoS) is introduced. It refers to the additional distance a user is willing to exchange to avoid an unsafe path. Main findings show that shared space can be a middle-ground solution, as it reports lower heterogeneity among individuals in terms of safety perceptions. The intensive use of e-scooters in mixed-traffic decreases the perceived safety of pedestrians, while e-bikers are threatened by the existence of heavy motorized traffic. Low mean VoS is also reported for e-scooters, demonstrating the unwillingness of potential micro-mobility service users to either detour or use this micro vehicle. The mean VoS of the e-bike is estimated as almost equal to that of the private car. It could be, hence, concluded that perceived safety can systematically explain the unobserved disutility of e-bikes.

DynaTrack: Machine Learning Aided Variable Speed Limit System

In the past decade or so, we have seen traffic congestion become a ginormous issue in the major cities of the world, the main reasons for the above being exponential growth in vehicle purchases, constant unplanned maintenance of the road networks, and so on. And as far as the current situation is concerned, it can be safely said that even though steps have been taken to counter the issue at hand, the improvement made has been close to nothing as the problem persists. The solution to this is being suggested is based on the concept of Variable Speed Limits, which says that the speed limits for the road segments be dependent on the traffic volume and situations on the road segment rather than being constant. The system would use the feed from CCTV cameras to keep a track of the flow variable, which lies within the low traffic limits, the speed limits would be increased accordingly. This would ensure convenience for travelers, reduce travel time, fuel consumption, and greenhouse gas emission, and will also improve economic gains, among other advantages.

Метод оцінки зв’язності вузлів бездротових епізодичних мереж за умови застосування безпілотних літальних апаратів

The paper considers a method for assessing the connectivity of nodes of wireless episodic networks (WEN) under the condition of using unmanned aerial vehicles (UAVs). It is proposed to perform an evaluation of the connectivity of a pair of nodes according to a method, which is based on: an evaluation of geometric connectivity, which is limited to the maximum range of radio visibility at the physical level and the vulnerability interval of a given multiple access protocol at the channel level; assessment of information connectivity, which takes into account the presence of not only a physical connection of a given reliability, but also the presence of a free channel resource, a given amount of transmission delay at a given traffic limit value; assessment of the duration of connectivity taking into account the mobility of network nodes. On the basis of analytical mathematical models, the duration of connectivity of mobile subscribers (nodes) (MS) of the WEN consisting of MS and UAVs in direct radio visibility conditions and taking into account relaying was investigated. The connectivity of a pair of nodes is determined by the characteristics of different levels of OSI information interaction, such as radio range, channel bandwidth, information transmission delay, etc. It is shown that the duration of connectivity is directly proportional to the size of the coverage zone and inversely proportional to the speed of movement of nodes. The nature (scenario) of node mobility also affects the duration of connectivity. The simulation of the movement of nodes was carried out under 4 scenarios: «march», «skirmish», «random wandering in the field» and «random wandering in the city». The largest values of the duration of connectivity correspond to the third scenario, and the smallest to the second (with a fixed radius of the coverage area and the speed of movement of nodes). Thus, the average connection duration of the UAV-pedestrian connection in the event of a «difference» will be of the order of 36 minutes, and the UAV-car connection of the order of 5 minutes. The obtained results can be used in the UAV network topology control method.

Optimal Scheduling in the Multiserver-job Model under Heavy Traffic

Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Essentially all of the theoretical work on multiserver-job systems focuses on maximizing utilization, with almost nothing known about mean response time. In simpler settings, such as various known-size single-server-job settings, minimizing mean response time is merely a matter of prioritizing small jobs. However, for the multiserver-job system, prioritizing small jobs is not enough, because we must also ensure servers are not unnecessarily left idle. Thus, minimizing mean response time requires prioritizing small jobs while simultaneously maximizing throughput. Our question is how to achieve these joint objectives. We devise the ServerFilling-SRPT scheduling policy, which is the first policy to minimize mean response time in the multiserver-job model in the heavy traffic limit. In addition to proving this heavy-traffic result, we present empirical evidence that ServerFilling-SRPT outperforms all existing scheduling policies for all loads, with improvements by orders of magnitude at higher loads. Because ServerFilling-SRPT requires knowing job sizes, we also define the ServerFilling-Gittins policy, which is optimal when sizes are unknown or partially known.

Structural Prediction Analysis of Cross-Sea Cable-Stayed Bridges during Operation Based on Existing Traffic Volumes

In order to study the safety state of the structure of a cross-sea cable-stayed bridge during its operation period, this paper proposes a combined long-term traffic prediction model based on the XGBoost (eXtreme Gradient Boosting) model and LSTM (Long Short Term Memory) model in the context of a cross-sea cable-stayed bridge in Qingdao. XGBoost is an optimized distributed gradient enhancement library. LSTM is a neural network for processing long sequence data. The LSTM model and the XGBoost model were first built separately, and then a genetic algorithm was used to select the optimal weight parameters to combine the two models for prediction. Based on the traffic prediction results of the combined LSTM-XGBoost model, a finite element model was established using numerical analysis. The effect of different traffic volumes on the deflection and stresses in the span of the main beam and the stresses in the diagonal cables was analyzed using the time course analysis method. From the point of view of structural safety, the maximum of future traffic limits and more reasonable average traffic speeds are given to provide a basis for the later management of the bridge.

Research on urban path selection of construction vehicles based on bi-objective optimization.

With the implementation of urban central rail transit and old city reconstruction projects, construction vehicles frequently enter and depart the urban area. And because of its large volume and other characteristics, it increases the risk probability and severity of urban traffic accidents. This study takes the transportation path selection of construction vehicles as the breakthrough point, weighs the transportation efficiency and safety of construction vehicles, establishes a bi-objective optimization model, involving constraints such as height limit, weight limit, speed limit, direction limit and traffic limit and uses genetic algorithm to solve it. Finally, through case analysis, the user preference is adjusted to conduct functional test and description of the model. The results indicate that the model has the function of transportation vehicle path optimization. In the meantime, compared with the safest route, the time-consuming of the optimal route decreases by 16% and the risk increases by 7.4%, while the time-consuming of it increases by 5% and the risk decreases by 15.4% compared with the shortest route. Moreover, the corresponding coefficients of time-consuming and safety preference can reach about 0.65, and the relevant stakeholders have high acceptance of the route. Further improvement of construction vehicle management mechanism based on path optimization is one of the limited ways to effectively improve the current situation of construction vehicle management.

WCFS: a new framework for analyzing multiserver systems

Multiserver queueing systems are found at the core of a wide variety of practical systems. Many important multiserver models have a previously-unexplained similarity: identical mean response time behavior is empirically observed in the heavy traffic limit. We explain this similarity for the first time. We do so by introducing the work-conserving finite-skip (WCFS) framework, which encompasses a broad class of important models. This class includes the heterogeneous M/G/k, the Limited Processor Sharing policy for the M/G/1, the Threshold Parallelism model and the Multiserver-Job model under a novel scheduling algorithm. We prove that for all WCFS models, scaled mean response time \(E[T](1-\rho )\) converges to the same value, \(E[S^2]/(2E[S])\), in the heavy-traffic limit, which is also the heavy traffic limit for the M/G/1/FCFS. Moreover, we prove additively tight bounds on mean response time for the WCFS class, which hold for all load \(\rho \). For each of the four models mentioned above, our bounds are the first known bounds on mean response time.

Logarithmic heavy traffic error bounds in generalized switch and load balancing systems

AbstractMotivated by applications to wireless networks, cloud computing, data centers, etc., stochastic processing networks have been studied in the literature under various asymptotic regimes. In the heavy traffic regime, the steady-state mean queue length is proved to be $\Theta({1}/{\epsilon})$ , where $\epsilon$ is the heavy traffic parameter (which goes to zero in the limit). The focus of this paper is on obtaining queue length bounds on pre-limit systems, thus establishing the rate of convergence to heavy traffic. For the generalized switch, operating under the MaxWeight algorithm, we show that the mean queue length is within $\textrm{O}({\log}({1}/{\epsilon}))$ of its heavy traffic limit. This result holds regardless of the complete resource pooling (CRP) condition being satisfied. Furthermore, when the CRP condition is satisfied, we show that the mean queue length under the MaxWeight algorithm is within $\textrm{O}({\log}({1}/{\epsilon}))$ of the optimal scheduling policy. Finally, we obtain similar results for the rate of convergence to heavy traffic of the total queue length in load balancing systems operating under the ‘join the shortest queue’ routeing algorithm.

Skorokhod Reflection Problem for Delayed Brownian Motion with Applications to Fractional Queues

Several queueing systems in heavy traffic regimes are shown to admit a diffusive approximation in terms of the Reflected Brownian Motion. The latter is defined by solving the Skorokhod reflection problem on the trajectories of a standard Brownian motion. In recent years, fractional queueing systems have been introduced to model a class of queueing systems with heavy-tailed interarrival and service times. In this paper, we consider a subdiffusive approximation for such processes in the heavy traffic regime. To do this, we introduce the Delayed Reflected Brownian Motion by either solving the Skorohod reflection problem on the trajectories of the delayed Brownian motion or by composing the Reflected Brownian Motion with an inverse stable subordinator. The heavy traffic limit is achieved via the continuous mapping theorem. As a further interesting consequence, we obtain a simulation algorithm for the Delayed Reflected Brownian Motion via a continuous-time random walk approximation.

Heavy traffic limits for queues with non-stationary path-dependent arrival processes.

In this paper, we develop a diffusion approximation for the transient distribution of the workload process in a standard single-server queue with a non-stationary Polya arrival process, which is a path-dependent Markov point process. The path-dependent arrival process model is useful because it has the arrival rate depending on the history of the arrival process, thus capturing a self-reinforcing property that one might expect in some applications. The workload approximation is based on heavy-traffic limits for (i) a sequence of Polya processes, in which the limit is a Gaussian–Markov process, and (ii) a sequence of P/GI/1 queues in which the arrival rate function approaches a constant service rate uniformly over compact intervals.

The Application of a Socio-Economic Indicator for Calculating the Bandwidth of a Backbone in a WAN

In a regional network, the graph branches that describe it are not loaded equally with data traffic. A branch that is loaded with traffic will depend on: the number of users in both nodes of the graph, the number of paths that pass through that branch which are defined by the algorithm for finding the shortest path, the position of the branch in the network as well as the position of WAN in other neighbors’ networks. The traffic on the branches that connect the nodes of a network is constantly changing. It is important to know the maximum load of a branch in order to adapt to the demand so that there are no communication barriers. The calculation of data traffic in these branches is possible to be calculated and to know the maximum traffic limit in the respective branches. The branches that are busiest with data traffic represent the backbone of the Network. The calculation of the bandwidth of the branch is affected not only by the number of users but also by their structure. In this paper, bandwidth calculation on a main branch in a graph is done through a case study using SEI.

Comprehensive Operation Risk Assessment of a Highway Maintenance Area Based on Reliability

To study the influence of various working conditions on traffic safety in the maintenance area of a mountain expressway, 675 groups of PTV VISSIM traffic simulation experiments were designed with various traffic organization modes, traffic volumes, traffic compositions, activity area lengths, and speed limit values. The results show that the activity area length of a closed lane, a compressed lane, and a borrowed opposite lane had no marked influence on the traffic conflicts. There was a significant positive correlation between the proportion of trucks and the number of traffic conflicts, and the number of traffic conflicts increased significantly with an increase in traffic volume. In the closed lane and borrowed opposite lane scenarios, the increase in traffic conflicts was more obvious with the increase in traffic volume. There were obvious differences in the number of traffic conflicts under different forms of traffic organization. The number of conflicts in the compressed lane scenario was the lowest, and in the borrowed opposite lane scenario the number of conflicts was the highest. There was a significant correlation between a decrease in the speed limit and an increase in the number of traffic conflicts. Finally, with traffic volume, truck proportion, and speed limit values as independent variables and reliability as a dependent variable, linear regression equations of reliability were established for three traffic organization scenarios: closed lane, borrowed opposite lane, and compressed lane.

Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms

We examine a queue-based random-access algorithm where activation and deactivation rates are adapted as functions of queue lengths. We establish its heavy traffic behavior on a complete interference graph, which turns out to be nonstandard in two respects: (1) the scaling depends on some parameter of the algorithm and is not the N/N2 scaling usually found in functional central limit theorems; (2) the heavy traffic limit is deterministic. We discuss how this nonstandard behavior arises from the idleness induced by the distributed nature of the algorithm. In order to prove our main result, we develop a new method for obtaining a fully coupled stochastic averaging principle.

Heavy traffic analysis for single-server SRPT and LRPT queues via EDF diffusion limits

Extending the results of Kruk (Queueing theory and network applications. QTNA 2019. Lecture notes in computer science, vol 11688. Springer, Cham, pp 263–275, 2019), we derive heavy traffic limit theorems for a single server, single customer class queue in which the server uses the Shortest Remaining Processing Time (SRPT) policy from heavy traffic limits for the corresponding Earliest Deadline First queueing systems. Our analysis allows for correlated customer inter-arrival and service times and heavy-tailed inter-arrival and service time distributions, as long as the corresponding stochastic primitive processes converge weakly to continuous limits under heavy traffic scaling. Our approach yields simple, concise justifications and new insights for SRPT heavy traffic limit theorems of Gromoll et al. (Stoch Syst 1(1):1–16, 2011). Corresponding results for the longest remaining processing time policy are also provided.

A Dynamic Model for Managing Volunteer Engagement

Non-profit organizations that provide food, shelter, and other services to people in need, rely on volunteers to deliver their services. Unlike paid labor, non-profit organizations have less control over unpaid volunteers’ schedules, efforts, and reliability. However, these organizations can invest in volunteer engagement activities to ensure a steady and adequate supply of volunteer labor. We study a key operational question of how a non-profit organization can manage its volunteer workforce capacity to ensure consistent provision of services. In particular, we formulate a multiclass closed queueing network model to characterize the optimal engagement activities for the non-profit organization to minimize the costs of enhancing volunteer engagement and reducing abandonments, while maximizing productive work done by volunteers. Because this problem appears intractable, we formulate an approximating Browning control problem in the heavy traffic limit and study the dynamic control of that system. Our solution is a nested threshold policy with explicit congestion thresholds that indicate when the non-profit should optimally pursue various types of volunteer engagement activities. A numerical example calibrated using data from a large food bank shows that our dynamic policy for deploying engagement activities can reduce the food bank's total annual cost of its volunteer operations by 31%, while lowering its throughput by only 0.01%. This improvement in performance does not require any additional resources -- it only requires that the food bank strategically deploy its engagement activities based on the number of volunteers signed up to work volunteer shifts.

Staffing many‐server queues with autoregressive inputs

AbstractRecent studies reveal significant overdispersion and autocorrelation in arrival data at service systems such as call centers and hospital emergency departments. These findings stimulate the needs for more practical non‐Poisson customer arrival models, and more importantly, new staffing formulas to account for the autocorrelative features in the arrival model. For this purpose, we study a multiserver queueing system where customer arrivals follow a doubly stochastic Poisson point process whose intensities are driven by a Cox–Ingersoll–Ross (CIR) process. The nonnegativity and autoregressive feature of the CIR process makes it a good candidate for modeling temporary dips and surges in arrivals. First, we devise an effective statistical procedure to calibrate our new arrival model to data which can be seen as a specification of the celebrated expectation–maximization algorithm. Second, we establish functional limit theorems for the CIR process, which in turn facilitate the derivation of functional limit theorems for our queueing model under suitable heavy‐traffic regimes. Third, using the corresponding heavy traffic limits, we asymptotically solve an optimal staffing problem subject to delay‐based constraints on the service levels. We find that, in order to achieve the designated service level, such an autoregressive feature in the arrival model translates into notable adjustment in the staffing formula, and such an adjustment can be fully characterized by the parameters of our new arrival model. In this respect, the staffing formulas acknowledge the presence of autoregressive structure in arrivals. Finally, we extend our analysis to queues having customer abandonment and conduct simulation experiments to provide engineering confirmations of our new staffing rules.

Control Policies Approaching Hierarchical Greedy Ideal Performance in Heavy Traffic for Resource Sharing Networks

We consider resource sharing networks of the form introduced in work of Massoulié and Roberts as models for Internet flows. The goal is to study the open problem, formulated in Harrison et al. (2014) [Harrison JM, Mandayam C, Shah D, Yang Y (2014) Resource sharing networks: Overview and an open problem. Stochastic Systems 4(2):524–555.], of constructing simple form rate-allocation policies for broad families of resource sharing networks with associated costs converging to the hierarchical greedy ideal performance in the heavy traffic limit. We consider two types of cost criteria: an infinite horizon discounted cost and a long-time average cost per unit time. We introduce a sequence of rate-allocation control policies that are determined in terms of certain thresholds for the scaled queue-length processes and prove that, under conditions, both type of costs associated with these policies converge in the heavy traffic limit to the corresponding hierarchical greedy ideal (HGI) performance. The conditions needed for these results are satisfied by all the examples considered in the above cited paper of Harrison et al.

Optimisation of dynamic quantisation and control for quantised state feedback control system

Networked control systems (NCSs) are control systems closed through communication network and applied to remote control of robots, tele-surgery and numerous industrial applications. In NCS, data have to coarsely quantised when the communication network is restricted due to the traffic limit. Under the traffic limitation, the design of an appropriate quantiser is highly important in realising a desired control performance. Further, the coordination of quantisation and control input also plays a decisive role. Towards an optimal balance between the traffic capacity of network and the control performance, this study proposes an MPC based approach for quantised state feedback control systems with dynamic quantisers. In the proposed approach, the control input and the quantisation interval of the quantiser are optimised online. The proposed method can explicitly treat input/state constraints, the parameter of quantiser and other physical restriction. The effectiveness of the proposed method is demonstrated by simulations and experiments.