Optimal allocation in a queueing system with shared resources

Mapping knowledge domain (MKD) is an important application in bibliometrics, which is a method of visually presenting and explaining newly developed interdisciplinary scientific fields using data mining, information analysis, scientific measurement, and graphic rendering. This study combines applied mathematics, visual analysis technology, information science, and scientometrics to systematically analyze the development status, research distribution, and future trend of the heterogeneous traffic flow by using the MKD software tools VOSviewer and CiteSpace. Based on the MKD and Bibliometrics approaches, 4709 articles have been studied, which were published by Science Citation Index Expanded (SCIE) and Social Sciences Citation Index (SSCI) from 2004 to 2021 in the field of heterogeneous traffic flows. Firstly, this paper presents the annual numbers of articles, origin countries, main research organizations, and groups as well as the source journals on heterogeneous traffic flow studies. Then, cocitation analysis is used to divide heterogeneous traffic flow into three main research directions, which include “heterogeneous traffic flow model,” “traffic flow capacity analysis,” and “traffic flow stability analysis.” The keyword cooccurrence analysis is applied to identify five dominant clusters: “modeling and optimization methods,” “traffic flow characteristics analysis,” “driving behavior analysis,” “simulation experiment,” and “policies and barriers.” Finally, burst keywords were studied according to the publication date to present more clearly the change of research focus and direction over time.

We consider a single server queueing system with two classes of jobs: eager jobs with small sizes that require service to begin almost immediately upon arrival, and tolerant jobs with larger sizes that can wait for service. While blocking probability is the relevant performance metric for the eager class, the tolerant class seeks to minimize its mean sojourn time. In this article, we analyse the performance of each class under dynamic scheduling policies, where the scheduling of both classes depends on the instantaneous state of the system. This analysis is carried out under a certain fluid limit, where the arrival rate and service rate of the eager class are scaled to infinity, holding the offered load constant. Our performance characterizations reveal a (dynamic) pseudo-conservation law that ties the performance of both classes to the standalone blocking probabilities associated with the scheduling policies for the eager class. Furthermore, the performance is robust to other specifics of the scheduling policies. We also characterize the Pareto frontier of the achievable region of performance vectors under the same fluid limit, and identify a (two-parameter) class of Pareto-complete scheduling policies.

We prove homogenization for elliptic long-range operators in the random conductance model on random stationary point processes in d dimensions with Dirichlet boundary conditions and with a jointly stationary coefficient field. Doing so, we identify 4 conditions on the point process and the coefficient field that have to be fulfilled at different stages of the proof in order to pass to the homogenization limit. The conditions can be clearly attributed to concentration of support, Rellich--Poincaré inequality, non-degeneracy of the homogenized matrix and ergodicity of the elliptic operator.

Bifurcation analysis for a novel heterogeneous continuum model considering electronic throttle angle changes with memory

Modeling and analysis of heterogeneous traffic flow with mixed regular and connected human-driven vehicles considering driver stochasticity

With cooperative adaptive cruise control vehicles (CACC) development, the heterogeneous traffic flow of human-driven vehicles (HV) and CACC will appear on the same road. Although numerous studies have carefully analyzed the characteristic of the heterogeneous traffic flow, none of them considered the effect of the differences in acceptance of CACC by HV drivers on the heterogeneous traffic flow. In terms of the differences in car-following behaviors of HV drivers with diverse CACC acceptances, this paper deduces the capacity and stability of the heterogeneous traffic flow under different CACC penetration rates. Firstly, the HV driver’s car-following behavior model with different CACC acceptability is calibrated through a questionnaire. Then, the analytical framework of the fundamental diagram and stability of the heterogeneous traffic flow is derived, according to the differences of HV drivers’ acceptance of CACC. Finally, the paper analyzes the influence factors and effects of the heterogeneous traffic flow capacity and stability. The results indicate under different CACC penetration rates, the improvement of HV drivers’ acceptance of CACC increases the capacity and stability of the heterogeneous traffic flow. When CACC penetration rate is lower than 96.35% and HV drivers’ acceptance level of CACC is lower than the critical ratio, the popularity of CACC will decrease the stability of traffic flow. When the penetration rate of CACC is less than 34.76%, and HV drivers’ acceptance level of CACC is lower than the critical proportion, the popularization of CACC will decrease the capacity of heterogeneous traffic.

This paper proposes a novel Connected and Automated Vehicle (CAV) model as a scanner for heterogeneous traffic flows, which employs CAV on the road to detect traffic flow characteristics in multiple traffic scenes through various sensors. The model contains the hardware platform and software algorithm of CAV, and the analysis of traffic flow detection and simulation by Flow Project from Mobile Sensing Lab at UC Berkeley and Amazon AWS Machine Learning research grants based on SUMO, where the driving of the car is mainly controlled by Reinforcement Learning (RL). The simulation results showed that the traffic flow scanning, tracking and data recording by CAV are continuous and effective for the wide range and identification confirm function when CAV are in one lane. The effective detection area of CAV is in bow shape in the heterogeneous traffic flow, the occlusion rate is not associated with the lane position of CAV. Therefore, the calculated results should be filtered and optimized to enhance the confidence of heterogeneous traffic data collected. Currently, standards or most practitioners are not aware of this.

This paper is concerned with dynamic scheduling in a queueing system that has two independent Poisson input streams, two servers, deterministic service times and linear holding costs. One server can process both classes of incoming jobs, but the other can process only one class, and the service time for the shared job class is different depending on which server is involved. A bound on system performance is developed in terms of a single pooled resource, or super-server, whose capabilities combine those of the original two servers. Thereafter, attention is focused on the heavy traffic regime, where the combined capacity of the two servers is approximately equal to the total input rate. We construct a discrete-review control policy and show that if its parameters are chosen correctly as one approaches the heavy traffic limit, then its cost performance approaches the bound associated with a single pooled resource. Thus the discrete-review policy is proved to be asymptotically optimal in the heavy traffic limit. Although resource pooling in heavy traffic has been observed to occur in other network scheduling problems, there have been very few studies that rigorously proved the pooling phenomenon, or that proved the asymptotic optimality of a specific policy. Our discrete-review policy is obtained by applying a general method, called the BIGSTEP method in an earlier paper, to the parallel-server model.

Metamodeling and multi-objective optimization for buffer allocation in multi-product serial production lines

For certain stationary random setsX, densitiesDφ(X) of additive functionalsφare defined and formulas forare derived whenKis a compact convex set in. In particular, for the quermassintegrals and motioninvariantX, these formulas are in analogy with classical integral geometric formulas. The case whereXis the union set of a Poisson processYof convex particles is considered separately. Here, formulas involving the intensity measure ofYare obtained.

The availability of more realistic road conditions and dynamics provides sound ground to study the issues of Vehicular ad-hoc Network (VANET). In this chapter a new heterogeneous traffic flow based mathematical model is presented, to gain the time and space dynamics of vehicles. To achieve more accurate and realistic data about road conditions, microscopic parameters of varying safety distance between the vehicles and vehicular length are considered in the model. The density dynamics under different road scenarios are calculated under the influence of these constraints with the use of a defined mathematical model. The model is able to capture the impact of road constraints such as traffic lights and road incidents, on the traffic flow. The concept of Vehicular Ad-hoc Networks (VANET) has given mankind opportunities for secure and safe journeys on the roads. VANET is defined as a subclass of Mobile Ad-hoc Networks which holds the characteristics of ad-hoc networks. However due to the dynamic road conditions, traffic flow theory concepts, mobility constraints, human behaviours and vehicular characteristics VANET exhibits different dynamics. These factors have strong influences on the VANET architecture from physical to application layers. This highlights different areas of interest in VANET for researchers to investigate. This study aims to capture the impact of traffic flow theory constraints on the vehicular density under the heterogeneous traffic flow on the road. The microscopic and macroscopic characteristics of vehicles moving on the roads are utilized for the improvement of VANET connectivity dynamics.

Analysis of roadway capacity for heterogeneous traffic flows considering the degree of trust of drivers of HVs in CAVs

Being the predominant air interface of next-generation wireless standards, orthogonal frequency division multiple access (OFDMA) is well known for its flexibility in allocating subcarriers to different mobile users according to their different fast channel variations. Numerous research studies have demonstrated that OFDMA can bring substantial capacity gain when the subcarriers are optimally allocated. Nonetheless, practical systems can hardly afford optimal subcarrier allocation, because frequent re-optimization performed at the same timescale as fast fading variation would lead to excessively high computational and signaling costs. As a result, most practical systems settle for low-complexity schemes that operate far from the optimum, thus making them unable to enjoy the large capacity gain predicted by theoretical studies. To address this problem, we propose a novel alternative, termed the slow adaptive OFDMA, to drastically reduce the computational and signaling costs. The proposed scheme adapts subcarrier allocation at a much slower timescale than that of channel fading variation, yet achieves similar system capacity and quality of service (QoS) levels as the optimal fast adaptive OFDMA. Moreover, it possesses several attractive features. First, neither prediction of channel state information nor specification of channel fading distribution is needed for subcarrier allocation. As such, the algorithm is robust against any mismatch between actual channel state/distributional information and the one assumed. Secondly, although the optimization problem arising from our proposed scheme is non-convex in general, based on recent advances in chance-constrained optimization, we show that it can be approximated by a certain linear program with provable performance guarantees. In particular, we only need to handle an optimization problem that has the same structure as the fast adaptive OFDMA problem, yet we are able to enjoy lower computational and signaling costs. Last but not the least, instead of relying on standard but abstract linear program solvers such as the interior-point method to solve the aforementioned linear program, we can exploit its special structure and design a provably efficient algorithm for it. The proposed algorithm not only has a transparent engineering interpretation but is also easy to implement at the base stations of practical systems.

Suppose there is known the set of points visited by a transient random walk on the real line, but that there is no information concerning the order in which these points are visited. Such a set of points may aptly be called a random walk point process (RWPP), and the object of this paper is to study the class of such processes. This class arises as a generalization of certain one-dimensional clustering processes, and while this is how one of us (D.J.D.) originally came to consider them, it is not the only reason for persevering in this study. Like renewal processes, which are a special sub-class of RWPP's, any random walk point process can be specified by means of the step distribution of the underlying random walk. On the other hand our study does not show whether or not the converse question of determining the step distribution from the RWPP is always feasible. The more demanding question of determining the random walk itself from the RWPP is obviously possible only for very special step distributions. Those results which we obtain below in closed form appear to depend on assuming that at least one tail of the step distribution is exponential. However such results have immediate relevance to the problem of inferring the step distribution from the point process. In the simplest case considered (both tails exponential) we are led to a new model for a stationary point process on the real line that is typically highly over-dispersed. And a final raison d'etre for our study is to exhibit connections with other stochastic processes, notably Poisson cluster processes and, perhaps surprisingly, Markov branching processes and birth and death processes. In Section 2 we introduce our notation and quote and discuss results needed in the sequel from the theory of stationary point processes and the theory of random walks. Integral equations for the one-dimensional counting distribution of the RWPP are written down in Section 3, and their solution is derived when the step distribution has a double exponential form. In Section 4 the second order counting properties are considered and an explicit solution for the second order intensity is derived for the double exponential case. The inter-point properties of the process are considered in Section 5, explicit results being obtained when the dominant tail of the step distribution is exponential. The connection with birth and death processes is shown in that Section, and in the concluding Section 6, the connections with Poisson cluster processes and Markov branching processes are mentioned.

This paper proposes a computer simulation model of a heterogeneous traffic flow which consists of personal and public transport i.e., buses. The road topology is multi-lane and allows a personal vehicle to change lanes. The time evolution of the system is based on Nagel-Schreckenberg cellular automata model. This work illustrates the impact of the location of bus stops on bus traffic characteristics. The new definition of free flow for buses is given. Simulations have shown that the incorporation of buses in a mixed traffic flow has a positive impact on traffic flow. An increase in the number of buses leads to an increase in the average speed of personal cars. However, the average speed of all vehicles has a maximum at a certain ratio between passengers of buses and personal cars. Since the position of this maximum is not the same as for individual types of agents (buses or personal vehicles) this allows one to introduce the social dilemma.