Queue Length Research Articles

Study of Urban Arterial Road Off-Ramp Configuration in Highway Municipal Reconstruction

To reduce traffic congestion and improve the overall traffic capacity of roads, the municipal reconstruction of arterial roads from high-grade highways often involves setting up auxiliary roads on both sides of the road. This paper analyzes the existing methods of determining the configuration of urban arterial road off-ramps and proposes a novel design method, includes adding a “waiting for merging” section. Based on the traffic flow characteristics of the main roads, auxiliary roads, as well as off-ramps, second-stage deceleration theory and the insertable gap theory are applied. Considering the worst-case of diverted vehicles, a calculation model for the length of the urban arterial road off-ramps is proposed and utilized to calculate the advisory values for each segment of the off-ramps. Taking the reconstruction of an expressway in Hubei Province, China, as a case study, Vissim traffic simulation software was used to compare the proposed method with the traditional design method under four different traffic volumes. The results show that the proposed design method greatly improves the overall traffic capacity of roads compared with the traditional method, with a reduction of approximately 40% and 60% in delay time and queue length for the overall traffic, respectively. Furthermore, the research results can provide direct and effective design solutions and a basis for decision-making for setting the length of main and auxiliary road off-ramps.

Modeling and evaluating the impact of variable bus lane on isolated signal intersection performance

Dedicated Bus Lane (DBL) is a typical strategy to ensure priority for public transportation. However, when the frequency of bus departures is low, the DBL often remains vacant, reducing the efficiency of traffic utilization. Variable bus lane (VBL) strategy allows for the provision of service to social vehicles in specific scenarios, aiming to alleviate traffic congestion and improve emission efficiency at intersections. To analyze the impact of this strategy on dynamic queuing behavior and traffic efficiency at an isolated intersection, this paper proposes a multidimensional stochastic queuing model. The model incorporates various factors such as traffic demand, signal timing, bus arrival time, and the length of the variable area at intersections. By examining the steady-state distribution of queue length and calculating performance indicators, the effectiveness of VBL in improving intersection performance is evaluated. Numerical simulations have demonstrated that the proposed model accurately describes the vehicle queuing process at intersections under different conditions. Theoretical analysis confirms that the implementation of VBL strategy can effectively improve traffic efficiency at intersections and minimize the queue length of vehicles.

Optimizing the Timeliness of Hybrid OFDMA-NOMA Sensor Networks with Stability Constraints

In this paper, we analyze the timeliness of a multi-user system in terms of the age of information (AoI) and the corresponding stability region in which the packet rates of users lead to finite queue lengths. Specifically, we consider a hybrid OFDMA-NOMA system where the users are partitioned into several groups. While users in each group share the same resource block using non-orthogonal multiple access (NOMA), different groups access the fading channel using orthogonal frequency division multiple access (OFDMA). For this system, we consider three decoding schemes at the service terminals: interfering decoding, which treats signals from other users as interference; serial interference cancellation, which removes signals from other users once they have been decoded; and the enhanced SIC strategy, where the receiver attempts to decode for another user if decoding for a previous user fails. We present the average AoI for each of the three decoding schemes in closed form. Under the constraint of the stable region, we find the minimum AoI of each decoding scheme efficiently. The numerical results show that by optionally choosing the decoding scheme and transmission rate, the hybrid OFDMA-NOMA outperforms conventional OFDMA in terms of both system timeliness and stability.

Modeling and optimizing an AMS with DV policy, waiting servers, impatient customers, and failures: A queueing analysis

In this paper, we analyze an automated manufacturing system modeled as a queueing system with multiple servers, differentiated vacation (DV) policy, customer impatience, and server failures. We consider the waiting servers policy, where the servers wait for a random duration before leaving for a vacation once the system gets empty. Upon their return, if no customers are waiting, the servers may leave for a second type-2 vacation of shorter duration. The system may experience breakdowns and require immediate repair. During the repair period, customers are served at a lower rate, and they become impatient during busy, vacation, and repair periods, abandoning the queue if their timer expires. Further, based on the queue length, arriving customers may either join the system or balk with some probability. We use the matrix analytic method to derive the steady-state probability of the system and several performance measures. Moreover, we illustrate the effect of different system parameters on various performance measures. Additionally, we develop a cost model and optimize the system capacity, number of servers, and service rates such that cost per unit time is minimized. Finally, we analyze the impact of system parameters on the cost through numerical examples.

Resource management for computational offload in MEC networks with energy harvesting and relay assistance

In mobile edge computing (MEC) networks, the integrated application of energy harvesting (EH) and relay cooperation is a promising technology, which ensures the real-time performance of the system and computing power supply. Relay and EH cooperation also expand communication range and extend the battery life of energy-constrained devices. However, in wireless powered and relay-assisted MEC networks, it is challenging to jointly dispatch energy, and computing resources to coordinate heterogeneous performance requirements. To fill this gap, this paper examines the fundamental compromise between utility energy efficiency (UEE) and stable queue length in wireless powered and relay-assisted MEC network systems, and the amount of data transferred for each unit of energy is called UEE. The data queue and energy queue models are introduced and the constraints of stability of two queues in long term are included in the formulated problem. To tackle the fractional and nonconvex optimization problems, the Dinkelsbach method is utilized. Since optimization problems change from time to time and the long-term averaging queue stability is considered, the Lyapunov optimization theory is introduced to convert the non-convex problems into the solvable one. An online resource offloading allocation algorithm is proposed to determine the solution. In addition, the algorithm implements the control parameter V to achieve the compromise between UEE and stable queue length, while the impact of various parameters are also revealed on system performance.

Matched queues with matching batch pair [formula omitted]

In this paper, we develop the matrix-analytic method to discuss an interesting but challenging bilateral stochastic matching problem: A matched queue with matching batch pair (m,n) and two types of impatient customers, where the two types of customers arrive according to two independent Poisson processes. Once m A-customers and n B-customers are matched as a group, the m+n customers immediately leave the system. We show that this matched queue can be expressed as a novel bidirectional level-dependent quasi-birth-and-death (QBD) process whose analysis has its own interests, and specifically, computing the maximal non-positive inverse matrices of bidirectional infinite sizes by using the RG-factorizations. Based on this, we can provide an effective matrix-analytic method to deal with this matched queue, including the system stability, the average stationary queue lengths, the average sojourn times, and the departure process. We believe that the methodology and results developed in this paper can be applicable to studying more general matched queueing systems, which are widely encountered in many practical areas.

Multiple Table Models Based on Queuing Theory for Firefighting Traffic Problems

With the development of global urbanization, urban planning has been a hot spot of most concern. Since the traditional urban fire station setting method has been gradually unable to meet the emergency needs of a city. In this paper, a series of methods are developed to achieve the best balance between economic expenditure and reliability. According to the heat maps about emergency calls in a city in recent years, different types of alarm phones have obvious regional distribution characteristics. Inspired by the Queuing Theory algorithm, we abstract this complex problem into a parallel multi-server waiting queuing model to find each average queue length of three kinds of alarm calls and success in converting the multiplicity problem into solving the vehicle number and location problems respectively. Based on this planning problem, new combinations with different numbers of vehicles can be gotten. Then based on the assignment model, the optimal deployment plan can also be different with different numbers and geographical locations of the three kinds of stations. Our method significantly improves the firefighting traffic problems and can be applied in the actual situation.

Optimal information disclosure in a production-inventory queueing system

This study considers a production-inventory queueing system, where customers decide whether to wait for the item or leave without a purchase if a stockout occurs. The system manager determines the joint pricing and inventory control policy. In addition, the system manager can choose whether or not to provide information about the system state to arriving customers. Our strategic production-inventory queueing system includes the observable, unobservable, and almost unobservable systems, which are obtained by appropriately choosing the information disclosure policy by the system manager. In this study, we find the optimal information disclosure policy, as well as the optimal price and the optimal inventory control policy for the profit maximization and social welfare maximization. Under the optimal policy, the system manager should disclose the system state if and only if the queue length exceeds a certain threshold.

Management Policy in Urban Rail Transit System: Trade-Off between Social Distancing and Service Efficiency Using Simulation in the Post-Epidemic Era

The past COVID-19 pandemic introduced the world to the necessity of dealing with the trade-off between minimizing probability of contagion, and providing people with services they need. This trade-off stipulates that a large person-to-person distance will reduce contagion probability, but will render service inefficient, and vice versa. This work focuses on the urban rail transit (URT) hub, as an example of a busy passenger area, from which we can derive an optimal preparedness policy to use during the pandemic time of any coronaviruses. We use simulation methodology, based on the classical social force model, to represent behaviors and characteristics of pedestrians. Passenger flow movement process is a mechanism we explore to figure out how the epidemic management policy and pedestrian psychological-related behaviors interact with the URT system. The systems’ complexity regarding contagion-prevention distances are tested over a few scenarios: before/after the outbreak, and for different person-to-person distances demonstrating different crowd levels. A case study of Xinjiekou Station, Nanjing URT, China, enables assessment of passenger management policy with person-to-person distances of 0.5 m, 1.0 m and 2.0 m. Multi-scenario performance illustrates the trade-off in dynamic between the efficiency of pedestrians’ walking behaviors and the distancing needs for preventing coronaviruses transmission. The results show that queuing length with social distancing of 1.0 m and 2.0 m is increased by 4.17% and 21.22%. The average delays in boarding are 14.1 s and 22.5 s for 1.0 m and 2.0 m, which leads to 15.29% and 22.39% increases, respectively, in comparison with ordinary social distancing of about 0.5 m.

Operation Management of Grocery Retailer in the UK: A Case of Tesco

Tesco is the biggest grocery retailer in the UK focused on food products selling and some non-food services such as clothing, home appliances, financial, etc. Over the last five years, Tesco has had a healthy growth in revenues and net profits, which reflects the success of Tesco's operations management. The purpose of the study is to explore the successful operation management of Tesco company, which can bring some inspiration for other companies to grow. This paper mainly includes operation design (products, service, process, and layout design), resource planning and control, and capacity management. In terms of operation design, Tesco launched a new baby food range with absolutely no salt or sugar, no artificial colors or spices to protect children’s health; Clubcard, Scan as you go, staff visibility, and Online shopping & Delivery adopted for giving customers’ more benefits and convenience; Tesco belongs to mass service process, adopts tracking technology named thermal imaging cameras to monitor queue lengths, reduce customer waiting time, increasing service speed and flexibility. Tesco mainly uses a functional layout, keeps the layout of its stores the same to allow customers to quickly find the goods, saving shopping time, and designed the display locations of its products to increase its revenue. For Planning and control, Tesco belongs to ‘Produce to stock’, which shows the characteristics of a high volume of products, which can save customers’ time, because the products have been produced in advance for customers to buy. Regarding Capacity management, Tesco adopted a mixed strategy which is chase demand and demand management to manage mismatches. Effective operation management strategies have made outstanding contributions to the realization of Tesco's business objectives, profit increase, and long-term development.

Dynamic departure pushback control at airports: Part A—Linear penalty‐based algorithms and policies

AbstractAirport surface congestion can lead to significantly long taxi‐out times, thus resulting in increased fuel‐burn costs as well as excessive emissions of greenhouse gases. To curtail this undesirable syndrome, in this article, we propose a new penalty‐based dynamic departure pushback control (PDPC) strategy, which employs a linear penalty function dependent not only on the taxiway queue limit but also on the current queue length to ration the pushback frequency at airports, and trades taxiway queueing times with gate‐hold delays to minimize the total operational cost (fuel‐burn and gate‐hold costs). Using data from Beijing Capital International (PEK) airport, four different departure pushback control policies, namely: (i) no‐control (baseline case); (ii) traditional ‐control; (iii) PDPC with a constant taxiway limit; and (iv) PDPC with varying taxiway limits; are compared. Detailed Monte Carlo simulations, which showcase the sensitivity of the total cost function to various problem parameters are presented, and our results indicate that deploying the PDPC policy results in a 42% reduction in total operational costs and a 68% reduction in fuel‐burn (kg) as compared to the baseline case. To analytically reinforce these simulation results, an iterative Markov chain‐based optimization algorithm is also developed to estimate the optimal values of the pushback rate and taxiway queue limit that minimize the total cost function. Such an analytical framework is very useful in the absence of reliable airport data as it only requires estimates of the historical pushback request rates and service times at the taxiway, while yet retaining the capability to closely mirror the simulation results. Our Monte Carlo simulations as well as the Markov chain optimization model validate the strength and impact of the proposed PDPC policy, and demonstrate its practical efficacy in reducing airport surface congestion when applied using data from PEK airport.

Queues with resetting: a perspective

Abstract Performance modeling is a key issue in queuing theory and operation research. It is well-known that the length of a queue that awaits service or the time spent by a job in a queue depends not only on the service rate, but also crucially on the fluctuations in service time. The larger the fluctuations, the longer the delay becomes and hence, this is a major hindrance for the queue to operate efficiently. Various strategies have been adapted to prevent this drawback. In this perspective, we investigate the effects of one such novel strategy namely resetting or restart, an emerging concept in statistical physics and stochastic complex process, that was recently introduced to mitigate fluctuations-induced delays in queues. In particular, we show that a service resetting mechanism accompanied with an overhead time can remarkably shorten the average queue lengths and waiting times. We examine various resetting strategies and further shed light on the intricate role of the overhead times to the queuing performance. Our analysis opens up future avenues in operation research where resetting-based strategies can be universally promising.

A Stochastic Methodology for EV Fast-Charging Load Curve Estimation Considering the Highway Traffic and User Behavior

The theoretical impact of the electric vehicle (EV) market share growth has been widely discussed with regards to technical and socioeconomic aspects in recent years. However, the prospection of EV scenarios is a challenge, and the difficulty increases with the granularity of the study and the set of variables affected by user behavior and regional aspects. Moreover, the lack of a robust database to estimate fast-charging stations’ load curves, for example, affects the quality of planning, allocation, or grid impact studies. When this problem is evaluated on highways, the challenge increases due to the reduced number of trips related to the reduced number of charger units installed and the limited EVs range, which influence user anxiety. This paper presents a methodology to estimate the highway fast-charging station operation condition, considering regional and EV user aspects. The process is based in a block of traffic simulation, considering the traffic information and highway patterns composing the matrix solution model. Also, the output block estimates charging stations’ operational conditions, considering infrastructure scenarios and simulated traffic. A Monte Carlo simulation is presented to model entrance rates and charging times, considering the PDF of stochastic inputs. The results are shown for the aspects of load curve and queue length for one case study, and a sensibility study was conducted to evaluate the impact of model inputs.

Equilibrium balking strategies in unobservable queues with multiple vacations and an optional service

This paper examines equilibrium mixed strategies in unobservable Markovian queues featuring a second optional service with server vacations, where arriving customers may choose to join or balk the system. All customers arriving at the system receive the essential service, and some customers opt for the second service after the first service has been completed. Once all customers in the system have been served, the server takes the first of multiple vacations. If no customers are waiting upon from the vacation, then the server takes another vacation. In unobservable queues, arriving customers cannot know the queue length; however, the information pertaining to the server state may be available. By examining unobservable queues (fully unobservable and almost unobservable cases), it is possible to formulate an equilibrium joining strategy as well as the socially optimal probability of joining a fully unobservable queue. This paper also presents numerical examples illustrating how system parameters affect mixed equilibrium and socially optimal balking strategies.

Passenger flow bottleneck decongestion in subway stations: a simulation study

The impact of large passenger flow during peak hours causes serious congestion in subway stations, and passenger flow bottlenecks appear in many places, which affects travel efficiency and safety. How to eliminate the bottlenecks is an urgent problem to be solved. In this paper, we first analyze the causes and regions of bottlenecks, and we propose three decongestion solutions: (a) moving the security check machines from the station hall to the entrance channel; (b) adding isolation belts in front of the area of escalators; and (c) separating opposite passengers flow by using isolation belts. We conduct a case study on Guomao Station, Beijing, China to verify the effectiveness of the solutions. Specifically, we establish a microscopic model to simulate the passenger flow in a subway station, and the simulation results show that decongestion solutions can reduce the queueing length of security bottleneck by more than 30%, while decreasing the passenger density in non-paying areas of the station hall by more than 50%. The decongestion solutions proposed in this paper can eliminate the bottlenecks in subway stations effectively and practicably.

ВЛИЯНИЕ ОСТАТОЧНОЙ АВТОТРАНСПОРТНОЙ ОЧЕРЕДИ НА ПРОЦЕСС ДВИЖЕНИЯ АВТОМОБИЛЕЙ НА ГОРОДСКИХ РЕГУЛИРУЕМЫХ ПЕРЕСЕЧЕНИЯХ

This paper continues to investigate methods for separating turning vehicle flows at urban light-controlled intersections. The authors carried out mathematical modelling of the process of left-turn transport queue formation on the basis of existing dependencies, as well as the indicator of "residual motor transport queue". After studying the processes and existing mathematical models describing the formation of a vehicle queue at a light-controlled intersection, as well as modelling of the process depending on the "residual vehicle queue" parameter, we made an assumption about the type of mathematical model describing the process. To confirm the assumptions, we carried out studies of urban light-controlled intersections in Russian cities. Based on passive experiment, it was found that the value of the residual vehicle queue obeyed the exponential distribution law of a random variable. The length of the vehicle queue formed at the intersection depends on the residual vehicle queue parameter. A linear mathematical model describes the dependence. It was found that for an average urban regulated intersection, the required rotary-accumulative lane capacity was 9 and 5 automobiles with loading factor more than and less than 1, respectively. When the residual vehicle queue increases from 5 to 50 vehicles, the size of the vehicle queue at the regulated intersection in the left-turn direction increases in 5 times. The results of the study can be used to adjust the modes of operation of urban light-controlled intersections, as well as to estimate the length of turn-accumulative lanes.

Simple and Explicit Bounds for Multiserver Queues with 11−ρ Scaling

We consider the first-come-first-serve (FCFS) [Formula: see text] queue and prove the first simple and explicit bounds that scale as [Formula: see text] under only the assumption that interarrival times have finite second moment, and service times have finite [Formula: see text] moment for some [Formula: see text]. Here, ρ denotes the corresponding traffic intensity. Conceptually, our results can be viewed as a multiserver analogue of Kingman’s bound. Our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay. The strength of our bounds (e.g., in the form of tail decay rate) is a function of how many moments of the service distribution are assumed finite. Our bounds scale gracefully, even when the number of servers grows large and the traffic intensity converges to unity simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale better than [Formula: see text] in certain asymptotic regimes. In these same asymptotic regimes, we also prove bounds for the tail of the steady-state number in service. Our main proofs proceed by explicitly analyzing the bounding process that arises in the stochastic comparison bounds of Gamarnik and Goldberg for multiserver queues. Along the way, we derive several novel results for suprema of random walks and pooled renewal processes, which may be of independent interest. We also prove several additional bounds using drift arguments (which have much smaller prefactors) and point out a conjecture that would imply further related bounds and generalizations. We also show that when all moments of the service distribution are finite and satisfy a mild growth rate assumption, our bounds can be strengthened to yield explicit tail estimates decaying as [Formula: see text], with [Formula: see text], depending on the growth rate of these moments. Funding: Financial support from the National Science Foundation [Grant 1333457] is gratefully acknowledged. Supplemental Material: The supplemental appendix is available at https://doi.org/10.1287/moor.2022.0131 .

Lane Reduction and Queue Length Relationship on Arterial and Collector Roads

Geometric diversity of roads for an example is the narrowing of road segments. The purpose of this research is to determine whether lane reduction leads to significant queue lengths, observe the behaviour of drivers on those road segments, and compare the actual queue length to the queue length generated by PTV Vissim. The data used in this study consists of direct observations during peak hours in the morning, afternoon, and evening, along with simulations using PTV Vissim. The queue results obtained from PTV Vissim were validated using two types of tests. The research findings indicate a significant relationship between queue length and lane reduction during peak hours on workdays. However, during the evening peak hours on weekends, the queue length is not significantly affected by lane reduction. As a potential solution, widening each road segment in PTV Vissim was tested, which increased road capacity and slightly reduced the queues that occurred.

Performance Analysis of Unsignalized Intersection Using PTV VISSIM Software Modeling (Case Study of Sakra 4-way intersection, East Lombok)

Sakra 4-way intersection is one of the unsignalled intersections in East Lombok. At certain times of the day, there are frequent traffic jams and queues of moving vehicles at this intersection because the area surrounding the intersection is a commercial area, as evidenced by the presence of settlements, markets, mosques, village heads’ offices, shops, and other shopping centers. This research aims to determine the movement of traffic flow at the 4-way Sakra intersections in East Lombok using Vissim software modeling. Data collection was obtained from literature studies and direct surveys at the research site. Direct questionnaires at the research location and literature reviews were used to collect data. Using PTV VISSIM software modeling, the intersection of Sakra East Lombok was modeled under the current conditions on Monday and Sunday. The results showed that values for Monday were Queue Length (Qlen) 34.77 m and Tundaan (VehDelay) 19.95 sec / skr. The value of Tundaan (VehDelay) on Sundays is 16.68 sec/skr, the value of Queue Length (Qlen) on Sundays is 23.76 m, and the service level of the junction (LOS) on Monday and Sunday is C (not good). And for the movement of vehicle flow passing at intersection 4 Sakra East Lombok, which indicates the density of vehicles traffic flow is moderate, internal traffic barriers begin to affect speed and drivers still have adequate discretion over their speed and the lane they use on the road.

Downlink Scheduler for Delay Guaranteed Services Using Deep Reinforcement Learning

In this paper, we propose a novel scheduling scheme to guarantee per-packet delay in single-hop wireless networks for delay-critical applications. We consider several classes of packets with different delay requirements, where high-class packets yield high utility after successful transmission. Considering the correla-tionship of delays among competing packets, we apply a delay-laxity concept and introduce a new output gain function for scheduling decisions. Particularly, the selection of a packet takes into account not only its output gain but also the delay-laxity of other packets. In this context, we formulate a multi-objective optimization problem aiming to minimize the average queue length while maximizing the average output gain under the constraint of guaranteeing per-packet delay. However, due to the uncertainty in the environment (e.g., time-varying channel conditions and random packet arrivals), it is difficult and often impractical to solve this problem using traditional optimization techniques. We develop a deep reinforcement learning (DRL)-based framework to solve it. Specifically, we decompose the original optimization problem into a set of scalar optimization subproblems and model each of them as a partially observable Markov Decision Process (POMDP). We then resort to a Double Deep Q Network (DDQN)-based algorithm to learn an optimal scheduling policy for each subproblem, which can overcome the large-scale state space and reduce Q-value overestimation. Simulation results show that our proposed DDQN-based algorithm outperforms the conventional Q-learning algorithm in terms of reward and learning speed. In addition, our proposed scheduling scheme can achieve significant reductions in average delay and delay outage drop rate compared to other benchmark schemes.