Queue Length Research Articles

Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage

This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and proceed directly to the second stage for clearing service. The second stage has N service seats. All customers currently in the second stage are served simultaneously (i.e., clearing service). Once there are N customers in the second stage, the first stage will be blocked, and newly arriving priority customers will balk and leave without joining. We first formulate a two-dimensional Markov chain to analyze this queuing system and derive the stability condition. Subsequently, the stationary distribution of the system is derived using the matrix-analytic method and spectral expansion technique. Furthermore, analytical expressions for the mean queue length, mean sojourn time, and other performance measures are presented. Finally, some numerical examples are provided to illustrate the effects of various parameters, offering valuable insights for designing such two-stage tandem queuing systems.

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.

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.

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.

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.

Evaluasi Tingkat Pelayanan Pada Persimpangan Jalan Sisimangaraja Jalan-Alfalah Simpang Bersinyal

Intersections are the most important factor in determining the capacity and travel time on a road section. The development of transportation in the city of Medan has had an impact on increasing the movement of people, goods and services. This also greatly demands increased transportation facilities and infrastructure in the city of Medan. The increase in the number of vehicles that is not balanced with infrastructure will cause conflicts on roads, especially at the intersection of three Jalan-Sisingamangaraja Jalan .Alfalah To anticipate This requires further study or research. In this research, analysis of intersection performance calculations uses the 1997 (MKJI) guidelines. The survey was carried out on Monday 14 August 2023 to 20 August 2023. Then the peak hours were searched for the volume of vehicle flow crossing the three intersections. Then create a new cycle time for the intersection. The results of the analysis in this research, from survey results, by looking for new cycle times to reduce queue lengths and delays (Delay). The new cycle time obtained to reduce queue lengths and delays for the three intersections on the northern approach is 859.927 seconds/intersection. Then at the southern approach with a total delay of 2,056,013 sec/intersection and at the western approach with a delay of 307,555 sec/intersection. For existing conditions the queue length (QL) is 1321 meters for the northern approach, (QL) 1372 meters for the southern approach and (QL) 1321 meters for the west

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.

Stochastic queue profile estimation using license plate recognition data

Queue profile has garnered significant attention for its precise description of queue formation and dissipation at signalized intersections. License Plate Recognition (LPR) systems, recording full-sample lane-based departure times of individual vehicles, offer an ideal data source for queue profile estimation. Thus, this paper presents a stochastic queue profile estimation method utilizing LPR data. It adopts the classic Input-Output model as a baseline to reconstruct arrival and departure curves using departure information from LPR detectors at successive intersections. A pseudo departure curve is then derived from the distribution of free-flow travel time. The stochastic queue profile is further reconstructed by analyzing the relationship among these curves, accounting for potential lane changes and overtaking behavior. The proposed method is validated through empirical and simulation cases. The empirical case achieves accurate queue length estimation with a Mean Absolute Error (MAE) of 5.38 m, while the simulation case yields precise stochastic queue profiles with an MAE of 5.95 m and an average deviation of 2.40 m for queue length. Sensitivity analysis demonstrates the method's robustness across parameters like demand-to-capacity ratio, miss detection ratio, and overtaking ratio. This work holds promise for real-time signal control optimization and vehicular trajectory reconstruction.

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.

Improving resource allocation in the precisionmedicine Era: a simulation-based approach using R.

The application of personalized medicine in developing countries is a major challenge, especially for those with poor economic status. A critical factor in improving the application of personalized medicine is the efficient allocation of resources. In healthcare systems, optimizing resource allocation without compromising patient care is paramount. This tutorial employs a simulation-based approach to evaluate the efficiency of bed allocation within a hospital setting. Utilizing a patient arrival model with an exponential distribution, we simulated patient trajectories to examine system bottlenecks, particularly focusing on waiting times. Initial simulations painted a scenario of an 'unstable'system, where waiting times and queue lengths surged due to the limited number of available beds. This research offers insights for hospital management on resource optimization leading to improved patient care.

Modeling of traffic at a road crossing and optimization of waiting time of the vehicles

Traffic management is a critical activity, the population is increasing day by day and so the traffic on the road is also increasing. Traffic jams and long waiting queues of vehicles at the road crossing are now part of everyone's life. The traffic lights used at the crossing to regulate the traffic play a vital role in the smooth functioning of traffic movement. At a crossing of four roads, it has been observed that giving an equal amount of green light to all roads is meaningless since the arrival of traffic on different paths is different. Importantly, the arrival rate is responsible for all traffic jams, long queues, and increased waiting time. Therefore, this paper suggests a green light allocation scheme for all paths i depending on the arrival rate of the vehicles. Thus, the allocation of green light will be dynamic. Further, weight is also computed, where more arrival rate means more weight, thereby assigning more time to the green signal. This will help in reducing the long queue length, residual traffic, and long waiting times. On simulating the traffic with the traffic data, the proposed optimized green light allocation scheme to path i reduces the residue traffic to negligible, allowing smooth traffic flow even during peak hours. The work also provides a proficient optimization of the waiting time of vehicles accumulated during the red light. According to the simulation, the maximum time assigned for the green signal during the peak hour of 9:30 AM to 10:00 AM for paths i, where 1≤i≤4 is 39.96, 33.36, 26.64, and 20.04 seconds respectively. Similarly, during the second rush hour of 5:00 PM to 6:00 PM, the simulation assigns a green signal time of 41.4, 37.2, 24.84, and 16.56 seconds for corresponding paths 1–4. Thus, the proposed work suggests an effective traffic management scheme at the four-road crossing.

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.

Micro-Burst Aware ECN in Multi-Queue Data Centers: Algorithm and Implementation

With the development of multi-queue data centers, various efforts have leveraged Explicit Congestion Notification (ECN) to achieve high throughput and low latency for data communication. However, one of the deep-seated problems is that the micro-burst traffic in networks could cause the instantaneous queue length to exceed the ECN threshold, leading to significant mismarkings of ECN. Such mismarkings could further lead to severe network performance degradation. In this paper, we propose Micro-Burst aware ECN (MBECN+) to mitigate this issue. MBECN+ is essentially a novel scheme that decouples ECN threshold setting and ECN marking. First, it finds a more appropriate ECN threshold on a per-queue basis to eliminate the spurious congestion signals caused by micro burst traffic. Second, MBECN+ consists of a double-threshold ECN marking scheme that it marks the packets with ECN in a finer grain. Considering the queue backlog caused by micro-burst traffic, it marks the packets when they are dequeuing, instead of enqueuing. Furthermore, we analyze the feasibility of implementing MBECN+ on commodity layer-3 multi-queue switches. Through testbed experiments and large scale simulations, we demonstrate that MBECN+ can improve the throughput by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 20% and reduce FCT (flow completion time) by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> 40%. The throughput under MBECN+ improves by 1.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim 2.4\times$</tex-math></inline-formula> than DCTCP and 1.26 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim 1.35\times$</tex-math></inline-formula> than ECN*.

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.

Reliable and adaptive computation offload strategy with load and cost coordination for edge computing

There are several important factors to consider in edge computing systems including latency, reliability, power consumption, and queue load. Task replication requires additional energy costs in mobile edge offloading scenarios based on master-slave replication for fault tolerance. Excessive task offloading may lead to a sharp increase in the total energy consumption of the system including replication costs. Conversely, new tasks cannot enter the waiting queue and are lost, resulting in reliability issues. This paper proposes an adaptive task offloading strategy for balancing the edge node queue load and offloading cost (Lyapunov and Differential Evolution based Offloading schedule strategy, LDEO). The LDEO strategy innovatively customizes the Lyapunov drift-plus-penalty function by incorporating replication redundancy offloading costs to establish a balance model between the queue load and offloading cost. The LDEO strategy computes the optimal offloading decisions with dynamic adjustment characteristics by integrating a low-complexity differential evolution method, aiming to find the optimal balance point that minimizes the offloading cost while maintaining reliability performance. The experimental results show that compared with the existing strategies, LDEO strategy effectively reduces the redundancy of fault tolerance cost and the waiting time under the condition of ensuring that the task will not be discarded over time. It stabilizes the queue length in a reasonable range, controls the waiting time and loss rate of tasks, reduces the extra energy consumption paid by replication redundancy, and effectively realizes the optimal balance under multiple conditions.

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.

Single server queueing model with Poisson arrival and gamma service time distribution

Queueing theory is pivotal in understanding waiting lines and their pervasive role in everyday life. Its profound application spans across diverse sectors, including computer programming networks, healthcare, transportation, and so on. Researchers have applied many statistical distributions in analyzing queueing data. This article focuses on the analysis of a single server queueing system with Poisson input and service times distributed according to a two-parameter gamma distribution. The study elaborates on the construction and estimation of key queueing properties such as steady state equations, average number of customers in the system, average queue length, expected size of the non-empty queue, distribution of waiting time, average waiting time in the system, and average waiting time in the queue of the M/Gamma/1 queueing model using the two-parameter gamma distribution. Keywords: Gamma distribution; Poisson; service; single server; queuing model.

Simple analytical models for estimating the queue lengths from probe vehicles at traffic signals: A combinatorial approach for nonparametric models

This study develops a combinatorial approach for nonparametric short-term queue length estimation in terms of cycle-by-cycle partially observed queues from probe vehicles (PV). The method does not assume random arrivals and does not assume any primary parameters or estimation of any parameters but uses simple algebraic expressions that only depend on signal timing. For an approach lane at a traffic intersection, the conditional queue lengths given probe vehicle location, count, time, and analysis interval (e.g., at the end of the red signal phase) are represented by a Negative Hypergeometric distribution. The simple analytical estimators obtained are compared with parametric methods from literature and highway capacity manual methods using field test data and simulation data involving probe vehicles. The analysis indicates that the nonparametric models presented in this paper match the accuracy of the parametric ones used in the field test and simulated data for estimating queue lengths.

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 &amp; 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.