Queue Length Research Articles

Optimal resource management for multi-access edge computing without using cross-layer communication

We consider a Multi-access Edge Computing (MEC) system with a set of users, a base station (BS) with an attached MEC server, and a cloud server. The users can serve the service requests locally or can offload them to the BS which in turn can serve a subset of the offloaded requests at the MEC and can forward the requests to the cloud server. The user devices and the MEC server can be dynamically configured to serve different classes of services. The service requests offloaded to the BS incur offloading costs and those forwarded to the cloud incur additional costs; the costs could represent service charges or delays. Aggregate cost minimization subject to stability warrants optimal service scheduling and offloading at the users and the MEC server, at their application layers, and optimal uplink packet scheduling at the users’ MAC layers. Classical back-pressure (BP) based solutions entail cross-layer message exchange, and hence are not viable. We propose virtual queue-based drift-plus-penalty algorithms that are throughput optimal, and achieve the optimal delay arbitrarily closely but do not require cross-layer communication. We first consider an MEC system without local computation, and subsequently, extend our framework to incorporate local computation also. We demonstrate that the proposed algorithms offer almost the same performance as BP based algorithms. These algorithms contain tuneable parameters that offer a trade off between queue lengths at the users and the BS and the offloading costs.

ANALISIS KINERJA SIMPANG BERSINYAL TANAH AJI – KOTA MATARAM DENGAN SOFTWARE PTV VISSIM

The Tanah Aji signalized intersection is one of the crossroads in Mataram City that links Jalan Sriwijaya with Jalan Majapahit and Jalan Airlangga with Jalan Gajah Mada . The Department of Transportation (DISHUB) officially reactivated the Tanah Aji signalized intersection (APILL) on Wednesday, December 14 2022. The aim of this research is to determine the performance of the Tanah Aji signalized intersection in Mataram City in its existing condition and provide solutions to improve performance. the signalized intersection. Primary and secondary data collecting was part of the research methodology. Secondary data is in the form of location map data obtained from Google Earth, traffic light cycles, and video recordings of intersections from the Mataram City Transportation Department (DISHUB). Next, analytical modeling of existing conditions is carried out. The results obtained show that the existing conditions produce a level of service E. The solution by modeling the flyover on Jalan Majapahit and Jalan Sriwijaya produces a level of service C. Comparison of the performance of the Tanah Aji intersection, Mataram City in the existing condition and the flyover solution from the results of the Vissim software analysis, is the existing condition, it was found that the length of the vehicle queue was 92,077 m Jl. Srivijaya; 231,275 m Jl. Gajah Mada; 177,973 m Jl. Majapahit and 157,783 m Jl. Airlangga. The results of the flyover solution analysis showed that the vehicle queue length was 54.09 m Jl. Srivijaya; 201.15 m Jl. Gajah Mada; 76.95 m Jl. Majapahit and 107.71 m Jl. Airlangga

A finite state Markovian queue to let in impatient customers only during K-vacations

We investigate a matrix analysis study for a single-server Markovian queue with finite capacity, i.e. an M/M/1/N queue, where the single server can go for a maximum, i.e. a K number of consecutive vacation periods. During these vacation periods of the server, every customer becomes impatient and leaves the queues. If the server detects that the system is idle during service startup, the server rests. If the vacation server finds a customer after the vacation ends, the server immediately returns to serve the customer. Otherwise, the server takes consecutive vacations until the server takes a maximum number of vacation periods, e.g. K, after which the server is idle and waits to serve the next arrival. During vacation, customers often lose patience and opt for scheduled deadlines independently. If the customer’s service is not terminated before the customer’s timer expires, the customer is removed from the queue and will not return. Matrix analysis provides a computational form for a balanced queue length distribution and several other performance metrics. We design a ‘no-loss; no-profit cost model’ to determine the appropriate value for the maximum value of K consecutive vacation periods and provide a solution with a numerical illustration.

Explicit results for the distributions of queue lengths for a non-preemptive two-level priority queue

Explicit results for the distributions of queue lengths for a non-preemptive two-level priority queue

Optimizing traffic signal control for continuous‐flow intersections: Benchmarking against a state‐of‐practice model

AbstractContinuous‐flow intersections (CFI), also known as displaced left‐turn (DLT) intersections, aim to improve the efficiency and safety of traffic junctions. A CFI introduces additional cross‐over intersections upstream of the main intersection to split the left‐turn flow from the through movement before it arrives at the main intersection which decreases the number of conflict points between left‐turn and through movements. This study develops and examine a two‐step optimization model for CFI traffic signal control design and demonstrates its performance across more than 300 different travel demand scenarios. The proposed model is compared against a state‐of‐practice CFI signal control model as a benchmark. Microsimulation results suggest that the proposed model reduces average delay by 17% and average queue length by 32% for a full CFI compared with the benchmark signal control model.

A Cooperative Optimization Model for Variable Approach Lanes at Signaled Intersections Based on Real-Time Flow.

To resolve the congestion caused by imbalanced traffic at intersections, this paper establishes a model of the average delay deviation with the minimization of the average delay in the approach as the optimization objective. Then, the signal control scheme is further optimized based on the variable approach lanes setting. First, we investigate the threshold conditions for setting the VALs under different flows in a single approach direction. The results show that when the ratio of left-turn traffic exceeds the threshold range of 0.20~0.28, the function of the VALs needs to be changed from straight to left-turn. Then, based on the improved Webster's formula, an optimal timing method that aims at minimizing the average vehicle delay, minimizing the queue length, and maximizing the capacity, is proposed. Finally, taking the actual Huangke intersection in the Hefei demonstration area as an example, three schemes are compared and analyzed in the case of a VAL at the intersection. The results show that under the cooperative optimization scheme proposed in this paper, the travel time and the efficiency of the intersection could be reduced by 18.7% and 9.9%, respectively, when compared with the original and Webster's schemes.

Data-driven bottleneck detection on Tehran highways

In metropolitan areas, traffic congestion has become a prevalent challenge due to rapid urbanization and increased vehicle usage, adversely impacting mobility, productivity, and quality of life. Identifying and mitigating persistent traffic bottlenecks is crucial for developing efficient transportation systems and guiding infrastructure planning decisions. This research proposes an innovative data-driven methodology to pinpoint recurrent traffic bottlenecks in Tehran's extensive highway network, addressing the limitations of traditional traffic monitoring methods. Through data mining and image processing techniques applied to 16 months of traffic flow maps from Google Maps, diverse information is extracted, including traffic nodes, congestion hotspots, and locations with the longest queue lengths. The image processing approach involves color-based segmentation, pixel-level analysis, and machine learning algorithms to determine congestion levels across the highway network. The identified bottlenecks are validated against ground truth data from CCTV cameras, demonstrating a remarkable 92 % correlation for key identified points. The proposed approach leverages the power of advanced analytics to comprehensively analyze all major highways, including areas lacking CCTV infrastructure. The robust validation process reinforces the reliability of this data-driven solution in capturing real-world traffic dynamics. As urban mobility challenges escalate globally, the integration of diverse data sources and cutting-edge techniques will be instrumental in guiding intelligent transportation planning and policy decisions.

Market Penetration Rate Optimization for Mobility Benefits of Connected Vehicles: A Bayesian Optimization Approach

The advancements of connected vehicle (CV) technologies promise significant safety, mobility, and environmental benefits for future transportation systems. These benefits will largely rely on the market penetration rate (MPR) of CVs and connected infrastructure. However, higher MPR is not guaranteed to result in greater benefits in a transportation system in some cases even if we do not consider the deployment cost of CVs. Therefore, understanding the optimal CV MPR to achieve the best system benefits is informative and can provide some guidance for transportation agencies to use appropriate incentives or other policies to potentially affect the speed of CV adoption. Instead of using the traditional incremental method, this paper proposed a simulation-based approach combined with Bayesian optimization to determine the optimal CV MPR that achieves the highest performance benefits for a freeway segment. The proposed methodology is tested in the I-210 E (in California, U.S.) simulation freeway segment built and calibrated in Simulation of Urban Mobility software as a case study. The weighted sum of the average total travel time on the mainline and the average queue length of on-ramps is formulated as the objective function to optimize the CV MPR. Different weight combinations are tested as different scenarios. The optimization results of these scenarios show that, when the weight of total travel time is high, the optimal CV MPR tends to be high. On the contrary, when the weight of queue length increases, higher CV MPRs may not guarantee higher benefits for the traffic system. The globally optimal CV MPR can be as low as 3%. The case study also confirms the effectiveness of optimizing the CV MPR based on microsimulation and Bayesian optimization.

Double‐sided queues and their applications to vaccine inventory management

AbstractWe consider a double‐sided queueing model with batch Markovian arrival processes (BMAPs) and finite discrete abandonment times, which arises in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. While waiting to be matched, customers become impatient and may abandon the system without service. The abandonment time of a customer depends on its batch size and its position in the queue. First, we propose an approach to obtain the stationary joint distribution of age processes via the stationary analysis of a multi‐layer Markov modulated fluid flow process. Second, using the stationary joint distribution of the age processes, we derive a number of queueing quantities related to matching rates, fill rates, sojourn times and queue length for both sides of the system. Last, we apply our model to analyze a vaccine inventory system and gain insight into the effect of uncertainty in supply and demand processes on the performance of the inventory system. It is observed that BMAPs are better choices for modeling the supply/demand process in systems with high uncertainty for more accurate performance quantities.

Enhancing Work Zone Safety: Evaluating Static Merge Strategies Through Microscopic Traffic Simulation

Background The utilization of merging control has been proposed as a strategy to maximize the capacity of roads in work zone areas. The static Early Merge (EM) and static Late Merge (LM) controls are extensively implemented among these strategies. Although many studies have investigated the efficacy of these controls through the analysis of field data or microscopic traffic simulations, such comparisons are frequently conducted under different work zone conditions, which can result in inconsistent, contradictory conclusions. Materials and Methods A simulation study was carried out using the VISSIM microscopic traffic simulator within a self-developed work zone featuring a 2-to-1 lane closure setup to comprehensively assess and contrast the traffic efficiency of the EM and LM controls. Furthermore, through a comprehensive analysis and comparison of network performance within the designed work zone across various scenarios, including queue length, vehicle delays, and travel time, the significant VISSIM parameters influencing the system's performance were identified. Results The analysis revealed that the parameters CC1 (headway time) and CC2 (longitudinal following threshold) from the car-following model exert more significant influence in the simulated work zone throughput than the Safety Distance Reduction Factor (SDRF) parameter from the lane-changing model. Discussion According to the simulation findings, implementing the EM control is preferable when drivers display aggressive behavior and maintain relatively short safety distances (i.e., low CC1 values). Conversely, opting for the LM control is more advisable in work zone areas where drivers demonstrate cautious driving tendencies and maintain longer safety distances (i.e., high CC1 values). Conclusion The efficacy of static EM and LM was analyzed in a 2-to-1 lane closure work zone on a freeway using the microscopic traffic simulator VISSIM. Simulation results were compared to identify the most relevant VISSIM parameters that influence work zone throughput. Our results indicate that the parameters CC1 and CC2 from the car-following model have a more substantial impact than the SDRF parameter from the lane-changing model. In particular, our comparison results suggest that the work zone throughput decreases in both the EM and LM scenarios as the values of CC1 and CC2 increase. Additionally, SDRF has a relatively negligible effect on the network performance of both merge strategies.

The RaKJA Application for Designing Android the Based Road Section Performance

Abstract Performance analysis of road sections is usually carried out on road sections that have the potential for high traffic jams, then perform performance calculations and obtain recommendations for problems on these road sections. However, currently it is still difficult to calculate road performance because it has to be done manually in the calculations and looking for the necessary factors. This research aims to create an application to assist in calculating the performance of Android-based roads more easily and flexibly, this application is called RAKJa (Road Performance Analysis Design) which will be published generally on the Google Play Store so that it can be used by anyone who needs it. This RAKJa application will be developed based on the Indonesian Road Capacity Guidelines (PKJI 2014), this application gets results in the form of degree of saturation, level of service, average speed, delays and queue length automatically without needing to look for the required factors in the PKJI 2014 table. Application This RAKJa was created using the Game Maker Language programming language from the Game Maker Studio 2 developer. Calculation of road performance using the RAKJa application produces the same results as calculations carried out manually. Validating the accuracy of the application from previous research urban road performance data based on the PKJI 2014 and primary data obtained accurate results of 90%.

Queuing analysis for improving performance in bacterial vaccine quality control process

The aim of the research is to analyze and improve the performance of the vaccine quality control queuing system to reduce delays and achieve the firm’s long-term goal on vaccine production capacity. The research focuses on the Bacterial Vaccine Quality Control (BVQC) at the largest vaccine manufacturers in Indonesia and Southeast Asia. The vaccines handled by BVQC include TT, DTP, BCG, BioTT, BioTd, DT, Td, and DTP-Hb-Hib. The BVQC operates a queuing system with eight servers, each assigned a fixed task. The existing system experienced delays ranging from 13 % to 61 % from January to June 2022. After identifying the queuing characteristics of the existing system, improvement proposals were suggested by modifying the assignment of the servers. This proposal was then simulated in November 2022, resulting in improved performance with no delays, a reduction in the length of the queue in the system (Lq) from 2.88 to 2.59, and a reduction in the average time spent in the system (Ws) from 0.0099 to 0.0044. The research suggests that modifying server assignments can be an effective method for improving the performance of a queuing system in vaccine quality control. This can lead to reduced delays, optimized queue lengths, and improved overall efficiency, potentially enhancing the firm’s ability to meet vaccine demand in the future.

A multi-channel queue model to optimize service level and staff availability in bank industry

Staff scheduling in service organizations like banks, stores, call centers, and emergency centers is critical due to direct customer interaction and uncertain service demand. This research presents a multi-objective model for scheduling bank staff, focusing on uncertain customer arrival and service rates. The model aims to optimize customer service efficiency and maximize staff satisfaction through three objective functions: minimizing the customer waiting queue length (using an M/M/C system), minimizing the number of assigned employees, and maximizing employee satisfaction by considering preferred working times. By simulating Poisson distribution for client arrival and service times, we predicted the bank's queue system performance and optimized staffing levels using the proposed model. Tested with real data from Agribank in Iran, the results showed an 8% reduction in customer waiting times and a 53% increase in employee satisfaction, demonstrating significant improvements in service efficiency and workplace morale. These percentages highlight the model's ability to effectively balance operational efficiency and employee well-being, facilitated by its transparent work pattern structure. Given the NP-hard nature of the model, we employed a meta-heuristic approach (NSGA-II) and GAMS with the ε-constraint method to solve it. Comparative results indicated that NSGA-II outperformed GAMS in both solution quality and computational time

Queue Configurations and Operational Performance: An Interplay Between Customer Ownership and Queue Length Awareness

Problem definition: Contrary to traditional queueing theory, recent field studies in B2C services indicate that pooled queues may be less efficient than dedicated queues. Methodology/results: We use two online experiments in the healthcare delivery context to replicate this finding and assess the interplay of servers’ customer ownership and queue length awareness as potential underlying mechanisms. We operationalize customer ownership as the extent to which servers feel ownership toward their customers and queue length awareness as the extent to which servers are able to accurately quantify their number of customers. We find that, following a change in queue configuration, dedicated queues outperform pooled queues with respect to processing speed without sacrificing quality. The reduction in speed is partially mediated by the servers’ queue length awareness and partially suppressed by their ownership of customers in queue. The former is because servers turn out to be less likely to underestimate their load, which makes them work faster. The latter is because ownership of customers in queue may distract servers from the customer in service. When the queue configuration changes from a dedicated to a pooled one, the shorter processing times and higher levels of queue length awareness persist across the change, unlike the higher ownership of customers in the queue. Managerial implications: In discretionary service settings, switching to a dedicated queue is often beneficial in terms of operational performance, partly because the increased queue length awareness motivates servers to work faster; however, the increased degree of customer ownership of those in queue may distract them and result in a slowdown. Funding: This work was supported by the Wharton Behavioral Lab, the Claude Marion Endowed Faculty Scholar Award, the Wharton-INSEAD Alliance, and the Wharton Dean’s Research Fund. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.0202 .

Study of an Impedance Function for Mixed Traffic Flows Considering the Travel Time–Cost Characteristics of Long-Distance Electric Vehicle Trips

To quantify the travel time and cost characteristics of mixed traffic involving electric vehicles (EVs) and fuel-powered vehicles on roads, in this paper, we comprehensively consider three factors affecting road impedance: queue length, waiting time, and service rate. Initially, a time characteristic function and a cost characteristic function for mixed traffic impedance are constructed. From the perspective of travel time, we consider the impact of EV penetration on the actual road capacity and introduce a capacity coefficient to modify the BPR (Bureau of Public Roads) road impedance function. Given that different types of vehicles might need to wait at charging stations, we employ queuing theory to calculate the queuing time at these stations and construct an impedance model that considers travel time. From the perspective of travel costs, we account for the energy consumption costs and road usage fees for different types of vehicles. The energy consumption cost for travel mileage is obtained by multiplying the unit mileage energy consumption cost of mixed traffic by the travel mileage. For road usage fees, we adopt the conventional method of multiplying the per-kilometer rate for each vehicle type by the travel mileage, thus constructing an impedance model that incorporates travel costs. Finally, in the numerical analysis section, based on the vehicle travel mileage, we categorize travel into short-, medium-, and long-distance trips for analysis. With the constructed mixed traffic impedance model, we conduct a detailed analysis of the travel time and cost characteristics of mixed traffic over different travel distances. We explore the specific impacts of the electric vehicle penetration rate, traffic flow volume, and travel mileage on road impedance. The results indicate that as the penetration rate of electric vehicles increases, the total energy consumption of the transportation system significantly decreases. Moreover, at high electric vehicle penetration rates, although an increase in traffic flow leads to higher traffic impedance and longer travel times, the overall travel costs are reduced. This demonstrates that increasing the penetration rate of electric vehicles positively contributes to reducing the energy consumption and costs of transportation systems.

Assessing Traffic Performance: Comparative Study of Human and Automated HGVs in Urban Intersections and Highway Segments

This study conducts a comparative analysis of traf�ic dynamics at urban signalized intersections and on highways, incorporating both human-operated and automated heavy goods vehicles (HGVs) using the PTV VISSIM simulation model. It examines the impacts of automated driving technologies on critical traf�ic performance metrics such as queue length, travel time, vehicle delay, emissions, and fuel consumption. Initial �indings indicate that automation in HGVs enhances traf�ic �low, particularly by reducing queue lengths and vehicle delays. However, varying levels of automation from cautious to aggressive reveal complex trade-offs between operational ef�iciency and environmental impacts. On highways, automated HGVs demonstrate superior performance by reducing travel times and delays while increasing throughput compared to human-driven HGVs. These results underscore the operational bene�its of automated HGVs under diverse traf�ic conditionsand highlight their signi�icant implications for transportation planning and policy-making. This research contributes valuable insights into the integration of automated technologies in transportation systems, facilitating informed decision-making for stakeholders considering the adoption of these advancements in the current infrastructure.

Modelling and numerical simulation of sequencing strategies for connected and autonomous vehicles at signal-free intersections

The signal-free intersections employ connected and automated vehicle technology to manage vehicles passing through the intersection. Due to conflicting traffic flows in opposition directions, a proper sequencing of Connected and Autonomous Vehicles (CAVs) at signal-free intersections becomes critical to impacting intersection traffic performance. Based on an examination of CAV queueing rules under the most common sequencing strategies of First-Come-First-Serve (FCFS) and Longest-Queue-First (LQF), commonly employed as benchmarks for evaluating diverse innovative approaches to signal-free intersections, we propose a Dynamic-Queue-Service (DQS) strategy that is tailored to accommodate high traffic demand. To explicitly elucidate the impact of diverse traffic demand in conflicting directions on the queue uncertainty and stochasticity of CAVs, as well as to investigate how various sequencing strategies influence the equity of CAV traffic at signal-free intersections with regard to CAV queueing dynamics under different strategies, we have developed a double-input traffic queueing model and derived a range of metrics, including the queue length, delay, conditional queue length, and variance of queue length. In addition, for the three strategies, we performed a series of numerical simulations to investigate the queueing process of CAVs at signal-free intersections. Numerical results show that under different levels of traffic demand in the conflicting directions, the FCFS, LQF, and DQS strategies output diverse traffic queueing performances, and the DQS strategy is confirmed to be well-suited for the situation of high traffic demand in both conflicting directions.

Evaluasi Kinerja APILL di Simpang Empat Bundaran Burung Kota Palangka Raya

Burung Roundabout is an important roundabout for mobilizing the activities of people entering and leaving the city of Palangka Raya, with the increase in population and the rise in community activities the density of vehicles also increases significantly every year. Traffic problems can occur if there is a lack of coordination in each arm of the roundabout. The research objective is to know the performance of Weaving Area and the performance of APILL at Burung Roundabout. The obtained data consists of quantitative data from field survey data. The data is analyzed using Indonesian Road Capacity Manual (MKJI, 1997). The research result using the calculations from (MKJI, 1997) for the Weaving Area section show that the maximum Capacity (C) obtained is 11,125 smp/h at the DA section. The average traffic delay at the roundabout is 0,77 second/smp with the highest delay index (DS) is 0,22 at the CD section. Consequently the service level during peak hours is classified as grade A. The analysis of APILL at Burung roundabout has good traffic flow result. The highest capacity on the southern arm is 1566 smp/hour and the highest delay is 21 second/smp. The highest queue length is 22 meters on the Southern with a highest saturation degree of 0,44 on the Southern with indicates level of service index C.

Modeling residual-vehicle effects on uncertainty estimation of the connected vehicle penetration rate

In the transition to full deployment of connected vehicles (CVs), the CV penetration rate plays a key role in bridging the gap between partial and complete traffic information. Several innovative methods have been proposed to estimate the CV penetration rate using only CV data. However, these methods, as point estimators, may lead to biased estimations or suboptimal solutions when applied directly in modeling or system optimization. To avoid these problems, the uncertainty and variability in the CV penetration rate must be considered. Recently, a probabilistic penetration rate (PPR) model was developed for estimating such uncertainties. The key model input is a constrained queue length distribution composed exclusively of queues formed by red signals in undersaturation conditions with no residual vehicles. However, in real-world scenarios, due to random arrivals, residual vehicles are commonly carried over from one cycle to another in temporary overflow cycles in undersaturation conditions, which seriously restricts the applicability of the PPR model. To address this limitation, this paper proposes a Markov-constrained queue length (MCQL) model that can model the complex effects of residual vehicles on the CV penetration rate uncertainty. A constrained queue with residual vehicles is decomposed into four vehicle groups: observable constrained residual vehicles, unobservable constrained residual vehicles, unconstrained residual vehicles, and new arrivals. Although the first vehicle group is observable in the former cycle, the focus of this work is to model the residual vehicles from the second and third vehicle groups in combination with the new arrivals. The MCQL model includes four sub-models, namely, the residual-vehicle model, convolutional constrained queue model, constrained residual queue model, and observable residual queue model, to isolate and derive the distribution of the constrained vehicle set formed by the three latter vehicle groups. This distribution is then substituted into the PPR model to estimate the uncertainty. Comprehensive VISSIM simulations and applications to real-world datasets demonstrate that the proposed MCQL model can accurately model the residual-vehicle effect and estimate the uncertainty. Thus, the applicability of the PPR model is truly extended to real-world settings, regardless of the presence of residual vehicles. A simple stochastic CV-based adaptive signal control example illustrates the potential of the proposed model in real-world applications.

Finite MX/M/C Queue with State Dependent Service, Two-Class Arrivals and Impatient Customers

Objectives: 1. To compute the transition probabilities for the queueing system to be in different states. 2. To calculate the average system length and mean waiting time under the specified parameters. 3. To investigate and test the impact of system characteristics on the anticipated system length as well as mean waiting times. Method: MATLAB software is used for the Runge-Kutta method to calculate probabilities and system constants. Findings: An increase in Type-I arrival rate λ1 and Type-II arrival rate λ2 will cause both mean waiting times and queue length to increase, and they are reduced with an increase in service rates µ1 and µ2 of Type-I and Type-II classes. A rise in parameters such as special service rate µ3, probability of balking and reneging will result in a reduction in both mean waiting times and queue length. Novelty: This article covers a batch arrival finite Markovian queueing system with multi-server support and consumer impatience. In real time, all arrivals need not enter the queue at the same arrival rates, as it is based on the needs of the customer. In view of this, we have assumed two types of customers along with two different rates of arrival and state-dependent service. We did our work in transient mode, as time can influence the waiting lines. Also determined the system's performance indices and demonstrated the impact of the input parameters on the system's constants. Keywords: Batch Arrival, Customer Impatience, Two Class Customers, State Dependent Service, Multi Server Facility