Queueing System Research Articles

Implementasi Sistem Antrian Pasien Berbasis Website Pada Klinik Sehat Tamba Kelurahan Cilangkap

Clinics are health facilities that provide basic medical services, diagnosis, treatment, and care to patients with minor or non-emergency medical conditions. The development of information technology has triggered the need for information systems in the medical field to improve health services. One important factor in increasing patient satisfaction is minimizing waiting time. Long queues can reduce clinic efficiency and affect patient satisfaction. This study aims to implement a website-based patient queue system at the Tamba Sehat Clinic, with the hope of increasing service efficiency and patient satisfaction. In implementing the website queuing system, researchers used qualitative methods to understand the effectiveness of health services and patient experiences. Data was collected through interviews, observations, and literature studies. The implementation of the Website-Based Patient Queuing System at the Tamba Sehat Clinic has had a significant impact. People can now easily get a queue number online via mobile phone or computer, eliminating the need to queue directly at the clinic location. Tamba Sehat Clinic, which was established in January 2023, has seen increased efficiency with this system. Patients can quickly and efficiently get a queue number, ensuring that their time is spent productively. Additionally, adopting this technology helps clinics improve the quality of service to prospective patients, creating a more comfortable and efficient experience for those in need of healthcare services. Thus, the implementation of a website-based patient queue system has brought real benefits to the community and clinics.

The Mt/M/1 queueing system with impatient customers and multiple vacation

The Mt/M/1 queueing system with impatient customers and multiple vacation

Drone-Delivery Network for Opioid Overdose: Nonlinear Integer Queueing-Optimization Models and Methods

This study proposes an emergency network design model that uses a fleet of drones to deliver naloxone in response to opioid overdoses. The network is represented as a collection of M/G/K queueing systems with variable capacity and service time modelled as a decision-dependent random variable. The model is a complex queuing-based optimization problem which locates drone bases and dispatches drones to opioid incidents. The authors devise an efficient solution framework in which they linearize the multiple nonlinearities (fractional, polynomial, exponential, factorial terms), derive an equivalent mixed-integer linear reformulation, and design an outer approximation branch-and-cut algorithm. The authors demonstrate the generalizablity of the approach to any problem minimizing the response time of M/G/K queueing systems with unknown capacity. Tests on Virginia Beach data reveal that drones can decrease response time by 82%, increase survival chance by more than 273%, save up to 33 additional lives annually, and provide up to 279 additional quality-adjusted life years.

Analysis of the Effectiveness of Online-Based Patient Queue Management System Innovation: Study at the Dental and Oral Hospital, Universitas Muhammadiyah Yogyakarta, Indonesia

Long queues and long waiting times at dental and oral health services are frequent complaints from patients. This is caused by the time for dental and oral procedures which generally takes quite a long time compared to other health services. The Dental and Oral Hospital (RSGM) of Universitas Muhammadiyah Yogyakarta (UMY) implemented innovation in the form of an online patient queue management system to overcome this problem. This research aims to evaluate the effectiveness of the online queuing system. This study used a non-experimental observational design with a cross-sectional approach. Data was collected through a survey of 1000 patients who used the RSGM UMY online queue system. Data were analyzed using descriptive statistics and inferential statistical tests. The research results show that the RSGM UMY online queuing system is effective in reducing patient waiting time. The average patient waiting time with the online queuing system was 21.33 (SD 1.45) minutes, shorter than with the manual queuing system which averaged 112.32 (SD 8.23) minutes. Patients were also satisfied with the online queuing system, with 92.32 (SD 4.21) respondents stating they were satisfied. The online patient queue management system at RSGM UMY has proven effective in reducing patient waiting time and increasing patient satisfaction. This system can be a model for other RSGMs to improve the quality of their services.

EXPRESS: Admission Control in Multi-server Systems under Binary Reward Structure

We study a multi-server queueing system where a customer is satisfied (and generates a unit revenue) if their queueing time is at most a given constant. If the queueing time of the admitted customer exceeds this constant, the customer gets served, but is unsatisfied and generates no revenue. Such queueing systems arise in the context of modeling service systems where excessive delays are of concern. A key challenge is how to design an admission control policy to maximize the number of satisfied customers per unit time in the long run, assuming that we can observe the number of customers in the system at any time. We call this the binary reward structure system and show that a threshold-type admission policy is optimal. The optimal threshold policy has to be computed numerically. Hence we propose a square-root admission policy to approximate the optimal admission control policy, and compare the performance of these two policies. We derive an analytical upper bound on the performance of optimal admission control policy by deriving an optimal admission policy assuming we have full information over the queueing time of the admitted customers. This is equivalent to a queueing system where customers abandon the queue (i.e., leave without service) if their queueing time exceeds the given constant. We demonstrate that the optimal policy that includes customer abandonment, or alternatively, the optimal policy under full information, the optimal threshold policy, and the square-root admission policy, all exhibit identical performance in the asymptotic regions of the parameter space. Our numerical results indicate that the worst optimality gap of the square-root admission policy is within 3.9% of the optimal revenue, and implementing the square-root admission policy in the observable queueing system leads to a revenue loss that is at most 5.6% of the maximum possible revenue rate in the full information system. We also compare the binary reward structure with the more common linear reward structure where the system incurs holding cost per unit queueing time per customer. In addition, we also show that the analysis based on queueing time is applicable to the system time as well.

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.

Optimizing multi-skill call center staffing using queuing models: A study of service level

This paper discusses the staffing problem of a multi-skill call center based on queueing model. In this model, there are three types of calls and four types of agents with various skills. By using results from M/M/c and M/M/c/c queueing systems, we describe and obtain the state-transition rates of the study model. Then, we establish equations for the steady-state probabilities and compute the formula of the service level. Finally, we apply a numerical example through the derived results and calculate the steady-state probabilities, service levels, the optimal number of agents in each group, and illustrate how these influence factors in the whole system.

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.

A Study Comparing Waiting Times in Global and Local Queuing Systems with Heterogeneous Workers

A virtual marketplace or service-providing system must ensure minimal task response times. Varying working rates among the human workers in the system can lead to longer delays for certain tasks. The waiting time in the queue is crucially affected by the queueing architecture used in the system, whether global or local. Studies generally favor global queue systems over local ones, assuming similar processing rates. However, system behavior changes when workers are heterogeneous. In this research, we used simulation to compare the waiting times of tasks assigned to three categories of processing rates in both architectures and with various routing policies in local queues. We found that when using random tie-breaking, there was a correlation between waiting time duration and the proportion of tie-breaking events. Performance is improved when controlling these events using scheduling awareness of the workers’ processing rates. The global queue outperforms local queues when the workers are homogeneous. However, the push mechanisms that control the assignment processes and heterogeneity-aware algorithms improve local queue system waiting times and load balance. It is better than global queues when tasks are assigned to medium and fast workers, but it also enables specific slow workers’ assignments.

A Multi-Agent RL Algorithm for Dynamic Task Offloading in D2D-MEC Network with Energy Harvesting.

Delay-sensitive task offloading in a device-to-device assisted mobile edge computing (D2D-MEC) system with energy harvesting devices is a critical challenge due to the dynamic load level at edge nodes and the variability in harvested energy. In this paper, we propose a joint dynamic task offloading and CPU frequency control scheme for delay-sensitive tasks in a D2D-MEC system, taking into account the intricacies of multi-slot tasks, characterized by diverse processing speeds and data transmission rates. Our methodology involves meticulous modeling of task arrival and service processes using queuing systems, coupled with the strategic utilization of D2D communication to alleviate edge server load and prevent network congestion effectively. Central to our solution is the formulation of average task delay optimization as a challenging nonlinear integer programming problem, requiring intelligent decision making regarding task offloading for each generated task at active mobile devices and CPU frequency adjustments at discrete time slots. To navigate the intricate landscape of the extensive discrete action space, we design an efficient multi-agent DRL learning algorithm named MAOC, which is based on MAPPO, to minimize the average task delay by dynamically determining task-offloading decisions and CPU frequencies. MAOC operates within a centralized training with decentralized execution (CTDE) framework, empowering individual mobile devices to make decisions autonomously based on their unique system states. Experimental results demonstrate its swift convergence and operational efficiency, and it outperforms other baseline algorithms.

Optimal control of a two-phase heterogeneous service retrial queueing system with collisions and delayed vacations

Optimal control of a two-phase heterogeneous service retrial queueing system with collisions and delayed vacations

Predicting accurate batch queue wait times on production supercomputers by combining machine learning techniques

AbstractThe ability to accurately predict when a job on a supercomputer will leave the queue and start to run is not only beneficial for providing insights to users, but can also help enable non‐traditional HPC workloads that are not necessarily suited to the batch queue style‐approach that is ubiquitous on production HPC machines. However there are numerous challenges in achieving such a prediction with high accuracy, not least because the queue's state can change rapidly and depend upon many factors. In this work, we explore a novel machine learning approach for predicting queue wait times, hypothesising that such a model can capture the complex behavior resulting from the queue policy and other interactions to generate accurate job start times. For ARCHER2 (HPE Cray EX), Cirrus (HPE 8600), and 4‐cabinet (HPE Cray EX) we explore how different machine learning approaches and techniques improve the accuracy of our predictions, comparing against the estimation generated by Slurm. By combining categorization and regression models, we demonstrate that our approach delivers the most accurate predictions across our machines of interest, with the result of this work being the ability to predict job start times within 1 min of the actual start time for around 65% of jobs on ARCHER2 and 4‐cabinet, and 76% of jobs on Cirrus. When compared against what Slurm can deliver, via the backfill plugin, this represents around 3.8 times better accuracy on ARCHER2 and 18 times better for Cirrus. Furthermore our approach can accurately predicting the start time for three quarters of all job within 10 min of the actual start time on ARCHER2 and 4‐cabinet, and for 90% of jobs on Cirrus. Whilst the initial driver of this work was to better facilitate non‐traditional, interactive and urgent, workloads on HPC machines, the insights gained can also be used to provide wider benefits to users, enrich existing batch queue systems, and inform supercomputing center policy also.

Analysis of Queueing System with Dynamic Rating-Dependent Arrival Process and Price of Service

We consider a multi-server queueing system with a visible queue and an arrival flow that is dynamically dependent on the system’s rating. This rating reflects the level of customer satisfaction with the quality and price of the provided service. A higher rating implies a higher arrival rate, which motivates the service provider to increase the price of the service. A steady-state analysis of this system using the proposed mechanism for changing the rating and a threshold strategy for changing the price is performed. This is carried out via the consideration of a suitably constructed multidimensional Markov chain. The impact of the variation in the threshold defining the strategy for changing the price on the key performance indicators is numerically illustrated. The results can be used to make managerial decisions, leading to an increase in the effectiveness of system operations.

Multi-objective optimization of production system with staggered production

In the manufacturing industry, timely order fulfilment from diverse customers is important for operational profitability, given the constraints of limited production capacity. This paper proposes a novel queueing system for a production system, in which order processing times are categorised as regular or rush based on customer preference. The proposed queueing system employs variable service rates and service strategies in conjunction with staggered production to deal with heterogeneous arrivals. We compute the steady-state probability distribution and develop system performance indicators. The lower and upper bounds of the expected sojourn time for rush and regular orders are derived. Numerical results show that an appropriate switching policy can reduce rush orders by approximately 35% while regular orders increase by less than 10%, demonstrating significant improvement in order fulfilment management. We formulate a multi-objective optimisation problem and implement the NSGA-II algorithm to obtain Pareto optimal solutions. Finally, three regression models are proposed to determine the minimum cost and the associated optimal service rates, given the maximum acceptable value of the expected number of rush orders. The established models can explain at least 80% of the dataset of the optimal solutions and thus our numerical findings provide useful guidance for decision-makers and production managers.

Orbit while in service

In various real-life queueing systems, part of the service can be rendered without involvement or presence of the customers themselves. In those queues, customers whose service order is still in process may leave the service station, go to ‘orbit’ for a random length of time, and then return to find out if their order has been completed. Common examples are car’s annual maintenance works, food ordering, etc. In this paper, a thorough analysis of a single-server ‘orbit while in service’ queueing model with general service time is presented. Assuming an Exponentially distributed orbit time, we derive general formulae for the distributions of (i) a customer’s total residence time in the system; (ii) a customer’s net actual residence time in the system during service (not including orbit time); (iii) the time an orbiting customer is late to return, i.e., remains in orbit after his/her service has been completed; and (iv) the total number of customers in the system. Considering the family of Gamma-distributed service times (spanning the range of distributions between the Exponential and the Deterministic), as well as the Uniform distribution, we further derive explicit formulae for the distributions of the above variables. Under linear cost assumptions, the optimal mean orbit time is numerically calculated for each of the above service-time distributions. Figures depicting the behavior of the measures as functions of the parameters are presented.

Analysis Of Queueing System And Teller’s Serviceoptimization At The Sub-Branch Office Of Bank Bjb For The Regional Government Of West Bandung Regency

This study investigates the queuing system and service efficiency at the Bank BJB sub-branch office in West Bandung Regency, focusing on enhancing customer service operations. With the significant increase in banking sector customers in Indonesia, including a growth in accounts in both conventional and digital financial institutions, the banking industry faces challenges in maintaining speed and efficiency in customer service. Long queues and time-consuming services have led to customer dissatisfaction and reduced operational efficiency​​.The research examines the current performance of the queuing system and teller service time, analyzing the root causes of prolonged waiting and service times, and developing strategies to optimize these times​​. The Bank BJB KCP serves a varied customer base, with complex banking requirements that often lead to longer service times​​. The queuing system employs a multi-channel, single-phase model, and the tellers offer several services, each with its own service level agreement​​.Observational data collected over 12 working days revealed the busiest hours and performance metrics, indicating high congestion during peak hours​​. Root cause analysis, considering both teller and customer perspectives, identified key issues contributing to the queuing system's inefficiency. The study's findings aim to enhance the overall customer service efficiency at Bank BJB KCP.

Analyzing the age of information in prioritized status update systems under an interruption-based hybrid discipline

Motivated by real-life applications, a special research-work interest has been recently directed towards the prioritized status update systems, which prioritize the update streams according to their timeliness constraints. The preferential service treatment between priority classes is commonly based on classical disciplines, preemption and non-preemption. However, both disciplines fail to give an even satisfaction between all classes. In our work, an interruption-based hybrid preemptive/non-preemptive discipline is proposed under a single-buffer system modelled as an M/M/1/2 priority queueing system. Each class being served (resp. buffered) can be preempted unless its recorded number of service preemptions reaches the predetermined in-service (resp. in-waiting) threshold. All thresholds between classes are the controlling parameters of the whole system’s performance. Using the stochastic hybrid system approach, the age of information (AoI) performance metric is analyzed in terms of its statistical average along with the higher-order moments, considering a general number of priority classes. Closed-form results are also obtained for some special cases, giving analytical insights about the AoI stability in heavy loading conditions. The average AoI and its dispersion are numerically investigated for the case of a three-class network. The significance of the proposed model is manifested in achieving a compromise satisfaction between all priority classes by a thorough adjustment of its threshold parameters. Two approaches are proposed to clarify the adjustment of these parameters. It turned out that the proposed hybrid discipline compensates for the limited buffer resource, achieving more promising performance with low design complexity and low cost. Moreover, the proposed scheme can operate under a wider span of the total offered load, through which the whole network satisfaction can be optimized under some legitimate constraints on the age-sensitive classes.

An Encourage Arrival of Single-Server Queuing System with Defeat Balking and Feedback Customers

Abstract: In this paper, we develop a finite capacity Single-server Markovian queuing system with encourage arrival, defeat balking and feedback customers. The steady state solution and the system characteristic are derived for this model and various probabilistic and performance measures of the system are derived.

Smart Shopping Facilitator for Visually Impaired using Artificial Intelligence

Abstract: It is the state of a person in which one has to depend on others for their own needs. Visual impairment is one of the disabilities of a human being. To date numerous methods had been proposed to enhance the life style of visually impaired and blind people. Still purchasing products in the e-shopping application without others support is tricky one for them. The project describes a system that provides the guidance for them to identify and purchase their products in the e-commerce application. The audio instructions will assist them inside the e-commerce application based on the real time situations. To make the ecommerce in a smarter way the billing system is automated. Hence it eliminates the existing queuing system in the e-commerce. The ultimate aim of this system is to eliminate others support for visually impaired people in shopping and provide them a convenient and sophisticated environment.