Queueing Performance Research Articles

How Observed Queue Length and Service Times Drive Reneging Behavior in Queues

Customers who renege from a queue signal dissatisfaction with the wait, possibly leading to lost business opportunities. Service organizations need to understand how queue features observed by waiting customers drive decisions to renege. Through a series of experiments run in the lab and online, this article demonstrates a relative progress effect in queues. This behavioral effect is created when a series of fast service times are observed early in a wait, followed by slower service times that make the total wait equal to that in a comparable queue progressing at a steady rate. The observer experiences a fast depletion of the queue and a lower proportion of the original queue length remaining. This generates a sense of relative progress for the observer which leads to a reduction in renege behavior. In one of the studies, a relative progress effect enables participants to wait for a longer queue or longer duration compared to a benchmark queue without this effect. A simulation analysis, where individuals in a queue are modeled as experiencing a similar behavioral effect, shows that the individual-level effects lead to systematic differences in the queue performance. Behavioral effects that increase individual patience for some are shown to reduce the overall renege rate in the queue. Our findings suggest that queue practices that modulate the perception of relative progress can reduce renege behavior.

Using Discrete-Event Simulation to Model Web-Based Crisis Counseling Service Operation: Evaluation Study.

According to the Organisation for Economic Co-operation and Development, its member states experienced worsening mental health during the COVID-19 pandemic, leading to an increase of 60% to 1000% in digital counseling access. Hong Kong, too, witnessed a surge in demand for crisis intervention services during the pandemic, attracting both nonrepeat and repeat service users during the process. As a result of the continuing demand, platforms offering short-term emotional support are facing an efficiency challenge in managing caller responses. This aim of this paper was to assess the queuing performance of a 24-hour text-based web-based crisis counseling platform using a Python-based discrete-event simulation (DES) model. The model evaluates the staff combinations needed to meet demand and informs service priority decisions. It is able to account for unbalanced and overlapping shifts, unequal simultaneous serving capacities among custom worker types, time-dependent user arrivals, and the influence of user type (nonrepeat users vs repeat users) and suicide risk on service durations. Use and queue statistics by user type and staffing conditions were tabulated from past counseling platform database records. After calculating the data distributions, key parameters were incorporated into the DES model to determine the supply-demand equilibrium and identify potential service bottlenecks. An unobserved-components time-series model was fitted to make 30-day forecasts of the arrival rate, with the results piped back to the DES model to estimate the number of workers needed to staff each work shift, as well as the number of repeat service users encountered during a service operation. The results showed a marked increase (from 3401/9202, 36.96% to 5042/9199, 54.81%) in the overall conversion rate after the strategic deployment of human resources according to the values set in the simulations, with an 85% chance of queuing users receiving counseling service within 10 minutes and releasing an extra 39.57% (3631/9175) capacity to serve nonrepeat users at potential risk. By exploiting scientifically informed data models with DES, nonprofit web-based counseling platforms, even those with limited resources, can optimize service capacity strategically to manage service bottlenecks and increase service uptake.

Efficiency comparison of message brokers

The aim of the article is to compare three main brokers used in the development of web applications: RabbitMQ, Apache Kafka and Apache Pulsar. To conduct the research, a custom application was created to compare two key metrics in the context of message queue performance. These metrics are: latency and number of processed messages per second. The conducted experiments showed that in scenarios requiring processing of backlogged messages by the broker and in cases of minimizing the impact of the SSL protocol on broker performance, Apache Pulsar proved to be the best solu­tion. In the scenario examining message delivery delays, RabbitMQ turned out to be the best tool, while in the case of examining the stability of message processing in real-time, the best results were achieved with Apache Kafka.

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.

Bayesian analysis of Markov modulated queues with abandonment

AbstractWe consider a Markovian queueing model with abandonment where customer arrival, service and abandonment processes are all modulated by an external environmental process. The environmental process depicts all factors that affect the exponential arrival, service, and abandonment rates. Moreover, the environmental process is a hidden Markov process whose true state is not observable. Instead, our observations consist only of customer arrival, service, and departure times during some period of time. The main objective is to conduct Bayesian analysis in order to infer the parameters of the stochastic system, as well as some important queueing performance measures. This also includes the unknown dimension of the environmental process. We illustrate the implementation of our model and the Bayesian approach by using simulated and actual data on call centers.

Avaliação de desempenho do atendimento em uma emergência hospitalar do Rio de Janeiro: uma abordagem híbrida por meio de Simulação de Eventos Discretos e Análise Envoltória de Dados

Abstract The efficiency and quality of the emergency department are paramount to ensure that patients receive immediate and appropriate care. Issues such as lengthy waiting times, critical resource management and allocation, and patient scheduling are linked to increased morbidity and mortality, particularly among the elderly and vulnerable populations. This study aims to assess the performance of an emergency department hospital in Rio de Janeiro based on the analysis of resource utilization and queue performance. The methodology encompassed the development of the emergency macro-process, a preliminary statistical analysis of the collected data, and discrete event simulation under different demand conditions. The study found that the average length of stay in the emergency department was 58.12 minutes, potentially increasing to 104.58 minutes under a 15% demand stress. Improvement scenarios were tested, and their efficiencies were measured using data envelopment analysis in an output-oriented and constant return to scale model. The sensitivity analysis revealed that the proposed performance enhancements could make the hospital more responsive to demand peaks and emergencies, ensuring greater resilience and better resource utilization under adverse conditions.

Exploring the Diversified Development of Vocal Music Teaching Methods in Colleges and Universities Combined with Multi-Priority Dynamic Threshold Algorithm

Abstract Enhancing the integration of modern information technology with educational practices, particularly in the vocal classroom, is crucial for improving academic quality. This paper presents an optimization method aimed at addressing the limitations of the existing multi-priority dynamic threshold algorithm. The specific performance is as follows: first, on the original basis of the PDT-RED algorithm, the expected cache utilization is set to ensure the utilization of the buffer. The optimized OPDT-RED algorithm should be used to ensure that the data frame is received with a high probability. Then, according to the channel environment, the dynamic fullness threshold was adjusted, which improved the performance of the highest priority queue with a high transmission success rate. Lastly, the measurements of vocal characteristic parameters like pitch, rhythm, beat, melody, and others. The goal was to create a complete evaluation network model for vocal teaching, which was applied to actual cases. The model’s performance and its effectiveness were evaluated. After testing, the subjects’ vocal rhythmic tempo was below 60, while the range of the sample repertoire was between 60 and 90, presenting two different forms of expression. The model proposed in this paper has the optimal effect on the enhancement of expressive movements while singing; 15.33% of the students improved by two notches, and the vocal teaching model designed in this paper has a very good effect on vocal enhancement.

An extended queueing model for vehicles at signalized intersections considering the platoon correlated arrivals

The unpredictability and randomness of traffic arrivals are key contributors to the large variability in the delays experienced by vehicles at signalized intersections. Vehicles traveling between signalized intersections in the urban road networks typically move in platoons due to the fact that they are released at the upstream signalized intersections; however, most traffic queueing models ignore the feature of correlations in traffic flows. To fill this gap, this paper proposes a more flexible traffic queueing model for vehicles at signalized intersections by explicitly taking into account the platoon size and headway correlations between vehicles in a platoon, which can well incorporate a wide range of arrival processes. We derive the time-dependent joint distribution of queue length, arrival phase, and signal state, which can be used to achieve a more complete quantitative analysis of the dynamics of the vehicle queueing process over the signal state. Mean queue performance metrics, such as mean queue length and mean delay, are obtained. Traffic load intensity and the queue length of vehicles at any given stage within a signal cycle are also analytically determined. The various queueing performance metrics obtained in this study can provide a good understanding of the queueing process of vehicles arriving at signalized intersections in the platoon correlated arrivals. Our results in numerical experiments confirm that the feature of correlations in traffic flows cannot be ignored in traffic flow modeling because, given the same traffic volume, the queueing process of vehicles at signalized intersections will be further determined by arrival modes, platoon sizes, and correlated arrival characteristics.

Comparative Evaluation of Java Virtual Machine-Based Message Queue Services: A Study on Kafka, Artemis, Pulsar, and RocketMQ

Message Queue (MQ) services play a vital role in modern distributed systems as they enable asynchronous communication between services and facilitate the decoupling of various components of the system. Among the many MQ services available, Kafka, Apache Pulsar, Artemis, and RocketMQ are popular choices, each offering unique features and capabilities. As the adoption of MQ services continues to grow, choosing the appropriate service that can meet the requirements of the system has become increasingly challenging. Therefore, a comprehensive comparison of these services is crucial to determine the most suitable one for a specific use-case. This research paper presents a thorough evaluation of these MQ services based on critical metrics such as CPU utilization, memory usage, garbage collection, latency, and throughput. Based on our extensive review, no other research has delved into such a detailed evaluation, thereby establishing our work as a cornerstone in this field. The results of our study offer valuable insights into the strengths and limitations of each service. Our findings indicate that each message queue behaves differently inside the Java Virtual Machine (JVM). This work aims to assist developers and researchers in strategically deploying and optimizing MQ services based on specific system and use-case requirements. In addition to providing machine metrics, our results demonstrate the performance of each message queue under different load scenarios, making it a valuable resource for those seeking to ensure the effective functioning of their MQ services.

Asymptotic behavior of a system of two coupled queues when the content of one queue is very high

We consider a system of two parallel discrete-time single-server queues, queue 1 and queue 2. The service time of any customer in either queue is equal to 1 time slot. Arrivals during consecutive slots occur independently from slot to slot. However, the arrival streams into both queues are possibly mutually interdependent, i.e., during any slot, the numbers of arrivals in queue 1 and queue 2 need not be statistically independent. Their joint probability generating function (pgf) A(x, y) fully characterizes the queueing model. As a consequence of the possible intra-slot correlation in the arrival process, the numbers of customers present (“system contents”) in queues 1 and 2, at any given slot boundary, are not necessarily independent either. In a previous paper, we have already discussed the mathematical difficulty of computing their steady-state joint pgf U(z_1,z_2); explicit closed-form results can only be obtained for specific choices of A(x, y). In this paper, we therefore look at the problem from an other angle. Specifically, we study the (asymptotic) conditional steady-state behavior of the system under the condition that the content of queue 1 is (temporarily) very high (goes to infinity). For ease of terminology, we refer to the system as the “asymptotic system” in these circumstances. We prove that the asymptotic system is nearly identical to the original (unconditional) system, but with a modified joint arrival pgf A^*(x,y) that can be computed explicitly from A(x, y). This fundamental result allows us to determine the stability condition of queue 2 in the asymptotic system, and explicitly compute the classical queueing performance metrics of queue 2, such as the pgf, the moments and the approximate tail distribution of its system content, when this condition is fulfilled. It also leads to accurate approximative closed-form expressions for the joint tail distribution of the system contents in both queues, in the original (unconditional) system. We extensively illustrate our methodology by means of various specific (popular) choices of A(x, y). In some examples, where an explicit solution for U(z_1,z_2) or for the (approximative) joint tail distribution is known, we retrieve the known results easily. In other cases, new results are found for arrival pgfs A(x, y) for which no explicit results were known until now.

Comparison of single server queuing performance measures using fuzzy queuing models and intuitionistic fuzzy queuing models with infinite capacity

This paper presents boundless capacity, one server’s fuzzy and intuitionistic fuzzy queuing models. This study’s primary objective is to demonstrate and compare the performance of a single server queuing model with infinite capacity using fuzzy queuing theory and intuitionistic fuzzy queuing theory. This article demonstrates that intuitionistic fuzzy theory performs better when solving queuing problems. Furthermore, by integrating fuzzy queuing models into an intuitionistic fuzzy framework, their relevance in authentic situations is augmented. The fuzzy queuing theory model’s performance measurements are delivered as a range of values, but the intuitionistic fuzzy queuing theory model offers a broad array of values. In this context, the arrival and the service rates are both triangular (TFN) and intuitionistic triangular fuzzy numbers (TIFN). An assessment is performed to determine the evaluation criteria, employing a design protocol in which the fuzzy values are taken as-is without being turned into crisp values. As a result, in an ambiguous environment, we can use the proposed approach to pick scientific findings. In this study, we are using the TFN in an intuitionistic fuzzy environment, compensating for the degree of stability and denial so that the sum of both virtues is never higher than one. We proffered many non-normal arithmetic techniques for this sort of fuzzified integer. The envisaged compositions are intuitive and concise, as they evolved by utilising canonical algebraic mathematics. In real-world situations, this tactic is simple and straightforward to enact. The nearest interval number is then used to round a TIFN. The key advantage of this strategy is that it allows us to quickly solve a constrained unrestrained optimization model with TIFN coefficients using a multi-section heuristic. The prevailing methodologies and initiatives are destined to be relevant to different types of updated decision-making obstacles in focusing on economic equity, funding, presidency, and environmental sciences, which will be the focus of our future research. And two numerical problems are solved to showcase the sustainability of the suggested technique. In this queuing model, we predict a variety of components, including prospective queue length, expected system length, and sojourn time in both the queue and the system. The statistical analysis reveals that the quantified performance indicators of the intuitionistic fuzzy queuing model agree well with the performance measurements of the fuzzy queuing model. Even though the average correlation between the two concepts is nearly equivalent, TIFN provides a more extensive range of possibilities than TFN. Despite the fact that fuzzy set theory is used to contend with unpredictability in decision-making circumstances, it only relates to the extent of membership and lacks a model for reluctance. The fact that each asset’s affirmation and deprivation levels are comprehended is the special feature of intuitionistic fuzzy sets. As a consequence, it becomes more meticulous, suitable, and generalizable.

PEMODELAN DAN SIMULASI ANTRIAN UNTUK MEMPERBAIKI WAKTU TUNGGU POLIKLINIK VITREORETINA RS MATA “DR.YAP” YOGYAKARTA

Background: Queuing problems often occur in the health care industry, such as hospitals. The problem has arisen because many requests access the services, but it is in imbalance with the adequacy of providers. Increased outpatient visits at the vitreoretinal polyclinic at the “Dr. YAP” causes long queues and long waiting times. Meanwhile, waiting time is an essential indicator of service quality in hospitals and affects patient satisfaction. Queueing model and simulation can be one method to identify queuing process problems and find the most optimal queuing scenario.
 Objectives: Identify the queuing system model at the vitreoretinal polyclinic service at the “Dr. YAP”, analyze the vitreoretinal polyclinic queuing system’s performance measures, and identify the optimal queuing scenario through simulation to improve the total waiting time.
 Methods: This research was conducted in two stages. The first stage is a quantitative descriptive analysis where the queue performance parameters are calculated. Data collection techniques used in this
 research are observation to obtain primary data (patient arrival time, service time, and waiting time on each server) and interviews to get supporting data. The second stage is the study of model construction. At this stage, the simulation model is designed to predict changes in patient waiting time for several scenarios using Ms. Excel and JaamSim software.
 Results: The queuing system model in the vitreoretinal polyclinic is Multi-Channel Multi-Phase, consisting of 3 queue phases with more than 1 server. A total of 338 patients were served, and the patients’ largest distribution for total waiting time was patients who waited for > 2 hours (41.12%) and between 1-2 hours (37.57%). The longest waiting time is for a doctor’s check-up length of 1 hour and 47 minutes. Several queuing scenarios were made from several identified problems. The first scenario, simulating the doctor’s arrival on time, reduces 25% of the total waiting time to 1 hour and 20 minutes. In the second scenario, separating the laser procedure schedule reduces 4% of the waiting time to 1 hour and 43 minutes. By combining scenarios 1 and 2, the third scenario reduced the total waiting time by 29% to 1 hour and 16 minutes. The fourth scenario is carried out
 through modeling on the JaamSim software by adding one doctor and one nurse, and the result is that there is a decrease in waiting time and the number of patients waiting in queues.
 Conclusions: Hospitals can take several ways to improve the waiting time. The first is to improve the punctuality of doctor’s practice time. This effort can be made by evaluating the starting hours of a doctor’s
 practice following the doctor’s feasibility and using an information system that can send automatic messages to the patients regarding the doctor’s practice start time and the patient’s arrival time. The second is the separation of the queue for laser procedures from the polyclinic queue. Laser procedures for reserved patients can be scheduled before the start of practice, after the practice, or on another day. Third, the addition of a Retinal Subspecialist Doctor and nurses at certain hours when there is no retinal schedule. The doctor is a preferably permanent doctor who has first practice license at the “Dr. YAP” Eye Hospital.

The Effect of Operation Time of the Server on the Performance of Finite-Source Retrial Queues with Two-Way Communications to the Orbit

The Effect of Operation Time of the Server on the Performance of Finite-Source Retrial Queues with Two-Way Communications to the Orbit

Analysis of Hetrogeneous Feedback Queue Model in Stochastic and in Fuzzy Environment Using L-R Method

In this paper, we analyse a feedback queue network in stochastic and in fuzzy environment. We consider a model with three heterogeneous servers which are commonly attached to a server in starting. At the initial stage, all queue performance measures are obtained in steady-state that is in stochastic environment. After that, work is extended to fuzzy environment because practically all characteristics of the system are not exact, they are uncertain in nature. In the present work we use probability generating function technique, triangular fuzzy numbers, classical formulae for the calculation of all queue characteristics and L-R method to calculate queue characteristics in fuzzy environment.

Optimisasi Sistem Antrian di Era Pandemi untuk Meningkatkan Kinerja Pelayanan Stasiun Pengisian Bahan Bakar Umum (SPBU)

From the results of observations at petrol station 34–17521 South Tambun, it was found that in a certain period there were queues exceeding the service standard of petrol stations causing customers to leave the queue. This study aims to measure the performance of gas station queues and propose a queuing line system optimization strategy with Multi Channel Single Phase (M/M/S) queuing model. Collect data using in -depth observations and interviews. Queuing data was taken for two weeks during the COVID-19 pandemic, daily from 06.00 to 20.00 WIB. From the results of the study, service optimization strategy is proposed with 3 channels at 17.00 - 18.00 WIB and 2 channels at 06.00 - 07.00, 12.00 - 13.00, 16.00 - 17.00, and 18.00 - 19.00 to reduce the number of queues at 18.00 - 19.00. to achieve gas station performance targets and maintain customer satisfaction.

An Exact Method for a Class of Self-Similar M/Ga/1/K Queueing System of Internet Stream

In Internet stream monitoring, computing the expected parameters and distributions for the stream process under self-similarity and long-range dependency requires appropriate and exact methods queueing analyses to obtain performance of the Internet. Our method avoids fitting a non-heavy tailed distribution to Internet stream data by specifically fitting Gamma distribution to its service time process, which enhances the features of correlated events that explain self-similarity and long-range dependency compared to the classical memoryless assumptions of standard Poisson arrival and Exponential service. We propose the specific expectations of the parameters for a class of M/Ga/1/k queueing system (‘M’ represents a Markovian arrival process that follows Poisson distribution, ‘Ga’ represents a Gamma distribution service process, ‘1’ represents a single server, ‘k’ represents the buffer size) in an exact closed-form derivations using the Pollaczek Khintchine formulae alongside the Laplace transform to obtain the performance of queue. The adequacy of the proposed model was confirmed using simulated data of Internet traffic. Keywords- Gamma distribution, Internet stream, M/Ga/1/K model, Self-similarity, heavy-tail distribution

The injury severity score: an operations perspective

BackgroundThe statistical evaluation of aggregation functions for trauma grades, such as the Injury Severity Score (ISS), is largely based on measurements of their Pearson product-moment correlation with mortality. However, correlation analysis makes assumptions about the nature of the involved random variables (cardinality) and their relationship (linearity) that may not be applicable to ordinal scores such as the ISS. Moreover, using correlation as a sole evaluation criterion neglects the dynamic properties of these aggregation functions scores.MethodsWe analyze the domain and ordinal properties of the ISS comparatively to arbitrary linear and cubic aggregation functions. Moreover, we investigate the axiomatic properties of the ISS as a multicriteria aggregation procedure. Finally, we use a queuing simulation with various empirical distributions of Abbreviated Injury Scale (AIS) grades reported in the literature, to evaluate the queuing performance of the three aggregation functions.ResultsWe show that the assumptions required for the computation of Pearson’s product-moment correlation coefficients are not applicable to the analysis of the association between the ISS and mortality. We suggest the use of Mutual Information, a information-theoretic statistic that is able to assess general dependence rather than a specialized, linear view based on curve-fitting. Using this metric on the same data set as the seminal study that introduced the ISS, we show that the sum of cubes conveys more information on mortality than the ISS. Moreover, we highlight some unintended, undesirable axiomatic properties of the ISS that can lead to bias in its use as a patient triage criterion. Lastly, our queuing simulation highlights the sensitivity of the queuing performance of different aggregation procedures to the underlying distribution of AIS grades among patients.ConclusionsViewing the ISS, and other possible aggregation functions for multiple AIS scores, as mere operational indicators of the priority of care, rather than cardinal measures of the response of the human body to multiple injuries (as was conjectured in the seminal study introducing the ISS) offers a perspective for their construction and evaluation on more robust grounds than the correlation coefficient. In this regard, Mutual Information appears as a more appropriate measure for the study of the association between injury severity and mortality, and queuing simulations as an actionable way to adapt the choice of an aggregation function to the underlying distribution of AIS scores.

Performance analysis of an M/G/1 queue with bi-level randomized (p, N1, N2)-policy

This paper proposes an M/G/1 queueing model with bi-level randomized (p, N1, N2)-policy. That is, after all of the customers in the system are served, the server is closed down immediately. If N1(≥ 1) customers are accumulated in the queue, the server is activated for service with probability p(0 ≤ p ≤ 1) or still left off with probability 1 − p. When the number of customers in the system becomes N2(≥ N1), the server begins serving the waiting customers until the system becomes empty again. Using the total probability decomposition technique and the Laplace transform, we study the transient queue length distribution and obtain the expressions of the Laplace transform of the transient queue-length distribution with respect to time t. Then, employing L’Hospital’s rule and some algebraic operations, the explicit recursive formulas of the steady-state queue-length distribution, which can be used to accurately evaluate the probabilities of queue length, are presented. Moreover, some other important queuing performance indices, such as the explicit expressions of its probability generating function of the steady-state queue-length distribution, the expected queue size and so on, are derived. Meanwhile, we investigate the system capacity optimization design by the steady-state queue-length distribution. Finally, an operating cost function is constructed, and by numerical calculation, we find the minimum of the long-run average cost rate and the optimal bi-level threshold policy (N*1,N*2) that satisfies the average waiting time constraints.

Analysis of a single server batch arrival non-Markovian queuing model approach in classification of foot thermograms

In this article, a single server non-Markovian queuing model with Poisson arrivals in stacks of different sizes is discussed. The server provides clients with a general service at a time with a random duration setup time after completing the first level of service. Also, the setup time stage is introduced to carry out the preparatory work required for the stage 2 service and customers may renege during the setup phase. Additionally, the server is subject to random interruption during the third stage of service and it enters into the repair process immediately. The effect of the setup time stage, interruption and reneging in the defined queuing system are well analysed. Using the supplementary variable technique of queuing theory, the duration of the queue length of different states of the system in terms of probability generating functions and the queue performance measures are determined. The issue of characterised lines is very much clarified by a reasonable application and supported by a mathematical portrayal.

Performance Approximation for Time-Dependent Queues with Generally Distributed Abandonments

Many stochastic systems face a time-dependent demand. Especially in stochastic service systems, for example, in call centers, customers may leave the queue if their waiting time exceeds their personal patience. As discussed in the extant literature, it can be useful to use general distributions to model such customer patience. This paper analyzes the time-dependent performance of a multiserver queue with a nonhomogeneous Poisson arrival process with a time-dependent arrival rate, exponentially distributed processing times, and generally distributed time to abandon. Fast and accurate performance approximations are essential for decision support in such queueing systems, but the extant literature lacks appropriate methods for the setting we consider. To approximate time-dependent performance measures for small- and medium-sized systems, we develop a new stationary backlog-carryover (SBC) approach that allows for the analysis of underloaded and overloaded systems. Abandonments are considered in two steps of the algorithm: (i) in the approximation of the utilization as a reduced arrival stream and (ii) in the approximation of waiting-based performance measures with a stationary model for general abandonments. To improve the approximation quality, we discuss an adjustment to the interval lengths. We present a limit result that indicates convergence of the method for stationary parameters. The numerical study compares the approximation quality of different adjustments to the interval length. The new SBC approach is effective for instances with small numbers of time-dependent servers and gamma-distributed abandonment times with different coefficients of variation and for an empirical distribution of the abandonment times from real-world data obtained from a call center. A discrete-event simulation benchmark confirms that the SBC algorithm approximates the performance of the queueing system with abandonments very well for different parameter configurations. Summary of Contribution: The paper presents a fast and accurate numerical method to approximate the performance measures of a time‐dependent queueing system with generally distributed abandonments. The presented stationary backlog carryover approach with abandonment combines algorithmic ideas with stationary queueing models for generally distributed abandonment times. The reliability of the method is analyzed for transient systems and numerically studied with real‐world data.