Queueing Problems Research Articles

Deployment of Public Charging Stations for BEVs Using an Agent-Based Modeling Approach

A low utilization rate of public chargers and unmatched deployment of public charging stations (CSs) are partly attributed to inappropriate modeling of charging behavior and biased charging demand estimation. This study proposes an optimization methodology for public CS deployment, considering real charging behavior and interactions between battery electric vehicle (BEV) users and CSs. Realistic charging choice behavior is modeled based on surveys, and a dynamic charging decision chain is simulated, allowing interactions between BEV users and CSs through an agent-based modeling (ABM) approach. The charging-related activities are triggered by state of charge (SOC) levels randomly generated from distributions derived from real BEV operating data, including the random SOC levels at the start of a trip, the SOC level that prompts the user to charge the BEV, and the SOC level at which the user stops charging the BEV. A bi-level programming model is proposed to optimize the deployment schemes for building new CSs considering the existing CSs, to determine the location and the capacity of new CSs. The objective is to minimize the total time cost per BEV user, including travel time, charging time and waiting time in the queue. An application is conducted, for the deployment of fast CSs in Washington State, USA. The results show that our method could provide effective guidance for allocating new CSs that are good supplements to the existing heavy-load CSs to share their charging load and relieve their serious queuing problems. The optimized deployment scheme can efficiently alleviate long waiting times at existing CSs and leads to a more balanced utilization among CSs. The proposed approach is expected to contribute to better planning and deployment of public CSs, satisfaction of the booming charging demand and increased utilization of public CSs.

Implementing Online Ordering Systems for Small Culinary Businesses: A Case Study of Nasi Cia

In the era of culinary industry growth and digital transformation, the challenges for startups like Nasi Cia in managing rice orders are increasingly complex. In the environment of SMA Xaverius 1, the surge in visitors often results in problems in managing orders efficiently. The manual system used today proved insufficient to handle the increasing order load. The problem of long queues also affects the customer experience and can lead to losing potential customers. Lack of sales data management is also a problem that must be solved. To overcome these problems, an online ordering system was built and designed using the extreme programming method. With this application, Nasi Cia switches to a more effective ordering system with the aim of improving flexibility, responsiveness, and service quality, as well as reducing dependence on expensive food delivery applications such as Gojek and Grab. The results and conclusions of this research show that this application has been successfully built with the extreme programming development method. This online ordering application can be well received as evidenced by 91.4% of users strongly agree

Research on contactless intelligent medication pickup mode selection based on a hospital in China under COVID-19.

During an outbreak such as COVID-19, hospital staff needs to be in close contact with all types of patients visiting the hospital and the risk of cross-infection is extremely high. Payment and medication pickup is a mandatory part of a patient's hospital visit, with direct contact between healthcare workers and patients, and long waiting times in the hospital area, which can easily lead to the spread of disease infection. This paper designed the prototype of a contactless smart medicine cabinet based on RFID technology and optimized the patient consultation and medication pickup process to address these problems. We conducted a 50-day field observation of patients for consultation and medication pickup at the First Hospital in H city, Jiangsu Province, China, and randomly timed 1600 sets of data from Surgery (ophthalmology) and Internal patients, then we designed the prototype of a contactless smart medicine cabinet based on RFID technology, optimized the patient consultation and medication pickup process, comparing the traditional and intelligent models using AnyLogic. The results show that this contactless medicine cabinet was able to reduce the time taken by patients in consultation and medicine pickup by 18.74 minutes, increasing the overall efficiency of the consultation by 32.20%. The simulation revealed that this contactless intelligent medication pickup model was able to reduce the time taken by patients in consultation and medicine pickup, increasing the overall efficiency of the consultation, effectively reducing the frequency of contact between healthcare workers and patients, and reducing the risk of disease infection. The proposed technical model provides a new idea to solve the problems of long queues, low efficiency and high risk of infection for patients to consult and get medicine during epidemics. Especially within hospitals it has important theoretical and practical implications for epidemic prevention and control as well as future hospital management.

Electric Vehicle Aggregation in a PV-Battery Charging Station: A Contract-Based Approach

As the proportion of high-power fast charging piles increases, how to more stably aggregate electric vehicles to avoid market risks brought about by user charging behavior is an urgent problem for charging station operators. This is especially so for fast charging station operators. To address this issue, a retail package design method for PV-battery charging stations based on contract theory and Lyapunov optimization is proposed in this paper. The operator can formulate optimal charging and discharging packages under asymmetric information in the day-ahead and real-time stages. Packages with fixed power and prices will be offered to users to reduce the impact of user behavior uncertainty. In addition, the queuing problems of pile allocation and PV-battery energy management are resolved by the Lyapunov drift optimization method. The performance indicators, such as the average power and demand processing capability of in-station equipment, will be optimized while ensuring the stability of the queuing network. The simulation verifies that the proposed method can improve the operator's net income and make the social welfare approach the theoretical value under complete information. Moreover, it shows stronger stability in terms of user aggregation.

Whittle index approach to multiserver scheduling with impatient customers and DHR service times

We consider the optimal scheduling problem in a multiserver queue with impatient customers belonging to multiple classes. We assume that each customer has a random abandonment time, after which the customer leaves the system if its service has not been completed before that. In addition, we assume that the scheduler is not able to anticipate the expiration of the abandonment times but only knows their distributions and how long each customer has been in the system. Many papers consider this scheduling problem under Poisson arrivals and linear holding costs assuming further that both the service times and the abandonment times have exponential distributions. Even with these additional assumptions, the exact solution is known only in very few special cases. To tackle this tricky problem, we apply the Whittle index approach. Unlike the earlier papers, which were restricted to exponential service times, we allow the service time distributions for which the hazard rate is decreasing. The Whittle index approach is applied to the discrete-time multiserver queueing problem with discounted costs. As our main theoretical result, we prove that the related relaxed optimization problem is indexable and derive the corresponding Whittle index explicitly. Based on this discrete-time result, we develop a reasonable heuristic for the original continuous-time multiserver scheduling problem. The performance of the resulting policy is evaluated in the M/G/M setup by numerical simulations, which demonstrate that it, indeed, gives better performance than the other policies included in the comparison.

Network Calculus Theory and Application: A New Graduate Course for Engineering Students

With the development of modern networks, the quality of service guarantee has become even more important than before. However, various new types of traffic and heterogeneous network architecture make it quite challenging to evaluate the quality of service, such as delay and reliability. Therefore, a novel analysis method is needed to solve this situation. Network calculus is a theory used to analyze the queueing problems in networks, which is the main content to be taught in this graduate course. Before network calculus theory is introduced, the classical queueing theory will be taught. Then, the mathematical fundamentals of network calculus, such as min-plus algebra and cumulative arrival/service process, will be introduced. Next, two branches of network calculus, i.e., deterministic network calculus and stochastic network calculus, will be introduced separately, including the definition of deterministic/stochastic arrival curve and service curve, as well as important theorems, such as delay theorem, flow aggregation theorem, server concatenation theorem. After the theoretical knowledge, practical content will be taught in two parts. First, students are encouraged to establish system models based on their graduate research topics, analyze the service guarantee of their models, and present their work in class. Second, a traffic data collection platform will be taught, and students will collect various traffic data and analyze traffic characteristics based on network calculus theory. Based on the feedback from students during the past three years, students are satisfied with this new course because it focuses on frontier technology and the teaching activities are well-organized.

Enabling Delay-Guaranteed Congestion Control With One-Bit Feedback in Cellular Networks

Unexpected large packet delays are often observed in cellular networks due to huge network queuing caused by excessive traffic coming into the network. To deal with the large queue problem, many congestion control algorithms try to find out how much traffic the network can accommodate, either by measuring network performance or by directly providing explicit information. However, due to the nature of the control in which queue growth should be observed or the necessity to modify the overall network architecture, existing algorithms are experiencing difficulties in keeping queues within a strict bound. In this paper, we propose a novel congestion control algorithm based on simple feedback, ECLAT which can provide bounded queuing delay using only one-bit signaling already available in traditional network architecture. To do so, a base station or a router running ECLAT 1) calculates how many packets each flow should transmit and 2) analyzes when congestion feedback needs to be forwarded to adjust the flow’s packet transmission to the desired rate. Our extensive experiments in our testbed demonstrate that ECLAT achieves strict queuing delay bounds, even in the dynamic cellular network environment.

Implementasi API Payment Gateway Midtrans pada Sistem Reservasi Dokter Gigi Berbasis Mobile

Common problems with dental clinics include large queues of patients, lack of optimization of patient administration, and manual payment systems that make it difficult for patients. A mobile-based dental clinic reservation application that is integrated with the Midtrans payment system is a solution to the difficulty of administering reservations at dental clinics, reducing patient queue problems, and optimizing payments. This research method consists of problem identification, system analysis, system design, implementation, and testing. System implementation uses Android Studio software with the Kotlin programming language and the Jetpack Compose framework. Payment implementation using midtrans API services. For data storage and management using Firebase Firestore. There are two users, namely patient and admin, each of whom has a different role. Patients can make new reservations and make payments, while admins can accept or reject reservations and payments. Application testing is carried out using the black box testing method. The test results show that the application successfully passed the test for each parameter tested.

Modified Q-Learning Algorithm for Mobile Robot Path Planning Variation using Motivation Model

Path planning is an essential algorithm in autonomous mobile robots, including agricultural robots, to find the shortest path and to avoid collisions with obstacles. Q-Learning algorithm is one of the reinforcement learning methods used for path planning. However, for multi-robot system, this algorithm tends to produce the same path for each robot. This research modifies the Q-Learning algorithm in order to produce path variations by utilizing the motivation model, i.e. achievement motivation, in which different motivation parameters will result in different optimum paths. The Motivated Q-Learning (MQL) algorithm proposed in this study was simulated in an area with three scenarios, i.e. without obstacles, uniform obstacles, and random obstacles. The results showed that, in the determined scenario, the MQL can produce 2 to 4 variations of optimum path without any potential of collisions (Jaccard similarity = 0%), in contrast to the Q-Learning algorithm that can only produce one optimum path variation. This result indicates that MQL can solve multi-robots path planning problems, especially when the number of robots is large, by reducing the possibility of collisions as well as decreasing the problem of queues. However, the average computational time of the MQL is slightly longer than that of the Q-Learning.

UDL: a cloud task scheduling framework based on multiple deep neural networks

Cloud task scheduling and resource allocation (TSRA) constitute a core issue in cloud computing. Batch submission is a common user task deployment mode in cloud computing systems. In this mode, it has been a challenge for cloud systems to balance the quality of user service and the revenue of cloud service provider (CSP). To this end, with multi-objective optimization (MOO) of minimizing task latency and energy consumption, we propose a cloud TSRA framework based on deep learning (DL). The system solves the TSRA problems of multiple task queues and virtual machine (VM) clusters by uniting multiple deep neural networks (DNNs) as task scheduler of cloud system. The DNNs are divided into exploration part and exploitation part. At each scheduling time step, the model saves the best outputs of all scheduling policies from each DNN to the experienced sample memory pool (SMP), and periodically selects random training samples from SMP to train each DNN of exploitation part. We designed a united deep learning (UDL) algorithm based on this framework. Experimental results show that the UDL algorithm can effectively solve the MOO problem of TSRA for cloud tasks, and performs better than benchmark algorithms such as heterogeneous distributed deep learning (HDDL) in terms of task scheduling performance.

Exploring the Effectiveness of Preordering Technologies in the Food Industry to Other Technology Solutions

Abstract: There is frequently a sizable influx of people looking to interact, shop, or eat on college campuses as well as in public locations like food courts and retail malls. But because of the heavy traffic, there are frequently huge queues at the restaurants, which costs customers a lot of time. The current COVID-19 outbreak has also highlighted how crucial it is to minimise intimate contact between people. As a result, using contactless ordering and payment systems has grown in popularity as a way to reduce the spread of disease. Hence, using effective and secure contactless transaction technologies may help to improve customer service while also emphasising public health and safety. To solve the problem of lengthy queues at restaurants in congested public spaces. We will make an application which it let you schedule a certain time for your order to be ready by placing an advance food order while shopping or even from home. Then, simply go to the food outlet and collect your food, ready to enjoy. Our Work can be used in a restaurant and universities cafeteria.

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.

The Effect of Mobile Payment on Payment Waiting Time for Outpatients With Medical Insurance: Historically Controlled Study.

Waiting for a long time to make payments in outpatient wards and long queues of insured patients at the checkout window are common in many hospitals across China. To alleviate the problem of long queues for payment, many hospitals in China have established various mobile apps that those without health insurance can use. However, medically insured outpatients are still required to pay manually at the checkout window. Therefore, it is urgent to use information technology to innovate and optimize the outpatient service process, implement mobile payment for medically insured outpatients, and shorten the waiting time for outpatients, especially in the context of the COVID-19 epidemic. Furthermore, smartphone-based mobile payment for outpatients with health insurance could be superior to on-site cashier billing. This study aimed to investigate the impact of smartphone-based mobile payment in relation to different aspects, such as waiting time, satisfaction with patients' waiting time, payment experience, the proportion of those dissatisfied with payment, total outpatient satisfaction, and outpatient volume, and compare mobile payment with on-site payment. This was a historically controlled study. This study analyzed the outpatients' waiting time to make a medical insurance payment, their satisfaction with the waiting time and payment experience, the proportion of those dissatisfied with payment, and the outpatient volume of patients at Guangzhou Women and Children's Medical Center 1 year before and after the implementation of mobile payment for medical insurance in January 2021. An independent sample 2-tailed t test was used to compare waiting time, satisfaction with waiting time, and overall satisfaction. Paired sample 2-tailed t test was used to compare monthly outpatient visits. The chi-square test was used to compare the percentages of patients dissatisfied with payment. After the implementation of mobile payment for medical insurance outpatients, the patients' payment waiting time was significantly shortened (mean 45.28, SD 10.35 min vs mean 1.02, SD 0.25 min; t9014=53.396; P<.001), and satisfaction with waiting time and payment experience were significantly improved (mean 82.08, SD 3.17 vs mean 90.36, SD 3.45; t9014=-118.65; P<.001). Dissatisfaction with payment significantly decreased (10.27%, SD 2.18% vs 1.19% vs SD 0.30%; P<.001). The total satisfaction of outpatients significantly improved (mean 86.91, SD 3.23 vs mean 89.98, SD 3.31; t9014=-44.57; P<.001), and the outpatient volume increased (248,105.58, SD 89,280.76 vs 303,194.75, SD 53,773.12; t11=2.414; P=.03). Furthermore, payment efficiency improved, and the number of the on-site cashiers substantially decreased. Mobile payment for health insurance significantly shortened patients' payment waiting time; improved patient satisfaction on waiting time and payment experience and overall satisfaction; reduced the proportion of patients who were dissatisfied with payment and the cashier at the hospital; and increased monthly outpatient volume. This approach was effective and thus worthy of promoting.

A secured database monitoring method to improve databackup and recovery operations in cloud computing

In general, the company sometimes uses unregistered functions in database, which significantly improvesperformance, but does not leave the possibility of recovery except for backup. That is, actions must be performedimmediately after passing the session. A queue problem is likely to cause data loss and downtime of about aweek. In modern conditions, this can lead to the bankruptcy of the company. It can be seen that backup systemshave been installed and configured, but despite this, they have not succeeded in restoring within the time framespecified in the SLA. In this study, a secured database monitoring method was proposed to improve data backupand recovery operations in cloud computing. In this proposed method, the backup speed is directly proportionalto the amount of data, while having at least 30% annual data growth. In 3–4 years, the data at least doubled, butfor some companies, this number is even higher, while the backup speed does not change. Those terms and thoseSLAs that were relevant 3–4 years ago now need to be at least doubled. At the same time, business requirementsfor data recovery (recovery point objective/recovery time objective) continue to grow.

A secured database monitoring method to improve databackup and recovery operations in cloud computing

In general, the company sometimes uses unregistered functions in database, which significantly improvesperformance, but does not leave the possibility of recovery except for backup. That is, actions must be performedimmediately after passing the session. A queue problem is likely to cause data loss and downtime of about aweek. In modern conditions, this can lead to the bankruptcy of the company. It can be seen that backup systemshave been installed and configured, but despite this, they have not succeeded in restoring within the time framespecified in the SLA. In this study, a secured database monitoring method was proposed to improve data backupand recovery operations in cloud computing. In this proposed method, the backup speed is directly proportionalto the amount of data, while having at least 30% annual data growth. In 3–4 years, the data at least doubled, butfor some companies, this number is even higher, while the backup speed does not change. Those terms and thoseSLAs that were relevant 3–4 years ago now need to be at least doubled. At the same time, business requirementsfor data recovery (recovery point objective/recovery time objective) continue to grow.

A Secured Database Monitoring Method to Improve Data Backup and Recovery Operations in Cloud Computing

In general, the company sometimes uses unregistered functions in database, which significantly improves performance, but does not leave the possibility of recovery except for backup. That is, actions must be performed immediately after passing the session. A queue problem is likely to cause data loss and downtime of about a week. In modern conditions, this can lead to the bankruptcy of the company. It can be seen that backup systems have been installed and configured, but despite this, they have not succeeded in restoring within the time frame specified in the SLA. In this study, a secured database monitoring method was proposed to improve data backup and recovery operations in cloud computing. In this proposed method, the backup speed is directly proportional to the amount of data, while having at least 30% annual data growth. In 3–4 years, the data at least doubled, but for some companies, this number is even higher, while the backup speed does not change. Those terms and those SLAs that were relevant 3–4 years ago now need to be at least doubled. At the same time, business requirements for data recovery (recovery point objective/recovery time objective) continue to grow

ОСОБЛИВОСТІ РОЗВИТКУ МІЖНАРОДНИХ ПЕРЕВЕЗЕНЬ ЗАСОБАМИ ВАНТАЖНОГО АВТОТРАНСПОРТУ МІЖ УКРАЇНОЮ ТА КРАЇНАМИ-ЧЛЕНАМИ ЄС

The article examines the current trends in the development of international road transport in the context of cargo transportation by Ukraine with the EU Member States and analyzes the main factors of influence of development factors on the current state of the road transport system based on the technical, legal and economic basis of this type of foreign economic activity. The author considers the concept of "international transportation" and carries out a critical analysis based on the subjective and objective directions of definitions from various sources, characterizes the defining features of road transportation in terms of the regulatory and legal component, and determines the impact of modern challenges on the importance of road transport in Ukraine's foreign trade. The analysis of road transport in international transportation in relation to others is carried out and the technical features of international transportation with the countries of the European Union are characterized. On the basis of current statistical data, the author analyzes the domestic market of freight transport and identifies the main trends in the import of freight transport as a component of international transportation. A review of statistical data on international transportation permits and their impact on the quantitative component of flights to European countries as a factor in the development of international transportation and the corresponding number of vehicles with environmental performance in accordance with European standards is carried out. Based on the current data on the main aspects of cooperation between Ukraine and the EU countries, which include "customs visa-free regime", "transport visa-free regime" and zero rate of customs clearance of motor vehicles as factors of increasing the overall traffic of cargo transportation, the author makes a critical analysis based on the causal vision of the current development of international transportation in the context of the selected land transport connection and the factors hindering the development of international transportation, taking into account the operational component of international transportation processes. The article provides recommendations for solving the urgent problem of queues at customs checkpoints for selected international connections for the transportation of goods by road by optimizing the processes of existing transportation in terms of intermodal and multimodal format using rail and road modes of communication as one of the ways to achieve the overall synergistic effect of transportation, taking into account the main logistics criteria for transportation efficiency: time, distance and cargo safety.

IMPLEMENTASI METODE SHORTEST-JOB FIRST UNTUK PENJADWALAN PENGGUNAAN LABORATORIUM FISIKA DI SMA 1 PEGAJAHAN

Queuing problems can occur in many cases, including in the process of using the physics laboratory by patients. The use of the physics laboratory at SMA Negeri 1 Pegajahan experienced problems such as recording the Order Form which was still done manually, this resulted in frequent data accumulation, loss and even miscommunication. This study aims to make a schedule for the use of the physics laboratory to overcome the queue problem. In this study, the author uses the Shortest Job First (SJF) algorithm, which is a scheduling method by determining that each process in the ready queue will be executed based on the smallest burst time so that the waiting time is short for each process and the average waiting time is also short. Based on the existing problems, it can be concluded that there is a need for a physics laboratory scheduling system using the shortest job first method that can manage and determine the usage schedule according to the duration that has been made.

PERFORMANCE MEASURE OF MULTIPLE-CHANNEL QUEUEING SYSTEMS WITH IMPRECISE DATA USING GRADED MEAN INTEGRATION FOR TRAPEZOIDAL AND HEXAGONAL FUZZY NUMBERS

In this paper, a procedure to establish the different performance measures in terms of crisp value is proposed for two classes of arrivals and multiple channel queueing models, where both arrival and service rate are fuzzy numbers. The main idea is to convert the arrival rates and service rates under fuzzy queues into crisp queues by using graded mean integration approach, which can be represented as median rule number. Hence, we apply the crisp values obtained to establish the performance measure of conventional multiple queueing models. This procedure has shown its effectiveness when incorporated with many types of membership functions in solving queuing problems. Two numerical illustrations are presented to determine the validity of the procedure in this queueing model, which involved using trapezoidal and hexagonal fuzzy numbers. It can be concluded that graded mean integration approach is efficient with fuzzy queueing models to convert fuzzy queues into crisp queues. This finding has contributed to the body of knowledge by suggesting a new procedure of defuzzification as another efficient alternative.

MAD Dispersion Measure Makes Extremal Queue Analysis Simple

A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival- and service-time distributions. We address this extremal queue problem by measuring dispersion in terms of mean absolute deviation (MAD) instead of the more conventional variance, making available methods for distribution-free analysis. Combined with random walk theory, we obtain explicit expressions for the extremal interarrival- and service-time distributions and, hence, the best possible upper bounds for all moments of the waiting time. We also obtain tight lower bounds that, together with the upper bounds, provide robust performance intervals. We show that all bounds are computationally tractable and remain sharp also when the mean and MAD are not known precisely but are estimated based on available data instead. Summary of Contribution: Queueing theory is a classic OR topic with a central role for the GI/G/1 queue. Although this queueing system is conceptually simple, it is notoriously hard to determine the worst-case expected waiting time when only knowing the first two moments of the interarrival- and service-time distributions. In this setting, the exact form of the extremal distribution can only be determined numerically as the solution to a nonconvex nonlinear optimization problem. Our paper demonstrates that using mean absolute deviation (MAD) instead of variance alleviates the computational intractability of the extremal GI/G/1 queue problem, enabling us to state the worst-case distributions explicitly.