Regular Queue Research Articles

Performance Analysis of Two Different Types of Waiting Queues with Working Vacations

This work examines a new class of working vacation queueing models that contain regular (original) and retrial waiting queues. Upon arrival, a customer either starts their service instantly if the server is available, or they join the regular queue if the server is occupied. When it is empty, the server departs the system to take a working vacation (WV). The server provides services more slowly during the WV period. New customers join the retry queue (orbit), if the server is on vacation. The supplementary variable technique (SVT) examines the steady-state probability generating functions (PGFs) of queue size for different server states. Several system performances are numerically displayed, including system state probabilities, mean busy cycles, mean queue lengths, sensitivity analysis, and cost optimization values. The motivation for this model in a pandemic situation is to analyze new healthcare service systems and reflect the characteristics of patient services.

Customer segmentation and ex ante fairness: A queueing perspective

In this study, we analyze how customer perceptions of ex ante unfairness affect a service provider that offers a priority service option. Customers differ in their waiting time costs, but that information is private to each customer. To address this issue and maximize revenue, the service provider offers a regular queue and a priority queue with an additional fee, thereby inducing the self‐selection of customers into those two queues. The customers make their service‐joining decision, based on the publicized queue terms, before entering the queue. In such a service system, the priority customers pay to reduce their waiting time, which increases the average waiting time for regular customers, as compared with a “first come, first served” (FCFS) queue. This increase in the waiting time can lead to a perception of unfairness by the regular customers. In this paper, we model this ex ante unfairness perception as a negative utility for the regular customers that is proportional to the difference in the expected waiting times between the segmented regular queue and a nonsegmented FCFS queueing system and investigate the service provider's optimal decisions regarding segmentation and pricing. We find that, in a service system where customers can balk, the service provider should focus on only one service offering through a lower priority fee or differentiated services under certain conditions and charge a higher priority fee once the perception of unfairness is taken into consideration. An equilibrium sensitivity study provides guidance on how best to design, construct, and operate queues. Finally, we examine two extension cases in which (1) the customer ex ante unfairness perception is defined as proportional to the waiting time difference between regular and priority queues or (2) priority customers exhibit either a “negative ex ante unfairness perception” or “positive ex ante unfairness perception” of queueing. Our results are robust, and we identify conditions under which a heightened unfairness perception could be beneficial or detrimental to the service provider.

Design an Optimal Fractional Order PI Controller for Congestion Avoidance in Internet Routers

The main problem that degrade data transition in communication networks is the congestion, to achieve stable TCP network, an active queue management (AQM) is used for controlling congestion and saving regular queue length .In this paper, a robust Fractional Order PI (FOPI) controller is suggested to control the AQM system, Gray Wolf Optimization Algorithm (GWO) is used for tuning of the controller gains and the Integral Time Absolute Error (ITAE) is adopted as a fitness function for monitoring system response by minimizing its error value until reach an efficient and robust response. The transient analysis is used for comparing the suggested controller with two conventional controllers (PI & PID) to show the efficient behavior of suggested controller, then a robustness analysis is applied by adding disturbances positive and negative signals with value 150 packets at different time(15 sec, 30 sec) to the system also varying the queue size after each 40 sec to see the system response , the controller overcomes the disturbances signals with less than 3.5 sec and faces the queue size varying values and returning the system response to its desired value efficiently.

Computer Graphics and VR/AR: From Clouds, to Cartoons, to a 3-D Virtual Museum

Associate Editor-in-Chief Richard Zhang outlines published articles in this regular queue issue.

Visual Analysis and Processing of Diverse Data

Associate Editor-in-Chief Richard Zhang outlines published articles in this regular queue issue.

Provider-Only Patients: A Novel Approach to ED Volume Surge and Covid-19

Summary To address changes in the health care landscape precipitated by the Covid-19 pandemic, particularly the lack of health care personnel, the ED at Inova Fairfax Hospital developed a process to evaluate and treat patients under a Provider-Only Patients (POP) protocol involving only physicians or advanced practice providers (APPs). In this article, Inova reports on the development of the POP process and the outcomes of a cohort of patients with suspected Covid-19 who were seen in the ED as POP patients between December 1, 2021, and January 15, 2022. All of the POP patients had Covid-19–related complaints, had an Emergency Severity Index (ESI) of 4 or 5 (on a scale where 1 is most urgent and 5 is least urgent), required limited nursing intervention, were discharged, and were 21–64 years of age. Any patients who exhibited signs of hemodynamic instability (e.g., hypo- or hypertensive), had non–Covid-19 complaints, had room air oxygen saturation below 96%, were pregnant, had difficulty ambulating, and/or had inadequate social support were not considered to be a POP patient and were seen in the regular queue of patients. Inova developed a designated area in the ED where patients were seen and discharged directly by the provider. Patients were first triaged by a triage nurse or physician to determine POP status. As of January 2022, Inova’s ED had seen 640 POP and 2,386 non-POP ESI 4 and 5 subjects (4.4% of the total ED census). Although the mean time from ED arrival to bed favored non-POP patients by approximately 9 minutes, the mean time from initially being seen by a provider to the discharge disposition and the mean time from discharge disposition placement to leaving the ED significantly favored POP by 48 minutes and 66 minutes, respectively. No POP patients returned within 72 hours for admission to the hospital, which supports the integrity of the POP triage and care delivery process. The authors estimate that the 640 patients who were part of the POP process saved approximately 1,892.27 nursing and 705.1 provider hours during that 46-day study period. No additional physician or APP hours were required, which suggests that POP is a safe, efficient, and effective process that can significantly reduce provider-to-disposition times and overall discharge length of stay. In addition to its value in mitigating the pandemic-related staff shortage, the POP model may also be considered to address nonpandemic-related staffing challenges.

Design and Visualization for Exploring Real-World Data

The current issue features articles from our regular queue. A central theme of these articles is design and visualization for exploring real-world data. Also included is the winning entry of the 2018 VAST Challenge. Coming up in the May/June issue, we have a Special Issue, edited by Ligang Liu and Scott Schaeffer, on geometric modeling and processing, covering applications in computer graphics, vision, CAD/CAM, and VR/AR.

Stochastic monotonicity approach for a non-Markovian priority retrial queue

This paper considers a non-Markovian priority retrial queue which serves two types of customers. Customers in the regular queue have priority over the customers in the orbit. This means that the customer in orbit can only start retrying when the regular queue becomes empty. If another customer arrives during a retrial time, this customer is served and the retrial has to start over when the regular queue becomes empty again. In this study, a particular interest is devoted to the stochastic monotonicity approach based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary joint distribution of the embedded Markov chain of the considered system.

Equilibrium analysis of unobservable [formula omitted] priority queues with balking and homogeneous customers

We investigate equilibrium queueing strategies in an unobservable M∕M∕n non-preemptive priority queue with homogeneous customers. Arriving customers make decisions by choosing one of the three options: balking, joining the regular queue, or joining the priority queue with an additional fee. We adopt a sequential approach to analyze this two-dimensional queueing game. We first obtain the equilibrium choice between joining the priority or the regular queue given a fixed total joining rate, and then we determine the equilibrium total joining rate.

Proposal for public policies regarding the promotion of online passport scheduling

About 70% of Romanians who need to get their passports renewed wait in a queue instead of scheduling an online scheduling. The truth is that many forget that the time of waiting for hours on end in queues has set, and this aspect should disappear from the conception of many people who have experienced hard times many years ago. At a regular queue, a Romanian stays for at least 2 hours if he has not reached among the first persons, which is not at all beneficial for them, but neither for the employees. The objective of the public policy proposal is to promote online scheduling for passports by: reducing queues on passports, reducing the stress of employees who work directly with the public and maintaining a harmonious connection between people and the website https://epasapoarte.ro.

Analysis of the queue lengths in a priority retrial queue with constant retrial policy

In this paper, we analyze a priority queueing system with a regular queue and an orbit. Customers in the regular queue have priority over the customers in the orbit. Only the first customer in the orbit (if any) retries to get access to the server, if the queue and server are empty (constant retrial policy). In contrast with existing literature, we assume different service time distributions for the high- and low-priority customers. Closed-form expressions are obtained for the probability generating functions of the number of customers in the queue and orbit, in steady-state. Another contribution is the extensive singularity analysis of these probability generating functions to obtain the stationary (asymptotic) probability mass functions of the queue and orbit lengths. Influences of the service times and the retrial policy are illustrated by means of some numerical examples.

The setting and optimization of quick queue with customer loss

At the peak of a service system, customers may hesitate and even leave in the face of unavoidable queuing. This phenomenon not only affects the customer's satisfaction, but also causes the loss of the company's revenue. This paper establishes a fluid model of customer queuing behavior for the customer losses. The goal is to reduce the customer losses, and the setting and optimization method of quick queue in random service systems is studied. We construct two queuing models, in which one includes only regular queues and the other includes both regular and quick queues. We analyze the queuing systems, and describe the different forms of the objective function based on the fluid model of customer behavior. Then we compare and analyze the impact of the adoption of quick queues on the performance of the service system during peak period, and design a calculation method to obtain the optimal value for setting the number of quick queues. Thus, the overall performance of the system is optimized. Finally, we take the setting and optimization of quick queue in the supermarket service system as an example, which verifies the validity of the proposed method, and shows the reference value of this method to management practice.

Macroeconomic and distributional consequences of energy supply shocks in Nigeria

In spite of its vast oil endowments, Nigeria continues to experience sporadic domestic oil supply shortages. These oil shortages manifest in regular queues at fuel stations that are often empty and in thriving parallel markets that sprout all over the country. The shortages have resulted in huge economic and non-economic costs to the economy. This study investigates the causes of the shortages and provides quantitative estimates of the economic costs to the Nigerian economy using a survey and a computable general equilibrium (CGE) model. The findings from this study show very clearly that oil sector supply shocks are costly both directly and indirectly. Oil supply shocks result in lower real GDP, higher average prices and greater balance of payment deficits. Other macroeconomic variables such as private consumption, investment, government revenue and employment also decline. In addition, the distributional impact of the quantitative energy supply shocks is higher for poor households than rich households. We also find that the sectoral impacts are mixed, often depending on the oil intensity of the sector. Finally, our survey results show that many economic agents on the demand side are willing to pay higher prices if that will guarantee a stable oil supply. Few players in the market chain benefit from supply disruptions, while consumers and the poor bear the main burden of these shocks.

Queueing models with delayed state-dependent service times

In a state-dependent queueing model, the service rate is adjusted at both epochs of customer arrivals and departures. In certain situations, frequently changing service rates is neither economical nor practical. This paper studies an alternative queueing model in which the server changes its service rates, or service types, only at the beginning of service. The model is analyzed by using an embedded Markov chain technique. The probability generating functions for the steady-state queue length are determined for both queueing models with and without vacations. Two particular models are considered in detail. One is the delayed M/M/ c queue and the other is the delayed M/G i /1 queue with c service types. The performance measures such as the mean queue length and additional waiting time are calculated and compared with regular queues.

The stationary work in system of a G/G/1 gradual input queue

This paper is devoted to the study of a stationary G/G/1 queue in which work input is gradually injected into the system and the work load is processed at unit rate. First, assuming that the input process is stationary, the key formula for the stationary distribution of work in system is derived by appeal to the waiting time of the associated regular G/G/1 queue. The main contribution of this paper is the derivation of Laplace-Stieltjes transforms (LSTs) for the stationary distributions of work in system and related random variables in terms of integrations with respect to a waiting time distribution of the associated regular queue. The results are exemplified by giving explicit formulas for the LST of total work for M/Ek/1 and M/H2/1. The results generalize the results of Pan et al. (1991) for the M/M/1 gradual input queue.

The stationary work in system of a G/G/1 gradual input queue

This paper is devoted to the study of a stationary G/G/1 queue in which work input is gradually injected into the system and the work load is processed at unit rate. First, assuming that the input process is stationary, the key formula for the stationary distribution of work in system is derived by appeal to the waiting time of the associated regular G/G/1 queue. The main contribution of this paper is the derivation of Laplace-Stieltjes transforms (LSTs) for the stationary distributions of work in system and related random variables in terms of integrations with respect to a waiting time distribution of the associated regular queue. The results are exemplified by giving explicit formulas for the LST of total work for M/Ek /1 and M/H 2/1. The results generalize the results of Pan et al. (1991) for the M/M/1 gradual input queue.