Busy Period Research Articles

"Actually I Can Count My Blessings": User-Centered Design of an Application to Promote Gratitude Among Young Adults

Regular practice of gratitude has the potential to enhance psychological wellbeing and foster stronger social connections among young adults. However, there is a lack of research investigating user needs and expectations regarding gratitude-promoting applications. To address this gap, we employed a user-centered design approach to develop a mobile application that facilitates gratitude practice. Our formative study involved 20 participants who utilized an existing application, providing insights into their preferences for organizing expressions of gratitude and the significance of prompts for reflection and mood labeling after working hours. Building on these findings, we conducted a deployment study with 26 participants using our custom-designed application, which confirmed the positive impact of structured options to guide gratitude practice and highlighted the advantages of passive engagement with the application during busy periods. Our study contributes to the field by identifying key design considerations for promoting gratitude among young adults.

Contested and nervous spaces: exploring the environment of healthcare provision for international migrants in the Gauteng province of South Africa

ABSTRACT Background Notwithstanding the global goal of inclusive universal health coverage, and the notion of migrant-sensitive health systems, limited healthcare access or the exclusion of migrants from national health systems persists. South Africa has a rights-based constitution, but there is an inability or a failure of the health system to recognise and address the health needs of migrants. Objective To explore the intersection of the environment of healthcare provision for migrants and the everyday practices and behaviours of health workers and patients in the Gauteng province of South Africa. Methods The conceptual frameworks of health system responsiveness and social exclusion informed this institutional ethnographic study at 13 healthcare facilities in Gauteng province. We developed an observation guide to explore the intersection of culture and environment and its influence on healthcare provision to patients, especially migrants. Following ethics approval, we observed the facilities for 234 person-days. We used thematic analysis to analyse the data. Results Busy, frantic or nervous spaces, and contestations between patients and health workers, and among health workers formed part of the social and cultural environment of healthcare provision. The presence of migrant patients during busy periods served as a detonator for rude or discriminatory remarks, exacerbated by staff shortages and language barriers. Simultaneously, migrants exercised their agency by rebutting or confronting rude health workers. We also observed encouraging examples of kindness, caring and professionalism of health workers. Conclusion The study has implications for achieving a migrant-sensitive health system in South Africa.

Analysis of Single Server Markovian Queueing Model with Differentiated Working Vacation, Vacation Interruption, Soft Failure, Reneging of Customers

This article investigates the reneging of customers in M/M/1 model with differentiated working vacation, vacation interruption and soft failure. The customers come with rate λ and receives service during busy period with rate μ, where λ and μ obeys markovian distribution. In this model two distinct vacations are considered: one has been taken just after serving all customers in busy period with slow service rate θ as some soft failure occurs during working vacation (Vacation I). At an epoch of completion of working vacation, if any customers are present in the system, then the server moves to busy period for serving customers otherwise move to vacation II. During vacation II if customer comes then interruption is assumed to occur in the vacation and server returns to busy period otherwise remain in vacation .When an arriving customer finds server is on working vacation, it makes customer impatient and it start up an impatient timer T0 with an exponentially distributed rate α0 If service does not begin before T0 expires, the customer might renege with probability p without getting served or wait for their turn with probability 1-p=q. By using PGF technique we have derived different steady state probabilities and various system performances analytically. Effect of few parameters on different system performances have been shown numerically and illustrated graphically.

Scheduling optimization of continuous climb and descent operations in busy terminal airspace

Based on the current terminal airspace structure, a method for scheduling aircraft arrival and departure that integrates trajectory optimization, conflict detection and multi-objective optimization is proposed to help implement continuous climb and descent operations in busy terminal airspace. First, based on the multi-stage optimal control theory, the Gaussian pseudo-spectral method is used to propose a vertical profile optimization method for continuous climb and descent operations, and the trajectory optimization of continuous climb and descent operations based on the cost index is realized. Secondly, according to the wake turbulence interval and release interval used by the runway, and the horizontal and vertical intervals of air operations, the Mahalanobis distance is used to establish an aircraft conflict detection model. Then, considering the demands of air traffic control, airlines, airports and other operating units, a multi-objective scheduling model and method for aircraft arrival and departure that can achieve the optimization results are proposed. Finally, two sets of arrival and departure data at Guangzhou Baiyun Airport during busy periods are selected, multiple interval parameters are set, alternative paths are introduced, and case analysis and comparative studies are carried out. The results show that during the busy period dominated by departures, the terminal airspace of Guangzhou Baiyun Airport can achieve continuous climb and descent operations during busy periods; during the busy period dominated by arrivals, two aircraft could not be dispatched. The introduction of alternative paths can reduce the number of aircraft that cannot be dispatched.

Correlation analysis of long-span cable-stayed bridge strain response with environmental and operational variations based on feature selection

The structural response of large-span bridges is significantly influenced by environmental and operational conditions. This study employs a data-driven approach, which utilizes various techniques such as multiple linear regression, best subset regression, stepwise regression, Lasso regression, Ridge regression, and ElasticNet regression to analyze in detail the effects of environmental variables (temperature variables including temperature principal components, lateral temperature gradients, and vertical temperature gradients), and traffic loading on bridge strain response. Based on the analysis of 21 months of health monitoring data from a newly constructed cable-stayed bridge, Lasso regression is shown to perform best in predicting strains on the bridge deck and bottom slab. Furthermore, sensitivity analysis identifies several key influencing factors and quantifies their relative contributions to the strain. Although the 10-min average of the strain due to traffic loading has a minimal impact, the root mean square of the strain shows a significant correlation with the cumulative gross vehicle weight during busy traffic periods. The methodology proposed in this study helps to understand the strain response patterns of large-span bridges from a data perspective, and provides an effective approach to establishing a strain baseline model that eliminates environmental and operational variations.

Adaptive incentive mechanism with predictors for on-time attended home delivery problem

The widespread use of the Internet and smart devices has led to a fast growth in online shopping, offering new chances for online retailers to boost profits. However, this expansion has also brought various challenges, such as the heavy workload faced by delivery riders. To meet customers’ delivery time preferences and increase earnings, riders often work long hours, especially during busy periods. This study explores how historical delivery data can be used to balance workload in on-time attended home delivery. Drawing on the actual delivery operations and data of an online shopping platform, we propose a framework that combines delivery demand and customer behavior predictors with an adaptive incentive system to balance rider workload. Specifically focusing on same-day attended home delivery, we introduce a method to forecast future delivery demand, an algorithm to estimate customer choice behavior using a simple model, and an adaptive incentive system to influence customer decisions and achieve workload balance. We show that as order volume increases, the proposed incentive system achieves the pre-determined workload target. Using real data, we conduct numerical experiments which not only underscore the superior predictive performance of our models but also affirm the efficacy of the proposed incentive structure.

Time-dependent behaviour of an M/M/3 heterogeneous server queueing system with multiple vacations subject to system disaster

This research paper investigates the dynamic behaviour of a heterogeneous three-server queuing model with multiple vacation. The model also accounts for the possibility that a disaster could occur during busy periods or on vacation, in which case the restoration process would begin immediately. The time-dependent probabilities of system size are presented in the work with explicit equations computed in terms of modified Bessel functions, employing generating functions. To support the theoretical conclusions, numerical examples are given.

Calm Before the Storm?

Atlantic hurricane season poses an annual threat to the billions of dollars of oil and gas hardware pumping hydrocarbons from the depths of the US Gulf of Mexico (GOM). The region’s offshore production amounts to about 1.8 million B/D—roughly 14% of the total crude output in the US, according to the US Energy Information Administration, so any disruption is felt by oil markets across the globe. Prior to the 2024 hurricane season, forecasters pegged this year as primed to be particularly intense. Colorado State University (CSU), known for its storm prognostication, estimated that the basin would experience 23 named storms, with a dozen of those becoming hurricanes (winds of 74 mph or higher), and six of those strengthening to major hurricanes (winds of 111 mph or higher). Similarly, AccuWeather meteorologists expect between 20 and 25 named storms with a possibility of 30 or more. As the season enters its busy period, the basin has only experienced five named storms to date; however, many forecasters are sticking to their initial forecasts and continue to warn of an intense September/October period. “The months of September and October should be very active across the Atlantic,” said AccuWeather lead hurricane expert Alex DaSilva. “We continue to remain very concerned about rapid intensification. Sea-surface temperatures and ocean heat content are near record levels across most of the Atlantic basin. This can act like jet fuel for tropical systems. We also continue to believe that La Niña will emerge sometime in November. When water temperatures near the equator of the eastern Pacific Ocean are lower than the long-term historical averages for an extended period, La Niña is declared. Although this is a phenomenon in the Pacific, it has ramifications for weather patterns over the Atlantic Ocean. Specifically, La Niña can reduce the wind shear across the basin. When wind shear is lower, it makes it easier for tropical systems to take shape and strengthen.” The GOM has experienced one disruption in 2024 courtesy of Hurricane Beryl. Once a Category 5 storm (winds 155 mph and higher)—and the earliest-forming Category 5 storm on record—Beryl weakened as it crossed the southern Yucatán. The storm regained Category 1 strength as it crossed the far western offshore oil patch enroute to landfall near Matagorda Bay, Texas. Shell shut in production at its Perdido spar because of the storm as well as evacuated personnel from it and its Whale facility. Chevron moved all non-essential personnel off its Anchor floating production unit, which was undergoing commissioning at the time. The last major storm to cut a path straight through the heart of the US offshore oil patch was 2021’s Hurricane Ida. Ida tore through the region as a Category 4 storm before slamming into the Louisiana coast near Port Fourchon packing 150 mph winds on 29 August. The storm prompted the shut in of almost 100% of the Gulf’s oil and gas production and caused extensive damage to major hubs in the region, including the Shell-operated West Delta Block 143 complex. The facilities, which serve as the transfer station for production from Shell’s robust Mars corridor, were off line for several months.

Analysing the Performance of Queuing Model with the Busy Period Breakdown

Analysing the Performance of Queuing Model with the Busy Period Breakdown

A study on N-policy BMAP/G/1 queueing system

This study presents a simple approach for analyzing the BMAP/G/1 queueing system under N policy. In this policy, the server goes idle at the end of a busy period and the queue length is checked at every arrival moment. The idle server starts serving customers when the queue length reaches or above a predetermined number, namely N, and keeps doing so until the system is completely empty. We first use a simple sequential substitution approach to derive the system length distribution at departure epoch. A comparative study is also conducted to highlight the benefits and strength of our straightforward approach to that of the RG-factorization technique and the roots finding method. We extract the distribution of system length at a random time point by utilizing the remaining service time of a customer who is currently being served as the supplementary variable. The probability density function of the sojourn time distribution for an arbitrary customer of an incoming batch is also computed. We propose an expected linear cost function to estimate the optimal value of N at minimum cost. The validity of our analytic technique has been shown through a variety of numerical examples involving different service time distributions.

Optimizing Industrial Reliability: A Comparative Study of Hot and Cold Standby Configurations in Three-Unit Parallel Systems

This comparative research study explores the efficacy of two parallel systems, Model A employing a hot standby configuration and Model B utilizing a cold standby setup, each comprising three units operating based on demand. The investigation focuses on evaluating the reliability and cost-effectiveness of these systems, employing metrics such as Mean Time to System Failure, availability at full and reduced capacity, repairer busy periods, downtime, and profit analysis using Semi-Markov and regenerative point techniques. Results reveal that Model B (cold standby) outperforms Model A (hot standby) across multiple parameters, including Mean Time to System Failure, availability, repairer busy periods, downtime, and profitability. Specifically, Model B demonstrates higher values for Mean Time to System Failure, Availability at full and reduced capacity, Busy period for repairmen, and Profit in Rs. Consequently, it is inferred that Model B proves to be more reliable and efficient than Model A. These findings underscore the potential advantages of employing cold standby configurations in similar machinery setups, offering insights to enhance system performance and minimize downtime, thus suggesting avenues for optimizing cold standby parallel systems based on the study's outcomes.

Cost optimization for system stability and orbital search under working vacation and starting failure by using the ANFIS soft computing

This article deals with the concepts of a single server retrial queueing model with balking, orbital search under working vacation and starting failure. If the server is busy, the prospective consumer may either enter the pool or leave the system; if the server is idle, the arriving client begins providing its services instantaneously. We assume the server is unstable since it did not start during the usual busy period. Instead of being completely unavailable at some point during the working vacation, the server will operate at a slow rate. Following the completion of the vacation period, the server either searches the orbit for clients or returns to idle mode, during which it resumes normal operations and continues to serve customers. The essential and adequate conditions for system stability have been discovered. The supplementary variable approach has been utilised to generate the stationary probability distribution and a few performances metrices. To justify the suggested paradigm, several numerical examples and special cases are presented. We have used the ANFIS soft computing strategy to assess the outcomes of the analytical and neural fuzzy methods.

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.

Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

This paper deals with an M/G/1 feedback retrial G-queue and delayed repair incorporating Bernoulli working vacation. Arrivals of both favorable and unfavorable consumers are two independent Poisson processes. The server is subjected to breakdown during the regular busy period due to the arrival of unfavorable customers and then the server will be down for a short period of time. Further, the concept of delay time is also discussed. After the fulfillment of regular service, the dissatisfied consumer may re-join the orbit to receive another service as a feedback consumer. During the working vacation period, the server provides the service to consumers at a reduced rate. By applying the supplementary variable technique (SVT), we have analyzed the steady-state probability generating function (PGF) for the system size and orbit size. In addition, we have presented the system performance, reliability indicators, and stochastic decomposition property. Finally, we provided numerical examples to illustrate our model’s mathematical results.

Exact results for the distribution of the partial busy period for a multi-server queue

Exact results for the distribution of the partial busy period for a multi-server queue

Sample-Path Large Deviations for Unbounded Additive Functionals of the Reflected Random Walk

We prove a sample-path large deviation principle (LDP) with sublinear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space [Formula: see text] equipped with the [Formula: see text] topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area under the busy period of the Markov random walk, and we show that it exhibits a heavy-tailed behavior. Funding: The research of B. Zwart and M. Bazhba is supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant 639.033.413]. The research of J. Blanchet is supported by the National Science Foundation (NSF) [Grants 1915967, 1820942, and 1838576] as well as the Defense Advanced Research Projects Agency [Grant N660011824028]. The research of C.-H. Rhee is supported by the NSF [Grant CMMI-2146530].

Study of a two types of general heterogeneous service queueing system in a single server with optional repeated service and feedback queue

This paper addresses a model on a single server queue and two service representatives. After a customer is served, he/she has the three options: opting for receive the same service again (re-service), joining as a new customer for another regular service (feedback), or leaving the service system altogether. To ensure the queueing system is Markovian, we introduce an additional variable (supplementary variable) and using this approach, we derive the explicit distribution of queue size at random and departure epochs. Additionally, we determine the distribution of response time, inter-departure time, and busy period. By using the embedded Markov chain technique we have also derived the queue size distribution at departure epoch. We have also presented the cost analysis of the model with some numerical examples. The numerical illustration validates our findings and provides valuable insights into the queuing system.

Prioritization in the Presence of Self-ordering Opportunities in Omnichannel Services

Motivated by the popularity of mobile-order-and-pay applications, especially in fast-casual food restaurants and coffee shops, we study omnichannel service systems—where customers can employ mobile applications for self-ordering—with respect to sojourn times, throughput, and social welfare. Our models are two-stage queues with two customer classes: Walk-ins and mobiles. We identify Pareto efficient prioritization policies, highlighting trade-offs between each class’s mean sojourn times. We allow customers to make strategic joining decisions based on their anticipated delays under an information structure where walk-ins observe partial queue length information. We draw from a wide array of techniques, including steady-state, transient, busy period, hitting-time analyses, and matrix analytic methods. We showcase the significance of prioritization on the system throughput and social welfare. We demonstrate settings where a traditional service system’s (typically beneficial) transformation to an omnichannel reduces throughput. Our analysis highlights the importance of prioritization policy choice for an efficient transition to an omnichannel service system. The throughput-optimal policy choice highly depends on the operational parameters and customer patience levels; implementing a wrong policy can yield a significant loss in throughput and profitability.

P25 Nowhere to hide: broad-spectrum antimicrobial guideline adherence in outpatients

Abstract Background The NHS Acute Trusts Standard1 contract requires a 10% reduction in broad-spectrum antibiotics by 10% by March 2024 from a 2017 baseline. Co-amoxiclav is a broad-spectrum antibacterial that comprises 30% of broad-spectrum consumption at University Hospitals Birmingham. It is widely used across all specialities and is a perfect candidate to review to influence downward trend in consumption. Outpatient prescriptions do not receive the same level of scrutiny from pharmacy or antimicrobial stewardship team as inpatient prescriptions. If deviations from guidelines are identified, then this could be a potential area to address to reduce consumption. Methods Sixty outpatient co-amoxiclav prescriptions were reviewed to assess appropriateness of prescribing during December 2022. Parameters assessed included the indication and duration of co-amoxiclav therapy and adherence to Trust antimicrobial guidelines. The speciality prescribing outpatient co-amoxiclav was also documented to identify whether prescribing trends could be identified. Results Of 60 reviewed outpatient prescriptions written in December 2022, 54 were issued by acute medicine with other specialities including cardiothoracic, renal medicine, elderly care, ENT, urology and cardiology. All prescriptions had a documented indication and duration, however only three were adherent to Trust antimicrobial guidelines. The graph below represents the different indications co-amoxiclav was prescribed for to outpatients across all three hospital sites. Co-amoxiclav was most frequently prescribed for respiratory tract infections, followed by skin and then urinary tract infections. Conclusions This audit has highlighted that outpatient co-amoxiclav is commonly prescribed inappropriately and does not comply with Trust antimicrobial guidelines. The speciality most frequently prescribing outpatient co-amoxiclav inappropriately was acute and emergency medicine. The lack of clarity regarding the infection indication is a potentially important factor in this setting, resulting in broad-spectrum antimicrobial use to cover multiple potential bacterial infections. A limitation of this audit is it was carried out over a short and busy winter period.

Analysis of M/M/1 Model with Complete Breakdown during Busy Period, Optional Server with Limited Service, Complete Vacation and Delay in Repair

In this paper we have analyzed a single server Markovian queueing model with an optional server for limited-service time, complete breakdown during busy period, complete vacation with some delay in repair. Customers arrival follow Poisson’s distribution with rate λ. Service time during busy period is exponentially distributed with rate. The server goes under complete breakdown during busy period and hence sent for repairing. During breakdown an optional server with limited-service time is available for serving customers rather than stopping service. This optional server after completing busy period moves to working vacation for limited time period, where service time during this period is slower than busy period service time as server has some prior commitments or work to finish. As the limited-service time finishes, the server goes for a complete vacation and will not serve any customer during this period. If main server gets repaired, it immediately resumes busy period but if some delay occurs in repairing of main server, then optional server after completing vacation, will act as main server and resumes busy period until main server get repaired. The closed form expression of various system probabilities is derived. Various system performance measures like waiting time, queue length have been evaluated. Finally, some numerical and graphical results have been shown to model the impact of some parameters on different performance measures.