Busy Period Research Articles

Spectral distribution and semigroup properties of a queueing model with exceptional service time

<p>In this paper, we studied the spectrum and semigroup properties of the M/G/1 queueing model with exceptional service time for the first customer in each busy period. First, we described the point spectrum of the system operator that corresponds to the model, and we prove that the system operator has an uncountable infinite number of eigenvalues on the left-half complex plane. Second, by using the spectrum analysis and semigroup theory, we obtained that the spectrum-determined growth (SDG) condition holds and the semigroup is not asymptotically stable, compact, eventually compact, or even quasi-compact. Finally, in order to clarify the results of spectral distribution, some numerical analysis were conducted.</p>

Analysis of single server repairable queueing system with many kinds of service, single working vacation and standby server

We consider a single server queueing model in which the customers arrive according to a Markovian Arrival Process (MAP). We modeled this queueing system with many kinds of service where the customers can choose any kind from the server. Each kind of service follows Phase-type (PH) distribution. We analyzed the model with breakdown, repair, single working vacation and standby server. A standby server works only when the main server is breakdown while serving the customer during a busy or vacation period. Using the matrix-geometric approach, we examined the model. A few real-world examples have been given, and several graphical and numerical examples have also been provided.

Accident Response Time Enhancement Using Drones: A Case Study in Najm for Insurance Services

One of the main reasons for mortality among people is traffic accidents. The percentage of traffic accidents in the world has increased to become the third in the expected causes of death in 2020. In Saudi Arabia, there are more than 460,000 car accidents every year. The number of car accidents in Saudi Arabia is rising, especially during busy periods such as Ramadan and the Hajj season. The Saudi Arabia’s government is making the required efforts to lower the nations of car accident rate. This paper suggests a business process improvement for car accident reports handled by Najm in accordance with the Saudi Vision 2030. According to drone success in many fields (e.g., entertainment, monitoring, and photography), the paper proposes using drones to respond to accident reports, which will help to expedite the process and minimize turnaround time. In addition, the drone provides quick accident response and recording scenes with accurate results. The Business Process Management (BPM) methodology is followed in this proposal. The model was validated by comparing before and after simulation results which shows a significant impact on performance about 40% regarding turnaround time. Therefore, using drones can enhance the process of accident response with Najm in Saudi Arabia.

Performance study of the M/M(a,b)/1/MWV queuing system with types of breakdowns

Abstract This paper analyses the M/M(a,b)/1/MWV queuing model with various types of breakdowns. During peak times, the system has breakdown due to server unavailability. The model considers system with two types of breakdowns. The system may breakdown in two different ways during busy and working vacation stages. Customer arrives to the system with parameter λv which follows Poisson distribution and server provides service in regular busy period with parameter µrb and under the multiple working vacations it provides service with parameter µwv with exponential distribution. In this model batches of customers are served under General Bulk Service Rule. The system may breakdown at any time. The breakdown that occurs during working vacation is denoted as βv 1 and the breakdown during busy state is denoted as βv 2. The steady-state equation, the performance of measures for the system and particular cases of described model are derived. Finally, a real life example demonstrated the validity of the model in a proper way.

Sensitivity Analysis of Edible Oil Refinery Industry using Machine Learning

This research paper discusses the use of machine learning for sensitivity analysis in the edible oil refinery industry. The edible oil refinery consists of four units, and subsystem A (Cleaning) contains parallel subcomponents that enable it to function in reduced capacity when some of its components fail. As a result, the system operates in reduced capacity and fails entirely when unit A fails. There is single repairman who is available for 24x7. The failure and repair time distributions are distinct and constant for each unit. Subunits B (Shelling), D (Crushing/Ribbing), and E (Expeller Pressing) are connected in series, so, if any of them malfunctions, the entire system fail. System parameters' behavior for various repair and failure rates is discussed graphically and in tabular form. Comparison of the Performance of system parameters is carried out using linear Classifier and Logistic Regression and graphs are drawn. From the comparative analysis of models, it is concluded that the linear classifier is better than logistic regression for MTSF, Busy Period of server and Availability.

On a retrial queue with negative customers, passive breakdown, and delayed repairs

AbstractThis paper studies an M/M/1 retrial queue with negative customers, passive breakdown, and delayed repairs. Assume that the breakdown behavior of the server during idle periods is different from that during busy periods. Passive breakdowns may occur when the server is idle, due to the lack of monitoring of the server during idle periods. When the passive breakdown occurs, the server does not get repaired immediately and enters a delayed repair phase. Negative customers arrive during the busy period, which will cause the server to break down and remove the serving customers. Under steady-state conditions, we obtain explicit expressions of the probability generating functions for the steady-state distribution, together with some important performance measures for the system. In addition, we present some numerical examples to illustrate the effects of some system parameters on important performance measures and the cost function. Finally, based on the reward-cost structure, we discuss Nash equilibrium and socially optimal strategy and numerically analyze the influence of system parameters on optimal strategies and optimal social benefits.

Analisis Sistem Antrian pada Pelayanan Customer Service (Studi Kasus: PT Bank BRI Cabang Raha)

Analisis Sistem Antrian pada Pelayanan Customer Service (Studi Kasus: PT Bank BRI Cabang Raha)

A multi-server retrial queueing-inventory system with asynchronous multiple vacations

This study deals with asynchronous server vacation and customer retrial facilities in a multi-server queueing-inventory system. Customers arrive according to a Poisson process. The system comprises identical servers, a finite-size waiting area, and a storage area. The service time is distributed exponentially. If each server finds insufficient customers and items in the system after the busy period, they start a vacation. Once the server’s vacation is over and it recognizes there is no chance of getting busy, it goes into an idle state; otherwise, it will take another vacation. Each server’s vacation period occurs independently of the other servers. The system accepts a control policy for inventory replenishment. For the steady-state analysis, Neuts and Rao’s matrix geometric approximation approach is used owing to the structure of an infinitesimal generator matrix. The necessary stability condition is computed. After calculating the sufficient system performance measures, an expected total cost of the system will be constructed and numerically incorporated with the parameters. Additional numerical analyses are conducted to examine customers’ waiting time in the queue and orbit and the expected customer loss rate.

A-316 Suboptimal Compliance to Postpartum Glucose Monitoring in a High-risk Pregnancy Population - A Single Center Study

Abstract Background Gestational diabetes mellitus (GDM) is a predictive factor in developing type 2 diabetes mellitus (T2DM) in affected mothers and their offspring. Its prevalence is increasing proportionally with the obesity epidemic, affecting 10% of pregnant women and 50% of which are likely to develop T2DM. Current guidelines by the American Diabetes Association and the American College of Obstetricians and Gynecologists recommend screening at 4–12 weeks with a 2-hour postpartum glucose tolerance test (OGTT) in patients with a history of GDM. However, several studies have reported suboptimal test ordering and completion rates attributable to the busy postpartum period and provider role confusion between primary care physicians and obstetricians. Due to the complex maternal-fetal cases encountered at our institution, the aim of this study is to evaluate the ordering and test completion rates amongst care providers and patients to ensure compliance with stipulated guidelines. Method We conducted a retrospective audit of women diagnosed with GDM who delivered at our institution from Jan 2019–Oct 2022. We abstracted data from electronic health records. Gestational diabetes was defined by one or more of the following: abnormal 3hr OGTT or 1-hour OGTT of >/=200 mg/dL at >/= 24 weeks. We excluded patients with pre-existing diabetes defined by diagnosis code or by an abnormal 1st trimester 3hr GTT or HbA1C and patients who did not return for a postpartum visit. We compared the proportions of patients with postpartum glucose monitoring orders (glucose tolerance tests or Hemoglobin A1C) to those without orders. Factors such as race, GDM management, provider type and insurance carrier were assessed as potential barriers to non-compliance. Results We identified 356 patients who were diagnosed with GDM during the study period. Of these, 158 patients were excluded who had pre-existing diabetes or did not return for postpartum care. The mean (SD) maternal age was 33.2 (6.0) years. Seventy-four percent (147/198) of patients had a postpartum glucose tolerance test order (Group A), and 26% (51/198) had no laboratory order for glucose monitoring (Group B). The proportion of patients with a completed test order was 24% (35/147), of which four results were abnormal (indicated for diabetes or pre-diabetes). There was no difference in parity, ethnicity, insurance type, diabetes management and provider type between the two groups. Poor compliance was observed in patients with glucose tolerance laboratory orders, while patients with an HbA1c order were 100% compliant. Conclusion Overall, this report demonstrates poor patient compliance with postpartum glucose tolerance testing. Although HbA1C is not recommended for postpartum glucose monitoring, patients were more likely to complete this test.

Analysis of a GIX/M/1 queue with two-stage vacation policy using shift operator method

In this paper, we investigate a GI X /M/1 queue with the two-stage vacation policy. The system will first enter a working vacation once the system becomes empty in the normal busy period, during which the service rate will be switched to a lower rate. After this working vacation, if the system is nonempty, the service rate will be switched to the normal rate immediately; otherwise, the system will enter multiple vacations during which the service rate reduces to zero until the system is nonempty after one vacation and a new normal busy period starts. The distinguishing feature of this paper is the use of a general algorithm for solving the difference equation based on the right shift operator method to obtain the queue length distribution at pre-arrival time and arbitrary time. Moreover, the sojourn time of arbitrary customer is analyzed. Finally, several typical numerical examples are provided to validate our computational algorithm.

M/M/1 Non-preemptive Priority Queuing System with Multiple Vacations and Vacation Interruptions

Non-preemptive priority queue system is a type of priority queue where customers with higher priorities cannot interrupt low priority one while being served. High priority consumers will still be at the head of the queue. This article discusses the non-preemptive priority queue system with multiple working vacations, where the vacation can be interrupted. Customers are classified into two classes, namely class I (non-preemptive priority customers) and class II, with exponentially distributed service rates. Customers will still receive services at a slower rate than during normal busy periods when they enter the system while it is on vacation. Suppose other customers are waiting in the queue after completing service on vacation. In that case, the vacation will be interrupted, and the service rate will switch to the busy period service rate. The model's performance measurements are obtained using the complementary variable method and analyzing the state change equation following the birth and death processes to find probability generating function for both classes. The results of the numerical solution show that the expected value number of customers and waiting time of customers in the queue for both class customers will be reduced when the vacation times rate (θ) and the vacation service rate (μ_0 ) increase.

Bosnian-Turkish Relations and Turkey's Role in the Bosnian Conflict Resolution (1992-1995)

The Bosnian crisis is one of the last major military conflicts in European history. The disintegration of Yugoslavia has laid the foundation for many of the processes taking place in the Balkan peninsula to this day. For the Bosnian side, the key factor influencing the outcome of the conflict was the intervention of external actors. Turkey has become one of Bosnia’s most active allies at this stage. This was due to many factors, including religious and cultural affinity, historical connections and geopolitical interests of Turkey in the Balkans, and the long-standing personal ties of political leaders. Moreover, the fact of the emergence of an Islamic state in Europe and, secondly, the attempt to adapt Turkey to the post-bipolar format of the world order seem to be the most important factors in Turkey’s Bosnian policy. This work is devoted to a brief but busy period of cooperation between Turkey and Bosnia and Herzegovina during the Bosnian War, during which the Bosniacs sought the status of an independent state. The subject of the study was the foreign policy contacts between Turkey and Bosnia (the official name at the period of war — the Republic of Bosnia and Herzegovina) aimed at settling the conflict. The various initiatives of the Turkish side at the level of the OIC, the United Nations, or in the framework of bilateral negotiations with different countries (USA, Russia, Croatia, etc.) are clear examples of such cooperation. Such actions contributed to the further signing of the peace agreements, as well as to the direction of Bosnian-Turkish relations at the present stage.

Reliability analysis and optimization design of a repairable k-out-of-n retrial system with two failure modes and preventive maintenance

This article deals with a repairable k-out-of-n: G system with retrial feature and two maintenance policies. All components in the system have two failure modes, mode a failure and mode b failure. When a component fails, the failed component will be repaired instantly if the repair equipment is idle. Otherwise, it enters into a retrial orbit and tries again after some time until it is repaired. The single repair equipment may be subject to breakdown in a busy period, and in order to improve system reliability, the idle repair equipment will be performed preventive maintenance. The Markov process theory and Laplace transform method are adopted to compute the reliability indexes of the system. Also, four optimization design models are constructed to determine the optimal repair rates of the components with two failure modes, and the minimization problems of the total expected cost function per unit time and the cost-effectiveness ratio are solved. To verify the correctness of the model, numerical analysis is executed to demonstrate the impact of each parameter on system reliability indexes, the optimal solutions of different optimization design models are obtained by using differential evolution algorithm and genetic algorithm.

Patient safety in emergency departments: a problem for health care systems? An international survey.

Patient safety in healthcare is one of the cornerstones of quality of care. The emergency department (ED) is by its very nature a place where errors and safety issues are liable to occur. The aim of the study was to assess health professionals' perception of the level of safety in EDs and to identify in which work domains safety appears most at risk. Between 30 January and 27 February 2023, a survey addressing the main domains of safety was distributed to ED health care professionals through the European Society of Emergency Medicine contact network. It addressed five main domains: teamwork, safety leadership, physical environment and equipment, staff/external teams, and organisational factors and informatics, with a number of items for each domain. Further questions about infection control and team morale were added. The Cronbach's alpha measure was calculated to assure internal consistency. A score was developed for each domain by adding the question's value using the following ranking: never (1), rarely (2), sometimes (3), usually (4), and always (5) and was aggregated in three categories. The calculated sample size needed was 1000 respondents. The Wald method was used for analysis of the questions' consistency and X2 for the inferential analysis. The survey included 1256 responses from 101 different countries; 70% of respondents were from Europe. The survey was completed by 1045 (84%) doctors and 199 (16%) nurses. It was noted that 568 professionals (45.2%) had less than 10 years' experience. Among respondents, 80.61% [95% confidence interval (CI) 78.42-82.8] reported that monitoring devices were available, and 74.7% (95% CI 72.28-77.11) reported that protocols for high-risk medication and for triage (66.19%) were available in their ED. The area of greatest concern was the disproportionate imbalance between needs and the availability of staff at times of greatest flow, considered sufficient by only 22.4% (95% CI 20.07-24.69) of doctors and 20.7% (95% CI 18.41-22.9) of nurses. Other critical issues were overcrowding due to boarding and a perceived lack of support from hospital management. Despite these difficult working conditions, 83% of the professionals said they were proud to work in the ED (95% CI 81.81-85.89). This survey highlighted that most health professionals identify the ED as an environment with specific safety issues. The main factors appeared to be a shortage of personnel during busy periods, overcrowding due to boarding, and a perceived lack of support from hospital management.

Strategic Analysis of Retrial Queues with Setup Times, Breakdown and Repairs

This paper considers a repairable M/M/1 retrial queueing model with setup times. Once the system is empty, the server will be closed down to reduce operating costs. And the system will be activated only when a new customer arrives. The customer who activates the server will enter the retrial orbit waiting to reapply for service. The server may break down during the busy period. First, the steady-state probability of the model is obtained by using the probability generating function method. And we derive performance measures of the system such as the queue length of the orbit, the numerical examples are given to show the sensitivity of the performance measures. Second, the cost function is established to find the minimum cost of the system, and we study the effects of some parameters on the cost by numerical examples. Finally, from the perspective of the customer and social planner, we construct the individual utility function and the social welfare function in the almost and fully unobservable cases, and then the optimal strategy of the customers is analyzed.

QUEUE SYSTEM ANALYSIS IN SERVICE OPTIMIZATION IN PT. BANK SULSELBAR MAIN BRANCH MAKASSAR CITY

PT. Bank Sulselbar is a regionally owned business entity engaged in banking services. Companies in the service sector must be able to provide the best service to meet the wishes of customers who require fast service. As the number of customers increases, there are queuing problems in serving customers, this problem results in many customers waiting for quite a long time. For this reason, this study aims to reduce the length of time waiting for customers to avoid queues that are too long . This research uses queuing theory analysis method with queuing model (M/M/S). The results of this study using queuing theory analysis, namely the model calculation (M/M/S) shows that the busy period occurs in the period 08.00-09.00, and 13.00-14.00 by adding 1 service facility from 6 to 7 customer service, there will be a decrease customer waiting time. The waiting time in the system in the time period of 08.00-09.00 from 25.15 minutes to 10.07 minutes, and the time period of 13.00-14.00 from 19.39 to 9.13 minutes

Comparative Analysis Between Three Reliability Models of a Two-Unit Complex Industrial System

This paper presents the reliability modelling and analysis of a complex industrial system with two units operating in parallel. To facilitate the study, real failure-maintenance data of the system arecollected. Data depicts that a unit is repaired upon failure by a single repairman. Reliability indices of the system such as mean time between failures, availability, expected number of repairs, and expected busy period of the repairman are estimated using semi-Markov processes and regenerative processes. Finally, a comparative analysis between the reliability indices of three reliability models for the system is presented.

Estimation of House Cleanup Work Volume Based on Disaster Volunteer Center Work Management Data —The Case of the 2015 Joso City—

To understand the workload of house cleanup and related workforce shortage after a disaster, the actual work situation in disaster-stricken areas is accounted for by disaster volunteer work management data created by the Disaster Volunteer Center of Joso City in Ibaraki Prefecture at the time of the Kanto–Tohoku Heavy Rain Disaster in September 2015. Using the classification of inundation depth, judged from ground elevation, the weekly workload of house cleanup according to the work content is recorded to clarify the characteristics of each area. Comparing this with the inundated areas without destructions by water flow, near the bank break with house destructions, in the urban area, and around the farmland along the old road, a model to estimate the workload is constructed. It was observed that indoor work to recommence living in urban areas continued for a long time, while the work was completed in a relatively short time in the area along the old road. The area near the bank break, with a small number of houses, witnessed very few house destructions. Hence, it is not necessary to separately calculate the workload caused by house destructions. The appropriateness of the estimated results was verified by using a method to estimate the workload based on the amount of disaster waste. As a result, the total workload estimated by disaster volunteers and victims for the busy period of two months was a million people. In the case of the Joso City flood, very few houses were completely destroyed, therefore, regular living could be resumed swiftly and people settled there after the disaster due to its proximity to the metropolitan area. Hence, the population decreased by the flood was recovered in two years.

An analytical approach of Markov modulated Poisson input with feedback queue and repeated service under N-policy with setup time

ABSTRACT In this paper, we analyze an queue with general server setup time under -policy based on the case that the arrival rates vary according to the server’s status and a customer can repeat the same type of service. After the completion of service, the customer can also repeat the service as a feedback if he/she is not satisfied with his/her service. The steady-state analysis of the system has been carried out using the supplementary variable technique. Further, the expected busy period has been also derived. Finally, numerical and graphical results are included to illustrate the impact of parameters on the behavior of the model.

A single server retrial queue with event-dependent arrival rates

In this work, we consider a novel single-server retrial queue with event-dependent arrival rates. Contrary to other related works, the primary customers’ arrival rates depend on the last realized event, which refers either to a departure, or to an arrival of either type, or to when a customer arrives during a busy period, compared with others. Our motivation stems from the modeling of service systems, in which the customers express their willingness to join the system based on the last realized event. We investigate the stability conditions, and derive the stationary distribution both at service completion epochs, and at an arbitrary epoch. We also study the asymptotic behaviour under high rate of retrials. Performance measures are explicitly derived, and extensive numerical examples are performed to investigate the impact of event-dependency. Moreover, constrained optimisation problems are formulated and solved with ultimate goal to derive optimal joining probabilities.