Concurrent sequences of Bernoulli trials

2020 ◽  
Vol 104 (561) ◽  
pp. 435-448
Author(s):  
Stephen Kaczkowski
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Lottery Ticket ◽  
Bernoulli Trials ◽  
Expectation Values ◽  
Theoretical Probability ◽  
Expected Waiting Time

Probability and expectation are two distinct measures, both of which can be used to indicate the likelihood of certain events. However, expectation values, which are often associated with waiting times for success, may, at times, speak more clearly and poignantly about the uncertainty of an event than a theoretical probability. To illustrate the point, suppose the probability of choosing a winning lottery ticket is 2.5 × 10−8. This information may not communicate the unlikely odds of winning as clearly as a statement like, “If five lottery tickets are purchased per day, the expected waiting time for a first win is about 22000 years.”

scholarly journals Waiting Times and Defining Customer Satisfaction

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
T.M.B. Palawatta
Keyword(s):  
Customer Satisfaction ◽  
Waiting Time ◽  
Waiting Times ◽  
Important Variable ◽  
Time Study ◽  
Continuous Variables ◽  
Review Of Literature ◽  
Definition Of ◽  
Expected Waiting Time

Review of literature shows that there is no agreement about the definition of probably the most important, variable Satisfaction/Dissatisfaction. Satisfaction /Dissatisfaction equals Expectation minus Perception is the most widely used definition today. In this definition, there are a number of issues that have to be resolved. First, what exactly Satisfaction is? Is it disconfirmation? That is the gap between expectation and perception. Is it expectation? Or, is it perception? Further, there is no concrete definition about the expectation. Is it predicted service? Is it adequate service? In this study, the definition of satisfaction/dissatisfaction was tested using continuous variables expected waiting time, perceived waiting time, prior predicted waiting time, posterior predicted waiting time and the acceptable waiting time. Study found that disconfirmation between expected waiting time and the perceived waiting time is the best definition for satisfaction/dissatisfaction followed by expected waiting time and perceived waiting time. However, the influence of perceived waiting time is nearly negligible. Therefore, defining satisfaction/dissatisfaction as disconfirmation between expectation and perception is most appropriate. Furthermore, the study found that expectation is not prediction and is also not the acceptable (adequate) service.KeywordsExpectation, Perception, Satisfaction, Waiting Time

Public art and public space – Waiting stress and waiting pleasure

2015 ◽  
Vol 27 (1) ◽  
pp. 69-91 ◽  
Author(s):  
Harald Klingemann ◽  
Arne Scheuermann ◽  
Kurt Laederach ◽  
Birgit Krueger ◽  
Eric Schmutz ◽  
...  
Keyword(s):  
Public Space ◽  
Waiting Time ◽  
Waiting Times ◽  
Waiting Room ◽  
Surface Design ◽  
Social Time ◽  
Holistic Concept ◽  
Stress Behaviour ◽  
Expected Waiting Time ◽  
The Impact

The study presented here applies from an interdisciplinary perspective the “temporal know-how” of art and communication design as well as the social sciences to the exploration of the impact of two types of holistic artistic waiting room transformations on waiting experience and behaviour. The quasi-experiment was conducted in a hospital and in an administrative setting. Contrary to current information centred types of waiting management stressing ‘clock-time’ only and attempting to reduce objective waiting times, the artistic intervention follows a holistic concept by appealing to all the senses influencing felt time and social time. It comprises visual, acoustic, tactile/haptic and olfactory elements (fragrance management). The “observation-oriented” artistic intervention uses contemplative video works, ornamentation, relaxing fragrances and a corresponding seating design. The “action-oriented” room climate promotes communication and stimulating object and surface design, coupled with a subliminally stimulating fragrance environment. After a simultaneous one-week baseline measurement in both organizations, follow-up measures were conducted during one week of each type of intervention. Results are based on 482 personal interviews and 1950 observations of waiting clients: Perceived waiting time and objective waiting time correlated only moderately (rp = 56) and expected waiting time was overestimated. In both waiting room settings, room transformations – compared to baseline measures – reduced waiting stress behaviour (however not perceived stress) and increased both positive overall room perception and the evaluation of specific room characteristics among clients/patients. Differences between the two room climates were not significant and effects appear to be stronger in the administrative space. The relatively short waiting times (16–20 min) and high levels of waiting satisfaction at baseline might have limited the effect size of the holistic interventions. At the same time observed positive outcomes can be plausibly expected in waiting zones with much longer waiting times.

scholarly journals The weighted words collector

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Jérémie Du Boisberranger ◽  
Danièle Gardy ◽  
Yann Ponty
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
General Theorem ◽  
General Version ◽  
Real Numbers ◽  
Expected Number ◽  
Positive Real ◽  
Coupon Collector ◽  
International Audience ◽  
Expected Waiting Time

International audience We consider the word collector problem, i.e. the expected number of calls to a random weighted generator before all the words of a given length in a language are generated. The originality of this instance of the non-uniform coupon collector lies in the, potentially large, multiplicity of the words/coupons of a given probability/composition. We obtain a general theorem that gives an asymptotic equivalent for the expected waiting time of a general version of the Coupon Collector. This theorem is especially well-suited for classes of coupons featuring high multiplicities. Its application to a given language essentially necessitates knowledge on the number of words of a given composition/probability. We illustrate the application of our theorem, in a step-by-step fashion, on four exemplary languages, whose analyses reveal a large diversity of asymptotic waiting times, generally expressible as $\kappa \cdot m^p \cdot (\log{m})^q \cdot (\log \log{m})^r$, for $m$ the number of words, and $p, q, r$ some positive real numbers.

scholarly journals Success Run Waiting Times and Fuss-Catalan Numbers

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
S. J. Dilworth ◽  
S. R. Mane
Keyword(s):  
Power Series ◽  
Waiting Time ◽  
Geometric Distribution ◽  
Waiting Times ◽  
Exact Expression ◽  
Catalan Numbers ◽  
Auxiliary Equation ◽  
Bernoulli Trials ◽  
Asymptotic Results ◽  
Success Run

We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run ofkconsecutive successes in a sequence of independent Bernoulli trials, that is, the geometric distribution of orderk. We show that the series coefficients are Fuss-Catalan numbers and write the roots in terms of the generating function of the Fuss-Catalan numbers. Our main result is a new exact expression for the distribution, which is more concise than previously published formulas. Our work extends the analysis by Feller, who gave asymptotic results. We obtain quantitative improvements of the error estimates obtained by Feller.

scholarly journals Modelling the Mean Waiting Times for Queues in Selected Banks in Eldoret Town-Kenya

2019 ◽  
pp. 1-9
Author(s):  
Kenneth Kibet Karoney ◽  
Mathew K. Kosgei ◽  
Kennedy L. Nyongesa
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Waiting Times ◽  
Mathematical Study ◽  
Stochastic Delay ◽  
Time Bank ◽  
The Mean ◽  
Traffic Delay ◽  
To Come ◽  
Expected Waiting Time

The mathematical study of waiting lines is mainly concerned with queue performance measures where several applications have been drawn in past studies. Among the vast uses and applications of the theory of queuing system in banking halls, is the main focus of this study where the theory has been used to solve the problem of long queues as witnessed in banks leads to resource waste. The study aims to model the waiting times for queues in selected banks within Eldoret town, Kenya. The latter component was put under D/D/1 framework and therein its mean derived while the stochastic component was put under the M/M/c framework. Harmonization of the moments of the deterministic and the stochastic components was done to come up with the mean of the overall bank queue traffic delay. The simulation was performed using MATLAB for traffic intensities ranging from 0.1 to 1.9. The results reveal that both deterministic and the stochastic delay components are compatible in modelling waiting time. The models also are applicable to real-time bank queue data whereupon simulation, both models depict fairly equal waiting times for server utilisation factors below 1 and an infinitely increasing delay at rho greater than 1. In conclusion, the models that estimate waiting time were developed and applied on real bank queue data. The models need to be implemented by the banks in their systems so that customers are in a position to know the expected waiting time to be served as soon as they get the ticket from the ticket dispenser.

scholarly journals Interhospital referral of colorectal cancer patients: a Dutch population-based study

2021 ◽  
Author(s):  
A. K. Warps ◽  
◽  
M. P. M. de Neree tot Babberich ◽  
E. Dekker ◽  
M. W. J. M. Wouters ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Cancer Patients ◽  
Waiting Time ◽  
Secondary Care ◽  
Advanced Disease ◽  
Waiting Times ◽  
Tertiary Care ◽  
Disease Stage ◽  
Colorectal Cancer Patients ◽  
Tertiary Care Hospitals

Abstract Purpose Interhospital referral is a consequence of centralization of complex oncological care but might negatively impact waiting time, a quality indicator in the Netherlands. This study aims to evaluate characteristics and waiting times of patients with primary colorectal cancer who are referred between hospitals. Methods Data were extracted from the Dutch ColoRectal Audit (2015-2019). Waiting time between first tumor-positive biopsy until first treatment was compared between subgroups stratified for referral status, disease stage, and type of hospital. Results In total, 46,561 patients were included. Patients treated for colon or rectal cancer in secondary care hospitals were referred in 12.2% and 14.7%, respectively. In tertiary care hospitals, corresponding referral rates were 43.8% and 66.4%. Referred patients in tertiary care hospitals were younger, but had a more advanced disease stage, and underwent more often multivisceral resection and simultaneous metastasectomy than non-referred patients in secondary care hospitals (p<0.001). Referred patients were more often treated within national quality standards for waiting time compared to non-referred patients (p<0.001). For referred patients, longer waiting times prior to MDT were observed compared to non-referred patients within each hospital type, although most time was spent post-MDT. Conclusion A large proportion of colorectal cancer patients that are treated in tertiary care hospitals are referred from another hospital but mostly treated within standards for waiting time. These patients are younger but often have a more advanced disease. This suggests that these patients are willing to travel more but also reflects successful centralization of complex oncological patients in the Netherlands.

scholarly journals E-Triage Systems for COVID-19 Outbreak: Review and Recommendations

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2845
Author(s):  
Fahd Alhaidari ◽  
Abdullah Almuhaideb ◽  
Shikah Alsunaidi ◽  
Nehad Ibrahim ◽  
Nida Aslam ◽  
...  
Keyword(s):  
Population Growth ◽  
Disease Severity ◽  
Waiting Time ◽  
Transmission Rate ◽  
Waiting Times ◽  
Triage System ◽  
Disease Symptoms ◽  
Comprehensive Review ◽  
Severity Levels ◽  
Growth And Aging

With population growth and aging, the emergence of new diseases and immunodeficiency, the demand for emergency departments (EDs) increases, making overcrowding in these departments a global problem. Due to the disease severity and transmission rate of COVID-19, it is necessary to provide an accurate and automated triage system to classify and isolate the suspected cases. Different triage methods for COVID-19 patients have been proposed as disease symptoms vary by country. Still, several problems with triage systems remain unresolved, most notably overcrowding in EDs, lengthy waiting times and difficulty adjusting static triage systems when the nature and symptoms of a disease changes. In this paper, we conduct a comprehensive review of general ED triage systems as well as COVID-19 triage systems. We identified important parameters that we recommend considering when designing an e-Triage (electronic triage) system for EDs, namely waiting time, simplicity, reliability, validity, scalability, and adaptability. Moreover, the study proposes a scoring-based e-Triage system for COVID-19 along with several recommended solutions to enhance the overall outcome of e-Triage systems during the outbreak. The recommended solutions aim to reduce overcrowding and overheads in EDs by remotely assessing patients’ conditions and identifying their severity levels.

493 Evaluation of Patient Waiting Times for Plain Radiographs Whilst Attending Outpatient Clinics in A Tertiary Orthopaedic Centre

2021 ◽  
Vol 108 (Supplement_2) ◽  
Author(s):  
Z Hayat ◽  
E Kinene ◽  
S Molloy
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Time Frame ◽  
Outpatient Clinics ◽  
Contributing Factors ◽  
Time Data ◽  
Work Related ◽  
Mean Waiting Time ◽  
Appointment Time ◽  
Related Stress

Abstract Introduction Reduction of waiting times is key to delivering high quality, efficient health care. Delays experienced by patients requiring radiographs in orthopaedic outpatient clinics are well recognised. Method To establish current patient and staff satisfaction, questionnaires were circulated over a two-week period. Waiting time data was retrospectively collected including appointment time, arrival time and the time at which radiographs were taken. Results 84% (n = 16) of radiographers believed patients would be dissatisfied. However, of the 296 patients questioned, 56% (n = 165) were satisfied. Most patients (89%) felt the waiting time should be under 30 minutes. Only 36% were seen in this time frame. There was moderate negative correlation (R=-0.5); higher waiting times led to increased dissatisfaction. Mean waiting time was 00:37 and the maximum 02:48. Key contributing factors included volume of patients, staff shortages (73.7%), equipment shortages (57.9%) and incorrectly filled request forms. Eight (42.1%) had felt unwell from work related stress. Conclusions A concerted effort is needed to improve staff and patient opinion. There is scope for change post COVID. Additional training and exploring ways to avoid overburdening the department would benefit. Numerous patients were open to different days or alternative sites. Funding requirements make updating equipment, expanding the department and recruiting more staff challenging.

Some general results for many server queues

1973 ◽  
Vol 5 (01) ◽  
pp. 153-169 ◽  
Author(s):  
J. H. A. De Smit
Keyword(s):  
Integral Equations ◽  
Waiting Time ◽  
Queue Length ◽  
Joint Distribution ◽  
Waiting Times ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
Many Server Queues ◽  
The Many ◽  
Busy Cycle

Pollaczek's theory for the many server queue is generalized and extended. Pollaczek (1961) found the distribution of the actual waiting times in the model G/G/s as a solution of a set of integral equations. We give a somewhat more general set of integral equations from which the joint distribution of the actual waiting time and some other random variables may be found. With this joint distribution we can obtain distributions of a number of characteristic quantities, such as the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. For a wide class of many server queues the formal expressions may lead to explicit results.

HOW TO REPORT AND MONITOR THE PERFORMANCE OF WAITING LIST MANAGEMENT

2002 ◽  
Vol 18 (3) ◽  
pp. 611-618
Author(s):  
Markus Torkki ◽  
Miika Linna ◽  
Seppo Seitsalo ◽  
Pekka Paavolainen
Keyword(s):  
Hallux Valgus ◽  
Waiting Time ◽  
Varicose Vein ◽  
Elective Surgery ◽  
Waiting Times ◽  
Waiting List ◽  
Mean Waiting Time ◽  
Number Of Patients ◽  
Potential Problems ◽  
Queue Discipline

Objectives: Potential problems concerning waiting list management are often monitored using mean waiting times based on empirical samples. However, the appropriateness of mean waiting time as an indicator of access can be questioned if a waiting list is not managed well, e.g., if the queue discipline is violated. This study was performed to find out about the queue discipline in waiting lists for elective surgery to reveal potential discrepancies in waiting list management. Methods: There were 1,774 waiting list patients for hallux valgus or varicose vein surgery or sterilization. The waiting time distributions of patients receiving surgery and of patients still waiting for an operation are presented in column charts. The charts are compared with two model charts. One model chart presents a high queue discipline (first in—first out) and another a poor queue discipline (random) queue. Results: There were significant differences in waiting list management across hospitals and patient categories. Examples of a poor queue discipline were found in queues for hallux valgus and varicose vein operations. Conclusions: A routine waiting list reporting should be used to guarantee the quality of waiting list management and to pinpoint potential problems in access. It is important to monitor not only the number of patients in the waiting list but also the queue discipline and the balance between demand and supply of surgical services. The purpose for this type of reporting is to ensure that the priority setting made at health policy level also works in practise.

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