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 Applications of Queuing Theory in Quantitative Business Analysis

2020 ◽  
pp. 253-257
Keyword(s):  
Quantitative Analysis ◽  
Waiting Time ◽  
Queuing Theory ◽  
Single Channel ◽  
Analysis Approach ◽  
Single Server ◽  
Expected Number ◽  
Queuing Model ◽  
Infinite Population ◽  
Expected Waiting Time

Queuing Theory provides the system of applications in many sectors in life cycle. Queuing Structure and basic components determination is computed in queuing model simulation process. Distributions in Queuing Model can be extracted in quantitative analysis approach. Differences in Queuing Model Queue discipline, Single and Multiple service station with finite and infinite population is described in Quantitative analysis process. Basic expansions of probability density function, Expected waiting time in queue, Expected length of Queue, Expected size of system, probability of server being busy, and probability of system being empty conditions can be evaluated in this quantitative analysis approach. Probability of waiting ‘t’ minutes or more in queue and Expected number of customer served per busy period, Expected waiting time in System are also computed during the Analysis method. Single channel model with infinite population is used as most common case of queuing problems which involves the single channel or single server waiting line. Single Server model with finite population in test statistics provides the Relationships used in various applications like Expected time a customer spends in the system, Expected waiting time of a customer in the queue, Probability that there are n customers in the system objective case, Expected number of customers in the system

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.”

A note on the convexity of performance measures of M/M/c queueing systems

1983 ◽  
Vol 20 (04) ◽  
pp. 920-923 ◽  
Author(s):  
Hau Leung Lee ◽  
Morris A. Cohen
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Control Problems ◽  
Traffic Intensity ◽  
Expected Number ◽  
Expected Waiting Time

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

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

scholarly journals Primes in short arithmetic progressions

2015 ◽  
Vol 11 (05) ◽  
pp. 1499-1521 ◽  
Author(s):  
Dimitris Koukoulopoulos
Keyword(s):  
Arithmetic Progression ◽  
Arithmetic Progressions ◽  
Real Numbers ◽  
Expected Number ◽  
Positive Real

Let x, h and Q be three parameters. We show that, for most moduli q ≤ Q and for most positive real numbers y ≤ x, every reduced arithmetic progression a( mod q) has approximately the expected number of primes p from the interval (y, y + h], provided that h > x1/6+ϵ and Q satisfies appropriate bounds in terms of h and x. Moreover, we prove that, for most moduli q ≤ Q and for most positive real numbers y ≤ x, there is at least one prime p ∈ (y, y + h] lying in every reduced arithmetic progression a( mod q), provided that 1 ≤ Q2 ≤ h/x1/15+ϵ.

scholarly journals Multi-Channel Preemptive Priority Model for Spectrum Mobility in Cognitive Radio Networks

2018 ◽  
Vol 8 (6) ◽  
pp. 5169
Author(s):  
S. E. Saad ◽  
I. F. Tarrad ◽  
A. A. Ammar
Keyword(s):  
Cognitive Radio ◽  
Cognitive Radio Networks ◽  
Waiting Time ◽  
Radio Networks ◽  
Preemptive Priority ◽  
Expected Number ◽  
Secondary Users ◽  
Basic Model ◽  
Proposed Model ◽  
Expected Waiting Time

Cognitive Radio techniques have been proposed for improving utilization of the spectrum by exploiting the unoccupied bands of the licensed spectrum. This paper proposes a preemptive multi-channel access model for prioritized cognitive radio networks using an iterative method of queuing theory to solve the spectrum scarcity problem. The proposed model formulates accurate closed form of an expected waiting time in the queue, an expected number of users in the queue, an expected waiting time in the system, and an expected number of users in the system. The results compared to the basic model (without preemptive priority) show that, the waiting time in queue and the waiting time in the system compared to the basic model will be improved by 92.99% and 33.15% respectively for class one secondary user. The results also show that, the waiting time in queue and the waiting time in the system will be improved by 43.25% and 15.42% respectively for class two secondary users. The proposed model investigates the desirable schedules of primary and secondary users.

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.

A note on the convexity of performance measures of M/M/c queueing systems

1983 ◽  
Vol 20 (4) ◽  
pp. 920-923 ◽  
Author(s):  
Hau Leung Lee ◽  
Morris A. Cohen
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Control Problems ◽  
Traffic Intensity ◽  
Expected Number ◽  
Expected Waiting Time

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

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.

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