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 On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service

2005 ◽  
Vol 2005 (3) ◽  
pp. 123-135 ◽  
Author(s):  
Kailash C. Madan ◽  
Z. R. Al-Rawi ◽  
Amjad D. Al-Nasser
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Waiting Time ◽  
Busy Period ◽  
Single Server ◽  
Queue Size ◽  
Single Vacation ◽  
The Mean ◽  
Expected Waiting Time ◽  
Heterogeneous Service

We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoulli schedules under a single vacation policy. We obtain explicit queue size distribution at a random epoch as well as at a departure epoch and also the mean busy period of the server under the steady state. In addition, some important performance measures such as the expected queue size and the expected waiting time of a customer are obtained. Further, some interesting particular cases are also discussed.

scholarly journals Assessment of patients waiting and service times in the ophthalmology clinic of a public tertiary hospital in Nigeria

2020 ◽  
Vol 54 (4) ◽  
pp. 231-237
Author(s):  
Lateefat B. Olokoba ◽  
Kabir A. Durowade ◽  
Feyi G. Adepoju ◽  
Abdulfatai B. Olokoba
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Sampling Technique ◽  
Tertiary Hospital ◽  
Cross Sectional Study ◽  
Ethical Review ◽  
Cross Sectional ◽  
Arrival Times ◽  
The Mean ◽  
Service Times

Introduction: Long waiting time in the out-patient clinic is a major cause of dissatisfaction in Eye care services. This study aimed to assess patients’ waiting and service times in the out-patient Ophthalmology clinic of UITH. Methods: This was a descriptive cross-sectional study conducted in March and April 2019. A multi-staged sampling technique was used. A timing chart was used to record the time in and out of each service station. An experience based exit survey form was used to assess patients’ experience at the clinic. The frequency and mean of variables were generated. Student t-test and Pearson’s correlation were used to establish the association and relationship between the total clinic, service, waiting, and clinic arrival times. Ethical approval was granted by the Ethical Review Board of the UITH. Result: Two hundred and twenty-six patients were sampled. The mean total waiting time was 180.3± 84.3 minutes, while the mean total service time was 63.3±52.0 minutes. Patient’s average total clinic time was 243.7±93.6 minutes. Patients’ total clinic time was determined by the patients’ clinic status and clinic arrival time. Majority of the patients (46.5%) described the time spent in the clinic as long but more than half (53.0%) expressed satisfaction at the total time spent at the clinic. Conclusion: Patients’ clinic and waiting times were long, however, patients expressed satisfaction with the clinic times.

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 Some reflections on the Renewal-theory paradox in queueing theory

1998 ◽  
Vol 11 (3) ◽  
pp. 355-368 ◽  
Author(s):  
Robert B. Cooper ◽  
Shun-Chen Niu ◽  
Mandyam M. Srinivasan
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Waiting Times ◽  
Renewal Theory ◽  
Vacation Models ◽  
Polling Models ◽  
Mean Waiting Time ◽  
The Mean ◽  
Expository Paper ◽  
Set Up

The classical renewal-theory (waiting time, or inspection) paradox states that the length of the renewal interval that covers a randomly-selected time epoch tends to be longer than an ordinary renewal interval. This paradox manifests itself in numerous interesting ways in queueing theory, a prime example being the celebrated Pollaczek-Khintchine formula for the mean waiting time in the M/G/1 queue. In this expository paper, we give intuitive arguments that “explain” why the renewal-theory paradox is ubiquitous in queueing theory, and why it sometimes produces anomalous results. In particular, we use these intuitive arguments to explain decomposition in vacation models, and to derive formulas that describe some recently-discovered counterintuitive results for polling models, such as the reduction of waiting times as a consequence of forcing the server to set up even when no work is waiting.

On the stochastic ordering of waiting times for patterns in sequences of random digits

1984 ◽  
Vol 21 (4) ◽  
pp. 730-737 ◽  
Author(s):  
Gunnar Blom
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Stochastic Ordering ◽  
Mean Waiting Time ◽  
Coin Tossing ◽  
The Mean

Random digits are collected one at a time until a pattern with given digits is obtained. Blom (1982) and others have determined the mean waiting time for such a pattern. It is proved that when a given pattern has larger mean waiting time than another pattern, then the waiting time for the former is stochastically larger than that for the latter. An application is given to a coin-tossing game.

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.

THEORETICAL ANALYSIS OF MEAN WAITING TIME FOR MESSAGE DELIVERY IN LATTICE AD HOC NETWORKS

2010 ◽  
Vol 19 (08) ◽  
pp. 1711-1741
Author(s):  
AKIRA OTSUKA ◽  
KEISUKE NAKANO ◽  
KAZUYUKI MIYAKITA
Keyword(s):  
Ad Hoc Networks ◽  
Waiting Time ◽  
Ad Hoc ◽  
Waiting Times ◽  
Traffic Patterns ◽  
Mobile Nodes ◽  
Approximate Methods ◽  
Mean Waiting Time ◽  
The Mean ◽  
Hoc Networks

In ad hoc networks, the analysis of connectivity performance is crucial. The waiting time to deliver message M from source S to destination D is a measure of connectivity that reflects the effects of mobility, and some approximate methods have been proposed to theoretically analyze the mean waiting time in one-dimensional ad hoc networks that consist of mobile nodes moving along a street. In this paper, we extend these approximate methods to analyze the mean waiting time in two-dimensional networks with a lattice structure with various flows of mobile nodes. We discuss how the mean waiting times behave in such complicated street networks and how to approximate two kinds of mean waiting times. We show that our approximate methods can successfully compute the mean waiting times for even traffic patterns and roughly estimate them for uneven traffic patterns in two-dimensional lattice networks. In these analyses, we consider two shadowing models to investigate how shadowing affects the waiting time. We also discuss the effect of different positions of S on the mean waiting time.

scholarly journals Waiting Times for Prostate Cancer Diagnosis in a Nigerian Population

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Olufunmilade A. Omisanjo ◽  
Olawale O. Ogunremi ◽  
Olufemi O. Akinola ◽  
Olaolu O. Adebayo ◽  
Olufemi Ojewuyi ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Teaching Hospital ◽  
Cancer Diagnosis ◽  
Waiting Time ◽  
Prostate Biopsy ◽  
Waiting Times ◽  
Prostate Cancer Diagnosis ◽  
Nigerian Population ◽  
The Mean ◽  
Patient Presentation

Background. Prostate biopsy remains an important surgical procedure in the diagnostic pathway for prostate cancer, but access to prostate biopsy service is poorly studied in the Nigerian population. While there has been a well-documented delay in patient presentation with prostate cancer in Nigeria, little is however known about how long patients wait to have a histological diagnosis of prostate cancer and start treatment after presenting at Nigerian hospitals. Method. This was a descriptive retrospective study to document the specific duration of the various timelines in getting a diagnosis of prostate cancer at the Lagos State University Teaching Hospital, Ikeja, Nigeria. Results. There were 270 patients. The mean age was 69.50 ± 8.03   years (range 45-90). The mean PSA at presentation was 563.2 ± 1879.2   ng / ml (range 2.05-15400), and the median PSA was 49.3 ng/ml. The median waiting times were (i) 10 days from referral to presentation; (ii) 30 days from presentation to biopsy; (iii) 24 days from biopsy to review of histology; (iv) 1 day from histology review to discussion/planning of treatment. The median overall waiting time from referral to treatment was 103 days. The mean time from presentation to biopsy was significantly shorter for patients with PSA of ≥50 ng/ml compared to those with PSA < 50   ng / ml . p = 0.048 . Overall, the median time from biopsy to histology was significantly shorter for patients whose specimens were processed in private laboratories (17 days) compared to those whose specimens were processed at the teaching hospital laboratory (30 days), p ≤ 0.001 . Conclusion. There is a significant delay within the health care system in getting a prostate cancer diagnosis in the Nigerian population studied. The major points of the identified delay were the waiting time from patient presentation to having a biopsy done and the histology report waiting time.

scholarly journals Managing Queues with Heterogeneous Servers

2011 ◽  
Vol 48 (2) ◽  
pp. 435-452 ◽  
Author(s):  
Jung Hyun Kim ◽  
Hyun-Soo Ahn ◽  
Rhonda Righter
Keyword(s):  
Waiting Time ◽  
Waiting Times ◽  
Structural Result ◽  
Batch Arrivals ◽  
Optimal Thresholds ◽  
Mean Waiting Time ◽  
Server Problem ◽  
The Mean ◽  
The Impact ◽  
Intuitive Proof

We consider several versions of the job assignment problem for an M/M/m queue with servers of different speeds. When there are two classes of customers, primary and secondary, the number of secondary customers is infinite, and idling is not permitted, we develop an intuitive proof that the optimal policy that minimizes the mean waiting time has a threshold structure. That is, for each server, there is a server-dependent threshold such that a primary customer will be assigned to that server if and only if the queue length of primary customers meets or exceeds the threshold. Our key argument can be generalized to extend the structural result to models with impatient customers, discounted waiting time, batch arrivals and services, geometrically distributed service times, and a random environment. We show how to compute the optimal thresholds, and study the impact of heterogeneity in server speeds on mean waiting times. We also apply the same machinery to the classical slow-server problem without secondary customers, and obtain more general results for the two-server case and strengthen existing results for more than two servers.

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

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