A sample path analysis of the M/M/1 queue

1989 ◽  
Vol 26 (02) ◽  
pp. 418-422 ◽  
Author(s):  
Francois Baccelli ◽  
William A. Massey
Keyword(s):  
Generating Functions ◽  
Queueing Networks ◽  
Transient Analysis ◽  
Bessel Functions ◽  
Sample Path ◽  
Laplace Transforms ◽  
Sample Path Analysis ◽  
Transient Distribution ◽  
The Past ◽  
Novel Approach

The exact solution for the transient distribution of the queue length and busy period of the M/M/1 queue in terms of modified Bessel functions has been proved in a variety of ways. Methods of the past range from spectral analysis (Lederman and Reuter (1954)), combinatorial arguments (Champernowne (1956)), to generating functions coupled with Laplace transforms (Clarke (1956)). In this paper, we present a novel approach that ties the computation of these transient distributions directly to the random sample path behavior of the M/M/1 queue. The use of Laplace transforms is minimized, and the use of generating functions is eliminated completely. This is a method that could prove to be useful in developing a similar transient analysis for queueing networks.

A sample path analysis of the M/M/1 queue

1989 ◽  
Vol 26 (2) ◽  
pp. 418-422 ◽  
Author(s):  
Francois Baccelli ◽  
William A. Massey
Keyword(s):  
Generating Functions ◽  
Queueing Networks ◽  
Transient Analysis ◽  
Bessel Functions ◽  
Sample Path ◽  
Laplace Transforms ◽  
Sample Path Analysis ◽  
Transient Distribution ◽  
The Past ◽  
Novel Approach

The exact solution for the transient distribution of the queue length and busy period of the M/M/1 queue in terms of modified Bessel functions has been proved in a variety of ways. Methods of the past range from spectral analysis (Lederman and Reuter (1954)), combinatorial arguments (Champernowne (1956)), to generating functions coupled with Laplace transforms (Clarke (1956)). In this paper, we present a novel approach that ties the computation of these transient distributions directly to the random sample path behavior of the M/M/1 queue. The use of Laplace transforms is minimized, and the use of generating functions is eliminated completely. This is a method that could prove to be useful in developing a similar transient analysis for queueing networks.

Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations

2018 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
Jia Xu ◽  
Liwei Liu ◽  
Taozeng Zhu
Keyword(s):  
Generating Functions ◽  
Transient Analysis ◽  
Bessel Functions ◽  
Queueing System ◽  
System Size ◽  
Heterogeneous Servers ◽  
Modified Bessel Functions ◽  
Multiple Vacations ◽  
Special Cases ◽  
Mean And Variance

AbstractWe consider anM/M/2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities, mean and variance of the system size at timetby employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

Extraordinary circumstances: Covid-19 – Italian Serie A scenario

2021 ◽  
pp. 175433712110192
Author(s):  
Milan Radojicic ◽  
Aleksandar Djokovic ◽  
Nikola Cvetkovic
Keyword(s):  
Cluster Analysis ◽  
Hierarchical Cluster Analysis ◽  
Hierarchical Cluster ◽  
Round Robin ◽  
The Past ◽  
Novel Approach ◽  
Round Robin Tournaments

Unpredictable and uncontrollable situations have happened throughout history. Inevitably, such situations have an impact on various spheres of life. The coronavirus disease 2019 has affected many of them, including sports. The ban on social gatherings has caused the cancellation of many sports competitions. This paper proposes a methodology based on hierarchical cluster analysis (HCA) that can be applied when a need occurs to end an interrupted tournament and the conditions for playing the remaining matches are far from ideal. The proposed methodology is based on how to conclude the season for Serie A, a top-division football league in Italy. The analysis showed that it is reasonable to play 14 instead of the 124 remaining matches of the 2019–2020 season to conclude the championship. The proposed methodology was tested on the past 10 seasons of the Serie A, and its effectiveness was confirmed. This novel approach can be used in any other sport where round-robin tournaments exist.

scholarly journals Trait anxiety and unplanned delivery mode enhance the risk for childbirth-related post-traumatic stress disorder symptoms in women with and without risk of preterm birth: A multi sample path analysis

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256681
Author(s):  
Sarah Sommerlad ◽  
Karin Schermelleh-Engel ◽  
Valentina Lucia La Rosa ◽  
Frank Louwen ◽  
Silvia Oddo-Sommerfeld
Keyword(s):  
Preterm Birth ◽  
Pain Intensity ◽  
Trait Anxiety ◽  
Sample Path ◽  
Delivery Mode ◽  
Ptsd Symptoms ◽  
Post Traumatic Stress ◽  
Sample Path Analysis ◽  
Childbirth Experience ◽  
Post Traumatic

Childbirth-related post-traumatic stress disorder (CB-PTSD) occurs in 3–7% of all pregnancies and about 35% of women after preterm birth (PTB) meet the criteria for acute stress reaction. Known risk factors are trait anxiety and pain intensity, whereas planned delivery mode, medical support, and positive childbirth experience are protective factors. It has not yet been investigated whether the effects of anxiety and delivery mode are mediated by other factors, and whether a PTB-risk alters these relationships. 284 women were investigated antepartum and six weeks postpartum (risk-group with preterm birth (RG-PB) N = 95, risk-group with term birth (RG-TB) N = 99, and control group (CG) N = 90). CB-PTSD symptoms and anxiety were measured using standardized psychological questionnaires. Pain intensity, medical support, and childbirth experience were assessed by single items. Delivery modes were subdivided into planned vs. unplanned delivery modes. Group differences were examined using MANOVA. To examine direct and indirect effects on CB-PTSD symptoms, a multi-sample path analysis was performed. Rates of PTS were highest in the RG-PB = 11.58% (RG-TB = 7.01%, CG = 1.1%). MANOVA revealed higher values of CB-PTSD symptoms and pain intensity in RG-PB compared to RG-TB and CG. Women with planned delivery mode reported a more positive birth experience. Path modeling revealed a good model fit. Explained variance was highest in RG-PB (R2 = 44.7%). Direct enhancing effects of trait anxiety and indirect reducing effects of planned delivery mode on CB-PTSD symptoms were observed in all groups. In both risk groups, CB-PTSD symptoms were indirectly reduced via support by medical staff and positive childbirth experience, while trait anxiety indirectly enhanced CB-PTSD symptoms via pain intensity in the CG. Especially in the RG-PB, a positive birth experience serves as protective factor against CB-PTSD symptoms. Therefore, our data highlights the importance of involving patients in the decision process even under stressful birth conditions and the need for psychological support antepartum, mainly in patients with PTB-risk and anxious traits. Trial registration number: NCT01974531 (ClinicalTrials.gov identifier).

Analysis of Feedback Retrial Queue with Starting Failure and Server Vacation

2016 ◽  
pp. 71-96
Author(s):  
K. Sathiya Thiyagarajan ◽  
G. Ayyappan
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Retrial Queue ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Steady State Analysis ◽  
Starting Failure ◽  
Dependent Probability ◽  
Bernoulli Vacation

In this chapter we discusses a batch arrival feedback retrial queue with Bernoulli vacation, where the server is subjected to starting failure. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of each service, the server either goes for a vacation with probability or may wait for serving the next customer. Repair times, service times and vacation times are assumed to be arbitrarily distributed. The time dependent probability generating functions have been obtained in terms of their Laplace transforms. The steady state analysis and key performance measures of the system are also studied. Finally, some numerical illustrations are presented.

Realization probability in closed Jackson queueing networks and its application

1987 ◽  
Vol 19 (03) ◽  
pp. 708-738 ◽  
Author(s):  
X. R. Cao
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Queueing Networks ◽  
Sample Path ◽  
Queueing Network ◽  
Jackson Network ◽  
The Mean ◽  
Service Times ◽  
A New Technique ◽  
Number Of Customers

Perturbation analysis is a new technique which yields the sensitivities of system performance measures with respect to parameters based on one sample path of a system. This paper provides some theoretical analysis for this method. A new notion, the realization probability of a perturbation in a closed queueing network, is studied. The elasticity of the expected throughput in a closed Jackson network with respect to the mean service times can be expressed in terms of the steady-state probabilities and realization probabilities in a very simple way. The elasticity of the throughput with respect to the mean service times when the service distributions are perturbed to non-exponential distributions can also be obtained using these realization probabilities. It is proved that the sample elasticity of the throughput obtained by perturbation analysis converges to the elasticity of the expected throughput in steady-state both in mean and with probability 1 as the number of customers served goes to This justifies the existing algorithms based on perturbation analysis which efficiently provide the estimates of elasticities in practice.

Transformational Leaders Help Their Employees Overcome Their Technophobia

2020 ◽  
Vol 16 (3) ◽  
pp. 70-85
Author(s):  
Odai Y. Khasawneh
Keyword(s):  
Technology Acceptance ◽  
New Technologies ◽  
New Technology ◽  
Transformational Leaders ◽  
Transformational Leader ◽  
The Past ◽  
Novel Approach ◽  
The Many ◽  
Narrow Context ◽  
Do So

The lack of technology acceptance in the workplace has haunted companies in the past and it seems that it will continue to do so in the future. One of the many variables that impact employees' acceptance of a new technology is technophobia; which previously has been studied within the narrow context of computers or few other technologies that are now outdated. In a novel approach, the current study examines employees' technophobia and how it impacts their technology acceptance. In addition, the moderating influence of transformational leadership is studied to determine whether that type of leadership would influence employees to overcome their technophobia. The data analysis confirms that technophobia and its subdimensions are still an issue that haunts the workplace. However, having a leader who's identified as a transformational leader can help employees overcome their technophobia. This study argues that it is vital for companies to understand the level and type of technophobia as well as what type of leadership their employees have before implementing any new technologies.

Sign in / Sign up

Export Citation Format

Share Document