scholarly journals Analysis of Impatient Customers in Queues with Bernoulli Schedule Working Vacations and Vacation Interruption

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Veena Goswami
Keyword(s):  
Performance Measures ◽  
System Size ◽  
Stochastic Decomposition ◽  
Model Parameters ◽  
The Mean ◽  
Working Vacations ◽  
Vacation Interruption ◽  
The Impact ◽  
Vacation Period ◽  
Bernoulli Schedule

This paper analyzes customers’ impatience in Markovian queueing system with multiple working vacations and Bernoulli schedule vacation interruption, where customers’ impatience is due to the servers’ vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular busy period with probability 1-q or continues the vacation with probability q. We obtain the probability generating functions of the stationary state probabilities and deduce the explicit expressions of the system sizes when the server is in a normal service period and in a Bernoulli schedule vacation interruption, respectively. Various performance measures such as the mean system size, the proportion of customers served, the rate of abandonment due to impatience, and the mean sojourn time of a customer served are derived. We obtain the stochastic decomposition structures of the queue length and waiting time. Finally, some numerical results to show the impact of model parameters on performance measures of the system are presented.

scholarly journals An M/M/1 Queue with Working Vacation and Vacation Interruption Under Bernoulli Schedule

2018 ◽  
Vol 7 (4.10) ◽  
pp. 448
Author(s):  
P. Manoharan ◽  
A. Ashok
Keyword(s):  
Geometric Approach ◽  
Stochastic Decomposition ◽  
Working Vacation ◽  
System Parameters ◽  
Mean Waiting Time ◽  
The Mean ◽  
Vacation Interruption ◽  
Mean Queue Length ◽  
Vacation Period ◽  
Bernoulli Schedule

This work deals with M/M/1 queue with Vacation and Vacation Interruption Under Bernoulli schedule. When there are no customers in the system, the server takes a classical vacation with probability p or a working vacation with probability 1-p, where . At the instants of service completion during the working vacation, either the server is supposed to interrupt the vacation and returns back to the non-vacation period with probability 1-q or the sever will carry on with the vacation with probability q. When the system is non empty after the end of vacation period, a new non vacation period begins. A matrix geometric approach is employed to obtain the stationary distribution for the mean queue length and the mean waiting time and their stochastic decomposition structures. Numerous graphical demonstrations are presented to show the effects of the system parameters on the performance measures.  

scholarly journals Finite Buffer GI/M(n)/1 Queue with Bernoulli-Schedule Vacation Interruption under N-Policy

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
P. Vijaya Laxmi ◽  
V. Suchitra
Keyword(s):  
Performance Measures ◽  
Finite Buffer ◽  
Supplementary Variable ◽  
Working Vacation ◽  
Variable Technique ◽  
Special Cases ◽  
Vacation Interruption ◽  
System Length ◽  
Vacation Period ◽  
Bernoulli Schedule

We study a finite buffer N-policy GI/M(n)/1 queue with Bernoulli-schedule vacation interruption. The server works with a slower rate during vacation period. At a service completion epoch during working vacation, if there are at least N customers present in the queue, the server interrupts vacation and otherwise continues the vacation. Using the supplementary variable technique and recursive method, we obtain the steady state system length distributions at prearrival and arbitrary epochs. Some special cases of the model, various performance measures, and cost analysis are discussed. Finally, parameter effect on the performance measures of the model is presented through numerical computations.

scholarly journals Optimization of Balking and Reneging Queue with Vacation Interruption underN-Policy

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
P. Vijaya Laxmi ◽  
V. Goswami ◽  
K. Jyothsna
Keyword(s):  
Performance Measures ◽  
Search Method ◽  
Model Parameters ◽  
Finite Buffer ◽  
Working Vacation ◽  
Swarm Optimization ◽  
Multiple Working Vacations ◽  
Working Vacations ◽  
Vacation Interruption ◽  
System Length

This paper analyzes a finite buffer multiple working vacations queue with balking, reneging, and vacation interruption underN-policy. In the working vacation, a customer is served at a lower rate and at the instants of a service completion; if there are at leastNcustomers in the queue, the vacation is interrupted and the server switches to regular busy period otherwise continues the vacation. Using Markov process and recursive technique, we derive the stationary system length distributions at arbitrary epoch. Various performance measures and some special models of the system are presented. Cost analysis is carried out using particle swarm optimization and quadratic fit search method. Finally, some numerical results showing the effect of model parameters on key performance measures of the system are presented.

AN M/G/1 RETRIAL QUEUE WITH GENERAL RETRIAL TIMES, WORKING VACATIONS AND VACATION INTERRUPTION

2014 ◽  
Vol 31 (02) ◽  
pp. 1440006 ◽  
Author(s):  
SHAN GAO ◽  
JINTING WANG ◽  
WEI WAYNE LI
Keyword(s):  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Supplementary Variable ◽  
Waiting Time Distribution ◽  
Working Vacation ◽  
Stationary Probability Distribution ◽  
Working Vacations ◽  
Vacation Interruption ◽  
Vacation Period ◽  
Conditional Stochastic Decomposition

We consider an M/G/1 retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. During the working vacation period, customers can be served at a lower rate. If there are customers in the system at a service completion instant, the vacation will be interrupted and the server will come back to the normal working level. Using supplementary variable method, we obtain the stationary probability distribution and some performance measures. Furthermore, we carry out the waiting time distribution and prove the conditional stochastic decomposition for the queue length in orbit. Finally, some numerical examples are presented.

scholarly journals Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience

2021 ◽  
Vol 13 (2) ◽  
pp. 367-395
Author(s):  
Shakir Majid ◽  
Amina Angelika Bouchentouf ◽  
Abdelhak Guendouzi
Keyword(s):  
Function Technique ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Vacation Interruption ◽  
The Impact ◽  
Number Of Customers ◽  
Vacation Period ◽  
System Characteristics ◽  
Bernoulli Schedule

Abstract In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.

Prediction of bottom dynamic conditions in coastal waters

1995 ◽  
Vol 46 (1) ◽  
pp. 359 ◽  
Author(s):  
J Persson ◽  
L Hakanson
Keyword(s):  
Coastal Areas ◽  
Model Parameters ◽  
Direct Connection ◽  
Digital Technique ◽  
Computer Data ◽  
Dynamic Conditions ◽  
Model Based ◽  
Open Sea ◽  
The Mean ◽  
The Impact

Bottom dynamic conditions (areas of accumulation, erosion or transportation) in aquatic ecosystems influence the dispersal, sedimentation and recirculation of most substances, such as metals, organic toxins and nutrients. The aim of the present work was to establish a simple and general method to predict sediment types/bottom dynamic conditions in Baltic coastal areas. As a working hypothesis, it is proposed that the morphometry and the absence or presence of an archipelago outside a given coastal area regulate what factors determine the prevailing bottom dynamic conditions. Empirical data on the proportion of accumulation bottoms (BA) were collected from 38 relatively small (1-14 km²) and enclosed coastal areas in the Baltic Sea. Morphometric data were obtained by using a digital technique to transfer information from standard bathymetric maps into a computer. Data were processed by means of multivariate statistical methods. In the first model, based on data from all 38 areas, 55% of the variation in BA among the areas was statistically explained by five morphometric parameters. The data set was then divided into two parts: areas in direct connection with the open sea, and areas inside an archipelago. In the second model, based on data from 15 areas in direct connection with the open sea, 77% of the variation in BA was statistically explained by the mean depth of the deep water (the water mass below 10 m) and the mean slope. In the third model, based on data from 23 areas inside an archipelago, 70% of the variation in BA was statistically explained by the mean slope, the topographic form factor, the proportion of islands and the mean filter factor (which is a relative measure of the impact of winds and waves from outside the area). The model parameters describe the sediment trapping capacity of the areas investigated.

The disasters queue with working breakdowns and impatient customers

2020 ◽  
Vol 54 (3) ◽  
pp. 815-825
Author(s):  
Mian Zhang ◽  
Shan Gao
Keyword(s):  
Size Distribution ◽  
Performance Measures ◽  
Sojourn Time ◽  
Queue Length ◽  
Slow Rate ◽  
System Size ◽  
Impatient Customers ◽  
Numerical Examples ◽  
The Mean ◽  
Mean Queue Length

We consider the M/M/1 queue with disasters and impatient customers. Disasters only occur when the main server being busy, it not only removes out all present customers from the system, but also breaks the main server down. When the main server is down, it is sent for repair. The substitute server serves the customers at a slow rate(working breakdown service) until the main server is repaired. The customers become impatient due to the working breakdown. The system size distribution is derived. We also obtain the mean queue length of the model and mean sojourn time of a tagged customer. Finally, some performance measures and numerical examples are presented.

scholarly journals M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Tao ◽  
Liyuan Zhang ◽  
Shan Gao
Keyword(s):  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Service Rate ◽  
Working Vacation ◽  
Stationary Probability Distribution ◽  
The Matrix ◽  
Vacation Interruption ◽  
Necessary And Sufficient ◽  
Vacation Period ◽  
Conditional Stochastic Decomposition

We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.

scholarly journals A Systematic Comparison of Microsimulation Models of Colorectal Cancer

2011 ◽  
Vol 31 (4) ◽  
pp. 530-539 ◽  
Author(s):  
Karen M. Kuntz ◽  
Iris Lansdorp-Vogelaar ◽  
Carolyn M. Rutter ◽  
Amy B. Knudsen ◽  
Marjolein van Ballegooijen ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Cancer Diagnosis ◽  
Cancer Incidence ◽  
Dwell Time ◽  
Model Parameters ◽  
Underlying Condition ◽  
Deep Model ◽  
The Mean ◽  
Microsimulation Models ◽  
The Impact

Background. As the complexity of microsimulation models increases, concerns about model transparency are heightened. Methods. The authors conducted model “experiments” to explore the impact of variations in “deep” model parameters using 3 colorectal cancer (CRC) models. All natural history models were calibrated to match observed data on adenoma prevalence and cancer incidence but varied in their underlying specification of the adenocarcinoma process. The authors projected CRC incidence among individuals with an underlying adenoma or preclinical cancer v. those without any underlying condition and examined the impact of removing adenomas. They calculated the percentage of simulated CRC cases arising from adenomas that developed within 10 or 20 years prior to cancer diagnosis and estimated dwell time—defined as the time from the development of an adenoma to symptom-detected cancer in the absence of screening among individuals with a CRC diagnosis. Results. The 20-year CRC incidence among 55-year-old individuals with an adenoma or preclinical cancer was 7 to 75 times greater than in the condition-free group. The removal of all adenomas among the subgroup with an underlying adenoma or cancer resulted in a reduction of 30% to 89% in cumulative incidence. Among CRCs diagnosed at age 65 years, the proportion arising from adenomas formed within 10 years ranged between 4% and 67%. The mean dwell time varied from 10.6 to 25.8 years. Conclusions. Models that all match observed data on adenoma prevalence and cancer incidence can produce quite different dwell times and very different answers with respect to the effectiveness of interventions. When conducting applied analyses to inform policy, using multiple models provides a sensitivity analysis on key (unobserved) “deep” model parameters and can provide guidance about specific areas in need of additional research and validation.

scholarly journals Performance Characteristics of Discrete-Time Queue With Variant Working Vacations

2020 ◽  
Vol 11 (2) ◽  
pp. 1-21
Author(s):  
P. Vijaya Laxmi ◽  
Rajesh P.
Keyword(s):  
Discrete Time ◽  
Cost Model ◽  
Probability Generating Function ◽  
System Size ◽  
Service Rate ◽  
Single Server ◽  
Working Vacation ◽  
Optimal Service ◽  
Working Vacations ◽  
Vacation Period

This article analyzes an infinite buffer discrete-time single server queueing system with variant working vacations in which customers arrive according to a geometric process. As soon as the system becomes empty, the server takes working vacations. The server will take a maximum number K of working vacations until either he finds at least on customer in the queue or the server has exhaustively taken all the vacations. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. The probability generating function of the steady-state probabilities and the closed form expressions of the system size when the server is in different states have been derived. In addition, some other performance measures, their monotonicity with respect to K and a cost model are presented to determine the optimal service rate during working vacation.

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