Correlation functions in queueing theory

1972 ◽  
Vol 9 (03) ◽  
pp. 604-616 ◽  
Author(s):  
S. K. Srinivasan ◽  
R. Subramanian ◽  
R. Vasudevan
Keyword(s):  
Waiting Time ◽  
Correlation Functions ◽  
Queueing Theory ◽  
Product Space ◽  
Point Processes ◽  
Time Interval ◽  
Important Criterion ◽  
Time Parameters ◽  
Set Up ◽  
Number Of Customers

The object of this paper is to study the actual waiting time of a customer in a GI/G/1 queue. This is an important criterion from the viewpoint of both the customers and the efficient functioning of the counter. Suitable point processes in the product space of load and time parameters for any general inter-arrival and service time distributions are defined and integral equations governing the correlation functions are set up. Solutions of these equations are obtained and with the help of these, explicit expressions for the first two moments of the number of customers who have waited for a time longer than w in a given time interval (0, T) are calculated.

Correlation functions in queueing theory

1972 ◽  
Vol 9 (3) ◽  
pp. 604-616 ◽  
Author(s):  
S. K. Srinivasan ◽  
R. Subramanian ◽  
R. Vasudevan
Keyword(s):  
Waiting Time ◽  
Correlation Functions ◽  
Queueing Theory ◽  
Product Space ◽  
Point Processes ◽  
Time Interval ◽  
Important Criterion ◽  
Time Parameters ◽  
Set Up ◽  
Number Of Customers

The object of this paper is to study the actual waiting time of a customer in a GI/G/1 queue. This is an important criterion from the viewpoint of both the customers and the efficient functioning of the counter. Suitable point processes in the product space of load and time parameters for any general inter-arrival and service time distributions are defined and integral equations governing the correlation functions are set up. Solutions of these equations are obtained and with the help of these, explicit expressions for the first two moments of the number of customers who have waited for a time longer than w in a given time interval (0, T) are calculated.

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.

Stochastic monotonicity properties of multiserver queues with impatient customers

1991 ◽  
Vol 28 (03) ◽  
pp. 673-682
Author(s):  
Partha P. Bhattachary ◽  
Anthony Ephremides
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Time Interval ◽  
Impatient Customers ◽  
Monotone Functions ◽  
Stochastic Monotonicity ◽  
Multiserver Queues ◽  
Monotonicity Properties ◽  
Number Of Customers

We consider multiserver queues in which a customer is lost whenever its waiting time is larger than its (possibly random) deadline. For such systems, the number of (successful) departures and the number of customers lost over a time interval are the performance measures of interest. We show that these quantities are (stochastically) monotone functions of the arrival, service and deadline processes.

A relation between stationary queue and waiting time distributions

1971 ◽  
Vol 8 (03) ◽  
pp. 617-620 ◽  
Author(s):  
Rasoul Haji ◽  
Gordon F. Newell
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Arrival Process ◽  
Time Interval ◽  
Queue Size ◽  
Random Time Interval ◽  
Queue Discipline ◽  
Stationary Waiting Time ◽  
Number Of Customers ◽  
First In First Out

A theorem is proved which, in essence, says the following. If, for any queueing system, (i) the arrival process is stationary, (ii) the queue discipline is first-in-first-out (FIFO), and (iii) the waiting time of each customer is statistically independent of the number of arrivals during any time interval after his arrival, then the stationary random queue size has the same distribution as the number of customers who arrive during a random time interval distributed as the stationary waiting time.

Stochastic monotonicity properties of multiserver queues with impatient customers

1991 ◽  
Vol 28 (3) ◽  
pp. 673-682 ◽  
Author(s):  
Partha P. Bhattacharya ◽  
Anthony Ephremides
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Time Interval ◽  
Impatient Customers ◽  
Monotone Functions ◽  
Stochastic Monotonicity ◽  
Multiserver Queues ◽  
Monotonicity Properties ◽  
Number Of Customers

We consider multiserver queues in which a customer is lost whenever its waiting time is larger than its (possibly random) deadline. For such systems, the number of (successful) departures and the number of customers lost over a time interval are the performance measures of interest. We show that these quantities are (stochastically) monotone functions of the arrival, service and deadline processes.

A relation between stationary queue and waiting time distributions

1971 ◽  
Vol 8 (3) ◽  
pp. 617-620 ◽  
Author(s):  
Rasoul Haji ◽  
Gordon F. Newell
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Arrival Process ◽  
Time Interval ◽  
Queue Size ◽  
Random Time Interval ◽  
Queue Discipline ◽  
Stationary Waiting Time ◽  
Number Of Customers ◽  
First In First Out

A theorem is proved which, in essence, says the following. If, for any queueing system, (i) the arrival process is stationary, (ii) the queue discipline is first-in-first-out (FIFO), and (iii) the waiting time of each customer is statistically independent of the number of arrivals during any time interval after his arrival, then the stationary random queue size has the same distribution as the number of customers who arrive during a random time interval distributed as the stationary waiting time.

scholarly journals Experimental assessment of harmonic contributions using a ternary pulse sequence

2021 ◽  
Vol 18 (3) ◽  
pp. 271-289
Author(s):  
Evgeniia Bulycheva ◽  
Sergey Yanchenko
Keyword(s):  
Real Time ◽  
Pulse Sequence ◽  
Wide Band ◽  
Voltage Source ◽  
Time Interval ◽  
Time Frequency ◽  
Grid Impedance ◽  
Set Up ◽  
Grid Voltage Distortion ◽  
Operational Modes

Harmonic contributions of utility and customer may feature significant variations due to network switchings and changing operational modes. In order to correctly define the impacts on the grid voltage distortion the frequency dependent impedance characteristic of the studied network should be accurately measured in the real-time mode. This condition can be fulfilled by designing a stimuli generator measuring the grid impedance as a response to injected interference and producing time-frequency plots of harmonic contributions during considered time interval. In this paper a prototype of a stimuli generator based on programmable voltage source inverter is developed and tested. The use of ternary pulse sequence allows fast wide-band impedance measurements that meet the requirements of real-time assessment of harmonic contributions. The accuracy of respective analysis involving impedance determination and calculation of harmonic contributions is validated experimentally using reference characteristics of laboratory test set-up with varying grid impedance.

scholarly journals Probability distributions of COVID-19 tweet posted trends use a nonhomogeneous Poisson process

2020 ◽  
Vol 1 (4) ◽  
pp. 229-238
Author(s):  
Devi Munandar ◽  
Sudradjat Supian ◽  
Subiyanto Subiyanto
Keyword(s):  
Social Media ◽  
Poisson Process ◽  
Exponential Distribution ◽  
Probability Distributions ◽  
Nonhomogeneous Poisson Process ◽  
Time Interval ◽  
Initial State ◽  
Time Intervals ◽  
Time Parameters ◽  
Parameter Values

The influence of social media in disseminating information, especially during the COVID-19 pandemic, can be observed with time interval, so that the probability of number of tweets discussed by netizens on social media can be observed. The nonhomogeneous Poisson process (NHPP) is a Poisson process dependent on time parameters and the exponential distribution having unequal parameter values and, independently of each other. The probability of no occurrence an event in the initial state is one and the probability of an event in initial state is zero. Using of non-homogeneous Poisson in this paper aims to predict and count the number of tweet posts with the keyword coronavirus, COVID-19 with set time intervals every day. Posting of tweets from one time each day to the next do not affect each other and the number of tweets is not the same. The dataset used in this study is crawling of COVID-19 tweets three times a day with duration of 20 minutes each crawled for 13 days or 39 time intervals. The result of this study obtained predictions and calculated for the probability of the number of tweets for the tendency of netizens to post on the situation of the COVID-19 pandemic.

scholarly journals Five-Year Experience of Liver Transplant at Kerman University of Medical Sciences: Afzalipoor Hospital

2020 ◽  
Author(s):  
Masood Dehghani
Keyword(s):  
Liver Transplantation ◽  
Liver Transplant ◽  
Cross Sectional Study ◽  
Outcome Data ◽  
Time Interval ◽  
Cross Sectional ◽  
The Past ◽  
Transplantation Center ◽  
Set Up ◽  
End Stage

Introduction: The only option for treatment of end stage liver diseases is liver transplantation. Afzalipour Hospital in Kerman, Iran is the third largest liver transplantation center in Iran. In this study, the outcomes of this center have been studied during the past 5 years. Methods: In this cross-sectional study, the pre and post transplantation’s clinical, demographic and outcome data of all patients who received liver transplant at Afzalipour Hospital during the past 5 years have been collected and reviewed. SPSS software ver. 16 was used to analyze the data. Results: Forty-three patients have received liver transplantation during this time interval. The 3-year survival rate of patients was 77%. The most common cause of death was primary nonfunction graft after transplantation. The most common complication was acute rejection (15%), all of which were successfully treated with corticosteroids. Conclusion:  Due to increment of cases of acute and chronic liver failure in the community and since the final treatment of these cases is liver transplantation, so there is need to develop liver transplant centers in the future. Quantitative and qualitative study of the activity of centers based liver transplant in Iran is necessary to set up successful centers.

scholarly journals Perishable Inventory System with Postponed Demands and Negative Customers

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Paul Manuel ◽  
B. Sivakumar ◽  
G. Arivarignan
Keyword(s):  
Steady State ◽  
Joint Probability ◽  
Inventory System ◽  
Arrival Process ◽  
Inventory Level ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Negative Customers ◽  
Perishable Inventory System ◽  
Number Of Customers

This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The lifetime of items in the stock and the lead time of reorder are assumed to be independently distributed as exponential. Demands that occur during the stock-out periods either enter a pool which has capacity N(<∞) or are lost. Any demand that takes place when the pool is full and the inventory level is zero is assumed to be lost. The demands in the pool are selected one by one, if the replenished stock is above s, with time interval between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The waiting demands in the pool independently may renege the system after an exponentially distributed amount of time. In addition to the regular demands, a second flow of negative demands following MAP is also considered which will remove one of the demands waiting in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are calculated and the total expected cost per unit time is also considered. The results are illustrated numerically.

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