Closed Form Approximations for Steady State Probabilities of a Controlled Fork-Join Network

2010 ◽  
pp. 420-435 ◽  
Author(s):  
Jonathan Billington ◽  
Guy Edward Gallasch
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Steady State Probabilities

scholarly journals Analysis of M/M/1 Queuing System with Customer Reneging During Server Vacations Subject To Server Breakdown and Delayed Repair

2018 ◽  
Vol 7 (4.10) ◽  
pp. 552
Author(s):  
Ch. Swathi ◽  
V. Vasanta Kumar
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Detailed Analysis ◽  
Performance Measures ◽  
Queuing System ◽  
Multiple Vacation ◽  
Delayed Repair ◽  
Server Breakdown ◽  
Number Of Customers ◽  
Steady State Probabilities

In this paper, we consider an M/M/1 queuing system with customer reneging for an unreliable sever. Customer reneging is assumed to occur due to the absence of the server during vacations.  Detailed analysis for both single and multiple vacation models during different states of the server such as busy, breakdown and delayed repair periods is presented. Steady state probabilities for single and multiple vacation policies are obtained. Closed form expressions for various performance measures such as average number of customers in the system, proportion of customers served and reneged per unit time during single and multiple vacations are obtained.   

A correlated queue with infinitely many servers

1986 ◽  
Vol 23 (01) ◽  
pp. 155-165 ◽  
Author(s):  
C. Langaris
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Service Time ◽  
Transient State ◽  
Laplace Transforms ◽  
Bivariate Distribution ◽  
Numerical Calculations ◽  
Output Process ◽  
Negative Exponential ◽  
Steady State Probabilities

This work analyses a queueing mechanism with infinitely many servers in which the interarrival interval T preceding the arrival of a customer and his service time S are assumed correlated. A bivariate distribution with negative exponential marginals is used and the Laplace transforms pn (z) of the system probabilities in transient state are obtained. Closed-form expressions for the steady-state probabilities pn and their moments are given too. Finally the output process is investigated and conclusions are drawn from numerical calculations.

A correlated queue with infinitely many servers

1986 ◽  
Vol 23 (1) ◽  
pp. 155-165 ◽  
Author(s):  
C. Langaris
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Service Time ◽  
Transient State ◽  
Laplace Transforms ◽  
Bivariate Distribution ◽  
Numerical Calculations ◽  
Output Process ◽  
Negative Exponential ◽  
Steady State Probabilities

This work analyses a queueing mechanism with infinitely many servers in which the interarrival interval T preceding the arrival of a customer and his service time S are assumed correlated. A bivariate distribution with negative exponential marginals is used and the Laplace transforms pn (z) of the system probabilities in transient state are obtained. Closed-form expressions for the steady-state probabilities pn and their moments are given too. Finally the output process is investigated and conclusions are drawn from numerical calculations.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

scholarly journals The truncated Hyper-Poisson queues: Hk/Ma,b/C/N with balking, reneging and general bulk service rule

2008 ◽  
Vol 18 (1) ◽  
pp. 23-36 ◽  
Author(s):  
A.I. Shawky ◽  
M.S. El-Paoumy
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Explicit Form ◽  
Recurrence Relations ◽  
Expected Number ◽  
Special Cases ◽  
Queue Discipline ◽  
Bulk Service ◽  
General Bulk Service Rule ◽  
Steady State Probabilities

The aim of this paper is to derive the analytical solution of the queue: Hk/Ma,b/C/N with balking and reneging in which (I) units arrive according to a hyper-Poisson distribution with k independent branches, (II) the queue discipline is FIFO; and (III) the units are served in batches according to a general bulk service rule. The steady-state probabilities, recurrence relations connecting various probabilities introduced are found and the expected number of units in the queue is derived in an explicit form. Also, some special cases are obtained. .

scholarly journals AHP PRIORITIES AND MARKOV-CHAPMAN-KOLMOGOROV STEADY-STATES PROBABILITIES

2015 ◽  
Vol 7 (2) ◽  
Author(s):  
Stan Lipovetsky
Keyword(s):  
Steady State ◽  
General Solution ◽  
Stochastic Modeling ◽  
Pairwise Comparison ◽  
System Of Equations ◽  
Pairwise Comparison Matrix ◽  
Pair Comparison ◽  
Priority Vector ◽  
Discrete States ◽  
Steady State Probabilities

<div class="MsoTitle" style="margin: 12pt 0in 15pt;"><p>An AHP matrix of the quotients of the pair comparison priorities is transformed to a matrix of shares of the preferences which can be used in Markov stochastic modeling via the Chapman-Kolmogorov system of equations for the discrete states. It yields a general solution and the steady-state probabilities. The AHP priority vector can be interpreted as these probabilities belonging to the discrete states corresponding to the compared items. The results of stochastic modeling correspond to robust estimations of priority vectors not prone to influence of possible errors among the elements of a pairwise comparison matrix.</p></div><div class="MsoTitle" style="margin: 12pt 0in 15pt;"> </div>

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