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.

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.   

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

Closed-form representations of the laplace transforms of bessel funtions

2000 ◽  
Vol 9 (3) ◽  
pp. 217-228 ◽  
Author(s):  
Klaus Rottbrand ◽  
Christian Weddigen
Keyword(s):  
Closed Form ◽  
Laplace Transforms

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.

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