Transient solution of an M[X]/G/1 queueing model with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time

2016 ◽  
Vol 25 (2) ◽  
pp. 196 ◽  
Author(s):  
G. Ayyappan ◽  
S. Shyamala
Keyword(s):  
Setup Time ◽  
Queueing Model ◽  
Transient Solution ◽  
Server Vacation ◽  
Bernoulli Schedule ◽  
Random Breakdowns

scholarly journals Fluid Queue Driven by anM/M/1Queue Subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Kolinjivadi Viswanathan Vijayashree ◽  
Atlimuthu Anjuka
Keyword(s):  
Death Process ◽  
Queueing Model ◽  
Fluid Queue ◽  
Stationary Analysis ◽  
Governing System ◽  
Matrix Geometric Method ◽  
Vacation Interruption ◽  
Model Subject ◽  
Steady State Probabilities ◽  
Bernoulli Schedule

This paper deals with the stationary analysis of a fluid queue driven by anM/M/1queueing model subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption. The model under consideration can be viewed as a quasi-birth and death process. The governing system of differential difference equations is solved using matrix-geometric method in the Laplacian domain. The resulting solutions are then inverted to obtain an explicit expression for the joint steady state probabilities of the content of the buffer and the state of the background queueing model. Numerical illustrations are added to depict the convergence of the stationary buffer content distribution to one subject to suitable stability conditions.

scholarly journals Maximum Entropy Approach for Un-Reliable Server Vacation Queueing Model with Optional Bulk Service

2012 ◽  
Vol 23 (1) ◽  
pp. 89-113
Author(s):  
Madhu Jain, Madhu Jain,
Keyword(s):  
Maximum Entropy ◽  
Performance Measures ◽  
Probability Generating Function ◽  
Single Server ◽  
Queueing Model ◽  
Time Service ◽  
Server Vacation ◽  
Single Vacation ◽  
Bulk Service ◽  
Essential Service

In this study, we consider a single server vacation queueing model with optional bulk service and an un-reliable server. A single server provides first essential service (FES) to all arriving customers one by one; apart from essential service, he can also facilitate the additional phase of optional service (OS) in batches of fixed size b( ≥ 1), in case when the customers request for it. The server may take a single vacation whenever he finds no customers waiting in the queue to be served. Moreover, the server is subjected to unpredictable breakdown while providing the first essential service. The vacation time, service time and repair time of the server are exponentially distributed. The steady state results are obtained in terms of probability generating function for queue size distributions. By using the maximum entropy analysis (MEA), we derive various system performance measures. A comparative study is performed between the exact and approximate waiting time of the system. By taking the numerical illustrations, the sensitivity analysis is done to explore the effect of different descriptors on various performance measures.

Analysis of M X / G /1 feedback queuewith two-phase service, compulsory server vacation and random breakdowns

OPSEARCH ◽  
2013 ◽  
Vol 51 (2) ◽  
pp. 235-256 ◽  
Author(s):  
M. C. Saravanarajan ◽  
V. M. Chandrasekaran
Keyword(s):  
Two Phase ◽  
Server Vacation ◽  
Random Breakdowns

scholarly journals Transient Solution of 𝑀𝑋/𝑀/𝐶 Queueing Model for Homogenous Servers, with Catastrophes, Balking & Vacation

2020 ◽  
Vol 5 (4) ◽  
pp. 65-69
Author(s):  
G. Kavitha ◽  
◽  
K.Julia Rose Mary ◽  
Keyword(s):  
Exponential Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Service Rate ◽  
Queueing Model ◽  
Transient Solution

In this paper we analyze 𝑴𝑿/𝑴/𝑪 Queueing model of homogenous service rate with catastrophes, balking and vacation. Here we consider the customers, where arrival follow a poisson and the service follows an exponential distribution. Based on the above considerations, under catastrophes, balking and vacation by using probability generating function along with the Bessel properties we obtain the transient solution of the model in a simple way.

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