A New Analysis of a Fluid Queue Driven By M/M/1 Queue

2021 ◽  
Vol 10 (3) ◽  
pp. 865-869
Keyword(s):  
Fluid Queue

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.

Approximating the heterogeneous fluid queue with a birth-death fluid queue

1995 ◽  
Vol 43 (5) ◽  
pp. 1884-1887 ◽  
Author(s):  
S. Blaabjerg ◽  
H. Andersson ◽  
H. Andersson
Keyword(s):  
Fluid Queue ◽  
Birth Death

ON THE WORKLOAD PROCESS IN A FLUID QUEUE WITH A RESPONSIVE BURSTY INPUT AND SELECTIVE DISCARDING

2003 ◽  
Vol 17 (4) ◽  
pp. 527-543
Author(s):  
Parijat Dube ◽  
Eitan Altman
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Feedback System ◽  
Moment Generating Function ◽  
General Distribution ◽  
Finite Buffer ◽  
Fluid Queue ◽  
The Stability ◽  
The Moment ◽  
Stationary Workload

We analyze a feedback system consisting of a finite buffer fluid queue and a responsive source. The source alternates between silence periods and active periods. At random epochs of times, the source becomes ready to send a burst of fluid. The length of the bursts (length of the active periods) are independent and identically distributed with some general distribution. The queue employs a threshold discarding policy in the sense that only those bursts at whose commencement epoch (the instant at which the source is ready to send) the workload (i.e., the amount of fluid in the buffer) is less than some preset threshold are accepted. If the burst is rejected then the source backs off from sending. We work within the framework of Poisson counter-driven stochastic differential equations and obtain the moment generating function and hence the probability density function of the stationary workload process. We then comment on the stability of this fluid queue. Our explicit characterizations will further provide useful insights and “engineering” guidelines for better network designing.

scholarly journals Distributional Properties of Fluid Queues Busy Period and First Passage Times

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1988
Author(s):  
Zbigniew Palmowski
Keyword(s):  
Markov Process ◽  
Busy Period ◽  
First Passage Time ◽  
Passage Time ◽  
Fluid Queue ◽  
First Passage ◽  
Fluid Queues ◽  
Distributional Properties ◽  
Finite State ◽  
Passage Times

In this paper, I analyze the distributional properties of the busy period in an on-off fluid queue and the first passage time in a fluid queue driven by a finite state Markov process. In particular, I show that the first passage time has a IFR distribution and the busy period in the Anick-Mitra-Sondhi model has a DFR distribution.

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