V-uniform ergodicity for fluid queues

2019 ◽  
Vol 34 (1) ◽  
pp. 82-91 ◽  
Author(s):  
Yuan-yuan Liu ◽  
Yang Li
Keyword(s):  
Fluid Queues ◽  
Uniform Ergodicity

scholarly journals Volume and duration of losses in finite buffer fluid queues

2015 ◽  
Vol 52 (3) ◽  
pp. 826-840 ◽  
Author(s):  
Fabrice Guillemin ◽  
Bruno Sericola
Keyword(s):  
Busy Period ◽  
Buffer Capacity ◽  
Exact Expression ◽  
Loss Probability ◽  
Finite Buffer ◽  
Fluid Queues ◽  
Buffer Content ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Arrival Processes

We study congestion periods in a finite fluid buffer when the net input rate depends upon a recurrent Markov process; congestion occurs when the buffer content is equal to the buffer capacity. Similarly to O'Reilly and Palmowski (2013), we consider the duration of congestion periods as well as the associated volume of lost information. While these quantities are characterized by their Laplace transforms in that paper, we presently derive their distributions in a typical stationary busy period of the buffer. Our goal is to compute the exact expression of the loss probability in the system, which is usually approximated by the probability that the occupancy of the infinite buffer is greater than the buffer capacity under consideration. Moreover, by using general results of the theory of Markovian arrival processes, we show that the duration of congestion and the volume of lost information have phase-type distributions.

scholarly journals A condition equivalent to uniform ergodicity

2005 ◽  
Vol 167 (3) ◽  
pp. 215-218
Author(s):  
Maria Elena Becker
Keyword(s):  
Uniform Ergodicity

scholarly journals Fluid queues and regular variation

1996 ◽  
Vol 27-28 ◽  
pp. 699-712 ◽  
Author(s):  
O.J. Boxma
Keyword(s):  
Regular Variation ◽  
Fluid Queues

Erlangized Fluid Queues with Application To Uncontrolled Fire Perimeter

2005 ◽  
Vol 21 (2-3) ◽  
pp. 631-642 ◽  
Author(s):  
David A. Stanford ◽  
Guy Latouche ◽  
Douglas G. Woolford ◽  
Dennis Boychuk ◽  
Alek Hunchak
Keyword(s):  
Fluid Queues

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.

Risk processes analyzed as fluid queues

2005 ◽  
Vol 2005 (2) ◽  
pp. 127-141 ◽  
Author(s):  
Andrei Badescu ◽  
Lothar Breuer ◽  
Ana Da Silva Soares ◽  
Guy Latouche ◽  
Marie-Ange Remiche ◽  
...  
Keyword(s):  
Fluid Queues ◽  
Risk Processes

Matrix-analytic methods for fluid queues with finite buffers

2006 ◽  
Vol 63 (4-5) ◽  
pp. 295-314 ◽  
Author(s):  
Ana da Silva Soares ◽  
Guy Latouche
Keyword(s):  
Matrix Analytic Methods ◽  
Finite Buffers ◽  
Fluid Queues ◽  
Analytic Methods
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