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 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 Fluid queues and regular variation

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

scholarly journals Continuous feedback fluid queues

2005 ◽  
Vol 33 (6) ◽  
pp. 551-559 ◽  
Author(s):  
Werner Scheinhardt ◽  
Nicky van Foreest ◽  
Michel Mandjes
Keyword(s):  
Fluid Queues ◽  
Continuous Feedback

Parallel fluid queues with constant inflows and simultaneous random reductions

2001 ◽  
Vol 38 (3) ◽  
pp. 609-620 ◽  
Author(s):  
Offer Kella ◽  
Masakiyo Miyazawa
Keyword(s):  
Poisson Process ◽  
Upper Bounds ◽  
Decay Rates ◽  
Fluid Queue ◽  
Linear Combinations ◽  
Fluid Queues ◽  
Constant Rate ◽  
Major Interest ◽  
Dimensional Distribution ◽  
Queues In Parallel

We consider I fluid queues in parallel. Each fluid queue has a deterministic inflow with a constant rate. At a random instant subject to a Poisson process, random amounts of fluids are simultaneously reduced. The requested amounts for the reduction are subject to a general I-dimensional distribution. The queues with inventories that are smaller than the requests are emptied. Stochastic upper bounds are considered for the stationary distribution of the joint buffer contents. Our major interest is in finding exponential product-form bounds, which turn out to have the appropriate decay rates with respect to certain linear combinations of buffer contents.

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