A Markov-modulated fluid flow queueing model under D -policy

2011 ◽  
Vol 18 (6) ◽  
pp. 993-1010 ◽  
Author(s):  
Jung Woo Baek ◽  
Ho Woo Lee ◽  
Se Won Lee ◽  
Soohan Ahn
Keyword(s):  
Fluid Flow ◽  
Queueing Model ◽  
Markov Modulated

Comparison Results for Markov-Modulated Recursive Models

1997 ◽  
Vol 11 (2) ◽  
pp. 203-217 ◽  
Author(s):  
Nicole Bäuerle ◽  
Ulrich Rieder
Keyword(s):  
Transition Matrix ◽  
Stochastic Ordering ◽  
Queueing Model ◽  
Recursive Models ◽  
Comparison Results ◽  
External Process ◽  
Consumption Model ◽  
System States ◽  
Markov Modulated ◽  
Time Division

We consider a general discrete-time stochastic recursive model that is influenced by an external Markov chain. Our aim is to investigate the effect that the transition matrix of the external process has on the system states of the model. To answer this question, we use new stochastic ordering concepts. Especially interesting are the results for infinite-stage Markov-modulated models. We illustrate our main results by three applications: an inventory model, a consumption model, and a queueing model for a time division multiplexing system.

scholarly journals Duality results for Markov-modulated fluid flow models

2011 ◽  
Vol 48 (A) ◽  
pp. 309-318 ◽  
Author(s):  
Soohan Ahn ◽  
Vaidyanathan Ramaswami
Keyword(s):  
Fluid Flow ◽  
Scaling Factor ◽  
Birth And Death Processes ◽  
Flow Models ◽  
Duality Results ◽  
Continuous State ◽  
Markov Modulated

We establish some interesting duality results for Markov-modulated fluid flow models. Though fluid flow models are continuous-state analogues of quasi-birth-and-death processes, some duality results do differ by the inclusion of a scaling factor.

A matrix exponential form for hitting probabilities and its application to a Markov-modulated fluid queue with downward jumps

2002 ◽  
Vol 39 (3) ◽  
pp. 604-618 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Hiroyuki Takada
Keyword(s):  
Fluid Flow ◽  
Matrix Exponential ◽  
Alternative Proof ◽  
Fluid Queue ◽  
Exponential Form ◽  
Hitting Probabilities ◽  
Finite State ◽  
Exponent Matrix ◽  
Markov Structure ◽  
Markov Modulated

We consider a fluid queue with downward jumps, where the fluid flow rate and the downward jumps are controlled by a background Markov chain with a finite state space. We show that the stationary distribution of a buffer content has a matrix exponential form, and identify the exponent matrix. We derive these results using time-reversed arguments and the background state distribution at the hitting time concerning the corresponding fluid flow with upward jumps. This distribution was recently studied for a fluid queue with upward jumps under a stability condition. We give an alternative proof for this result using the rate conservation law. This proof not only simplifies the proof, but also explains an underlying Markov structure and enables us to study more complex cases such that the fluid flow has jumps subject to a nondecreasing Lévy process, a Brownian component, and countably many background states.

A matrix exponential form for hitting probabilities and its application to a Markov-modulated fluid queue with downward jumps

2002 ◽  
Vol 39 (03) ◽  
pp. 604-618 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Hiroyuki Takada
Keyword(s):  
Fluid Flow ◽  
Matrix Exponential ◽  
Alternative Proof ◽  
Fluid Queue ◽  
Exponential Form ◽  
Hitting Probabilities ◽  
Finite State ◽  
Exponent Matrix ◽  
Markov Structure ◽  
Markov Modulated

We consider a fluid queue with downward jumps, where the fluid flow rate and the downward jumps are controlled by a background Markov chain with a finite state space. We show that the stationary distribution of a buffer content has a matrix exponential form, and identify the exponent matrix. We derive these results using time-reversed arguments and the background state distribution at the hitting time concerning the corresponding fluid flow with upward jumps. This distribution was recently studied for a fluid queue with upward jumps under a stability condition. We give an alternative proof for this result using the rate conservation law. This proof not only simplifies the proof, but also explains an underlying Markov structure and enables us to study more complex cases such that the fluid flow has jumps subject to a nondecreasing Lévy process, a Brownian component, and countably many background states.

scholarly journals Duality results for Markov-modulated fluid flow models

2011 ◽  
Vol 48 (A) ◽  
pp. 309-318
Author(s):  
Soohan Ahn ◽  
Vaidyanathan Ramaswami
Keyword(s):  
Fluid Flow ◽  
Scaling Factor ◽  
Birth And Death Processes ◽  
Flow Models ◽  
Duality Results ◽  
Continuous State ◽  
Markov Modulated

We establish some interesting duality results for Markov-modulated fluid flow models. Though fluid flow models are continuous-state analogues of quasi-birth-and-death processes, some duality results do differ by the inclusion of a scaling factor.

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