Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Ahn, Soohan; Badescu, Andrei L.; Ramaswami, V.

doi:10.1007/s11134-007-9017-x

Cited by 67 publications

(58 citation statements)

References 37 publications

(82 reference statements)

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“…In the bounded fluid model in [2,3,22], it is assumed that c i = 0 whenever i ∈ S 1 and M(t) = b or i ∈ S 2 and M(t) = 0. This behavior can be incorporated into our model at the upper boundary by definingŜ 0 = S 0 ∪ S 1 and lettingP 10 , partitioned according to S 0 ∪ S 1 , beP…”

Section: M(t) ϕ(T)) Behaves In a Manner Equivalent To (M(t) ϕ(T))mentioning

confidence: 99%

“…They have become highly successful in modeling a number of different aspects of the behavior of telecommunication networks and computer systems [13,23,24]. It has also quickly become evident that these models have tremendous application potential in many other areas, including risk processes in insurance [2,18], manufacturing systems [16], hydro-power generation [9], as well as environmental problems, such as modeling of coral reef resilience [15].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hitting Probabilities and Hitting Times for Stochastic Fluid Flows: The Bounded Model

Bean

O’Reilly²,

Taylor

2008

Prob. Eng. Inf. Sci.

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We consider a Markovian stochastic fluid flow model in which the fluid level has a lower bound zero and a positive upper bound. The behavior of the process at the boundaries is modeled by parameters that are different than those in the interior and allow for modeling a range of desired behaviors at the boundaries. We illustrate this with examples. We establish formulas for several time-dependent performance measures of significance to a number of applied probability models. These results are achieved with techniques applied within the fluid flow model directly. This leads to useful physical interpretations, which are presented.

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Section: M(t) ϕ(T)) Behaves In a Manner Equivalent To (M(t) ϕ(T))mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hitting Probabilities and Hitting Times for Stochastic Fluid Flows: The Bounded Model

Bean

O’Reilly²,

Taylor

2008

Prob. Eng. Inf. Sci.

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show abstract

“…All matrices have nice probabilistic interpretations. For more details see Ramaswami [15] and Ahn and Ramaswami [4].…”

Section: The Fluid Inventory Modelmentioning

confidence: 99%

A Jump-Fluid Production–inventory Model With a Double Band Control

Barron¹,

Perry²,

Stadje³

2014

Prob. Eng. Inf. Sci.

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We consider a production-inventory control model with two reflecting boundaries, representing the finite storage capacity and the finite maximum backlog. Demands arrive at the inventory according to a Poisson process, their i.i.d. sizes having a common phase-type distribution. The inventory is filled by a production process, which alternates between two prespecified production rates ρ 1 and ρ 2 : as long as the content level is positive, ρ 1 is applied while the production follows ρ 2 during time intervals of backlog (i.e., negative content). We derive in closed form the various cost functionals of this model for the discounted case as well as under the long-run-average criterion. The analysis is based on a martingale of the Kella-Whitt type and results for fluid flow models due to Ahn and Ramaswami.

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“…The two-sided reflection W (t) of X(t), with respect to the strip [0, B], is defined through (1), where W (t), L(t), U (t) are real continuous functions which satisfy the following conditions:…”

Section: Two-sided Reflectionmentioning

confidence: 99%

Markov-Modulated Brownian Motion with Two Reflecting Barriers

Ivanovs

2010

Journal of Applied Probability

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We consider a Markov-modulated Brownian motion reflected to stay in a strip [0, B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this result and explaining its simplicity. Moreover, this argument allows for generalizations including the distribution of the reflected process at an independent exponentially distributed epoch. Our second contribution concerns transient behavior of the reflected system. We identify the joint law of the processes t, X(t), J(t) at inverse local times.

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Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier

Cited by 67 publications

References 37 publications

Hitting Probabilities and Hitting Times for Stochastic Fluid Flows: The Bounded Model

Hitting Probabilities and Hitting Times for Stochastic Fluid Flows: The Bounded Model

A Jump-Fluid Production–inventory Model With a Double Band Control

Markov-Modulated Brownian Motion with Two Reflecting Barriers

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