Transient Analysis of Fluid Models via Elementary Level-Crossing Arguments

Ahn, Soohan; Ramaswami, V.

doi:10.1080/15326340500481788

Cited by 33 publications

(30 citation statements)

References 19 publications

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“…This was proved as Theorem 3.2.1 in [4] using a Kolmogorov differential equations approach, and also in [2] using a more rigorous treatment based on stochastic discretization. This result is indeed related to a change-ofvariables formula in integration, and underlying it is the simple fact that in phase i, a small dt increment in time results in a dx = ±c i dt change in the fluid level.…”

Section: State Distribution At Time Tmentioning

confidence: 99%

“…For completeness, we shall occasionally provide a sketch of their proofs but, for ease of reading and for maintaining the flow of ideas, shall use only simple arguments as in [4]; more rigorous and formal proofs can be given using stochastic discretization methods [2].…”

Section: Some Kernels and First Passage Timesmentioning

confidence: 99%

“…In the QBD process case, the velocities being unity do not show up explicitly in the duality results. An explanation of this can also be given in terms of the change of variables discussed in [4]; see Theorem 3.2.1 and Remark 3.2.3 therein. In any case, ignoring this and relying only on intuition based on the consideration of kinematic states alone, such as in Figure 1(a), can indeed lead to erroneous conclusions.…”

Section: Introductionmentioning

confidence: 99%

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Duality results for Markov-modulated fluid flow models

Ahn

Ramaswami²

2011

Journal of Applied Probability

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Section: State Distribution At Time Tmentioning

confidence: 99%

Section: Some Kernels and First Passage Timesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Duality results for Markov-modulated fluid flow models

Ahn

Ramaswami²

2011

Journal of Applied Probability

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“…In general, the fluid flow type analysis of MAP risk models is more probabilist in nature and relies heavily on the knowledge of the Laplace transform of various first passage times (see, e.g. Ahn and Ramaswami (2006) and Ramaswami (2006)). However, a drawback of these fluid flow MAMs for the purpose of ruin theory applications is their limitation to claim size distributions that are phase type, excluding heavy-tail claim size distributions (among others) from the analysis.…”

Section: U(y)mentioning

confidence: 99%

Perturbed MAP Risk Models with Dividend Barrier Strategies

Cheung

Landriault

2009

J. Appl. Probab.

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In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markovmodulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.

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“…For the determination of the cost functionals we use two tools: (a) the matrix-analytic approach and the theory of Markov-modulated fluid flows (initiated in a series of papers by Ahn and Ramaswami [1]- [3] and (b) an application of the optional sampling theorem to a special Kella-Whitt martingale.…”

Section: Mathematical Preliminariesmentioning

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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Transient Analysis of Fluid Models via Elementary Level-Crossing Arguments

Abstract: An analysis of the time-dependent evolution of the canonical Markov modulated fluid flow model is presented using elementary level-crossing arguments.

Cited by 33 publications

References 19 publications

Duality results for Markov-modulated fluid flow models

Duality results for Markov-modulated fluid flow models

Perturbed MAP Risk Models with Dividend Barrier Strategies

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

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