Proofs of Storage: Theory, Constructions and Applications

2013 ◽  
pp. 7-8 ◽  
Author(s):  
Seny Kamara
Keyword(s):  
Storage Theory

A note on seasonal Markov chains with gamma or gamma-like distributions

1979 ◽  
Vol 16 (1) ◽  
pp. 117-128 ◽  
Author(s):  
E. H. Lloyd ◽  
S. D. Saleem
Keyword(s):  
Markov Chain ◽  
Laplace Transform ◽  
Weighted Sums ◽  
Power Transformation ◽  
Exponential Form ◽  
Continuous State ◽  
Bessel Distribution ◽  
Storage Theory ◽  
Special Case ◽  
Type Of Transition

Weighted sums defined on a Markov chain (MC) are important in applications (e.g. to reservoir storage theory). The rather intractable theory of such sums simplifies to some extent when the transition p.d.f. of the chain {Xt} has a Laplace transform (LT) L(Xt+1; θ |Χ t=x) of the ‘exponential' form H(θ) exp{ – G(θ)x}. An algorithm is derived for the computation of the LT of Σat,Χ t for this class, and for a seasonal generalization of it.A special case of this desirable exponential type of transition LT for a continuous-state discrete-time MC is identified by comparison with the LT of the Bessel distribution. This is made the basis for a new derivation of a gamma-distributed MC proposed by Lampard (1968).A seasonal version of this process is developed, valid for any number of seasons.Reference is made to related chains with three-parameter gamma-like distributions (of the Kritskii–Menkel family) that may be generated from the above by a simple power transformation.

Infinite dams with inputs forming a Markov chain

1968 ◽  
Vol 5 (1) ◽  
pp. 72-83 ◽  
Author(s):  
M. S. Ali Khan ◽  
J. Gani
Keyword(s):  
Markov Chain ◽  
Storage Systems ◽  
Random Variables ◽  
Time Intervals ◽  
Storage Theory ◽  
Annual Time ◽  
Theory Of Storage ◽  
Independent And Identically Distributed

Moran's [1] early investigations into the theory of storage systems began in 1954 with a paper on finite dams; the inputs flowing into these during consecutive annual time-intervals were assumed to form a sequence of independent and identically distributed random variables. Until 1963, storage theory concentrated essentially on an examination of dams, both finite and infinite, fed by inputs (discrete or continuous) which were additive. For reviews of the literature in this field up to 1963, the reader is referred to Gani [2] and Prabhu [3].

Equilibrium behavior of a stochastic system with secondary input

1971 ◽  
Vol 8 (02) ◽  
pp. 252-260 ◽  
Author(s):  
İzzet Şahin
Keyword(s):  
Stochastic System ◽  
Queueing Theory ◽  
Risk Theory ◽  
Insurance Risk ◽  
Statistical Nature ◽  
Equilibrium Behavior ◽  
Continuous Output ◽  
Storage Theory

Summary Equilibrium behavior of a stochastic system with two types of input of different statistical nature and with linear continuous output is investigated. The results have applications in queueing theory, storage theory and insurance-risk theory.

Infinite dams with inputs forming a Markov chain

1968 ◽  
Vol 5 (01) ◽  
pp. 72-83 ◽  
Author(s):  
M. S. Ali Khan ◽  
J. Gani
Keyword(s):  
Markov Chain ◽  
Storage Systems ◽  
Random Variables ◽  
Time Intervals ◽  
Storage Theory ◽  
Annual Time ◽  
Theory Of Storage ◽  
Independent And Identically Distributed

Moran's [1] early investigations into the theory of storage systems began in 1954 with a paper on finite dams; the inputs flowing into these during consecutive annual time-intervals were assumed to form a sequence of independent and identically distributed random variables. Until 1963, storage theory concentrated essentially on an examination of dams, both finite and infinite, fed by inputs (discrete or continuous) which were additive. For reviews of the literature in this field up to 1963, the reader is referred to Gani [2] and Prabhu [3].

Time-dependent results in storage theory

1964 ◽  
Vol 1 (01) ◽  
pp. 1-46 ◽  
Author(s):  
N. U. Prabhu
Keyword(s):  
Original Model ◽  
Time Dependent ◽  
Comprehensive Treatment ◽  
Forthcoming Book ◽  
Time Dependent Behaviour ◽  
Ofthe Time ◽  
Storage Theory ◽  
Theory Of Storage ◽  
Dependent Behaviour ◽  
Made In

The probability theory of storage systems formulated by P. A. P. Moran in 1954 has now developed into an active branch of applied probability. An excellent account of the theory, describing results obtained up to 1958 is contained in Moran's (1959) monograph, Considerable progress has since been made in several directions-the study ofthe time-dependent behaviour ofstochastic processes underlying Moran's original model, modifications of this model, as well as the formulation and solution of new models. The aim of this paper is to give an expository account of these developments; a comprehensive treatment will be found in the author's forthcoming book [Prabhu (1964)].

A supply of storage theory with asymmetric information

1989 ◽  
Vol 9 (6) ◽  
pp. 573-581 ◽  
Author(s):  
Nabil T. Khoury ◽  
Jean-Marc Martel
Keyword(s):  
Asymmetric Information ◽  
Storage Theory

A note on seasonal Markov chains with gamma or gamma-like distributions

1979 ◽  
Vol 16 (01) ◽  
pp. 117-128 ◽  
Author(s):  
E. H. Lloyd ◽  
S. D. Saleem
Keyword(s):  
Markov Chain ◽  
Laplace Transform ◽  
Weighted Sums ◽  
Power Transformation ◽  
Exponential Form ◽  
Continuous State ◽  
Bessel Distribution ◽  
Storage Theory ◽  
Special Case ◽  
Type Of Transition

Weighted sums defined on a Markov chain (MC) are important in applications (e.g. to reservoir storage theory). The rather intractable theory of such sums simplifies to some extent when the transition p.d.f. of the chain {Xt } has a Laplace transform (LT) L(Xt +1; θ |Χ t=x) of the ‘exponential' form H(θ) exp{ – G(θ)x}. An algorithm is derived for the computation of the LT of Σat,Χ t for this class, and for a seasonal generalization of it. A special case of this desirable exponential type of transition LT for a continuous-state discrete-time MC is identified by comparison with the LT of the Bessel distribution. This is made the basis for a new derivation of a gamma-distributed MC proposed by Lampard (1968). A seasonal version of this process is developed, valid for any number of seasons. Reference is made to related chains with three-parameter gamma-like distributions (of the Kritskii–Menkel family) that may be generated from the above by a simple power transformation.

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