A finite dam with variable release rate

1975 ◽  
Vol 12 (1) ◽  
pp. 205-211 ◽  
Author(s):  
G. F. Yeo
Keyword(s):  
Poisson Process ◽  
Release Rate ◽  
Numerical Results ◽  
Basic Method ◽  
Carry Over ◽  
Special Case ◽  
Instantaneous Release ◽  
Finite Dam

This note considers a finite dam fed by independently and identically distributed (i.i.d.) inputs, being either (i) of at least size β (> 0) or (ii) negative exponentially distributed, occurring in a Poisson process. The instantaneous release rate may be a function r(·) of the content; additional and numerical results are given for the special case where r(x) = µxα (0 ≦ α<∞, 0 < µ <∞) is proportional to the αth power of the content. The basic method used in [7] for the special case r(x) = µx for obtaining the distribution of the number of steps and of the time to first overflowing is shown to carry over almost completely in case (i), but only partially so in case (ii).

A finite dam with variable release rate

1975 ◽  
Vol 12 (01) ◽  
pp. 205-211 ◽  
Author(s):  
G. F. Yeo
Keyword(s):  
Poisson Process ◽  
Release Rate ◽  
Numerical Results ◽  
Basic Method ◽  
Carry Over ◽  
Special Case ◽  
Instantaneous Release ◽  
Finite Dam

This note considers a finite dam fed by independently and identically distributed (i.i.d.) inputs, being either (i) of at least size β (&gt; 0) or (ii) negative exponentially distributed, occurring in a Poisson process. The instantaneous release rate may be a function r(·) of the content; additional and numerical results are given for the special case where r(x) = µxα (0 ≦ α&lt;∞, 0 &lt; µ &lt;∞) is proportional to the αth power of the content. The basic method used in [7] for the special case r(x) = µx for obtaining the distribution of the number of steps and of the time to first overflowing is shown to carry over almost completely in case (i), but only partially so in case (ii).

Average cost under the P M λ, τ policy in a finite dam with compound Poisson inputs

2003 ◽  
Vol 40 (02) ◽  
pp. 519-526
Author(s):  
Jongho Bae ◽  
Sunggon Kim ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Release Rate ◽  
Average Cost ◽  
Compound Poisson Process ◽  
Water Release ◽  
Compound Poisson ◽  
Long Run ◽  
Finite Dam

We consider the policy in a finite dam in which the input of water is formed by a compound Poisson process and the rate of water release is changed instantaneously from a to M and from M to a (M &gt; a) at the moments when the level of water exceeds λ and downcrosses τ (λ &gt; τ) respectively. After assigning costs to the changes of release rate, a reward to each unit of output, and a cost related to the level of water in the reservoir, we determine the long-run average cost per unit time.

scholarly journals Optimization under the PMλ,τ policy of a finite dam with both continuous and jumpwise inputs

2005 ◽  
Vol 42 (2) ◽  
pp. 587-594
Author(s):  
Kyung Eun Lim ◽  
Jee Seon Baek ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Release Rate ◽  
Average Cost ◽  
Long Run ◽  
Random Jumps ◽  
Finite Dam

We consider a finite dam under the policy, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. The long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty that is a function of the level of water in the reservoir.

scholarly journals Optimization under the P M λ,τ policy of a finite dam with both continuous and jumpwise inputs

2005 ◽  
Vol 42 (02) ◽  
pp. 587-594
Author(s):  
Kyung Eun Lim ◽  
Jee Seon Baek ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Wiener Process ◽  
Release Rate ◽  
Average Cost ◽  
Long Run ◽  
Random Jumps ◽  
Finite Dam

We consider a finite dam under the policy, where the input of water is formed by a Wiener process subject to random jumps arriving according to a Poisson process. The long-run average cost per unit time is obtained after assigning costs to the changes of release rate, a reward to each unit of output, and a penalty that is a function of the level of water in the reservoir.

Average cost under the PMλ, τ policy in a finite dam with compound Poisson inputs

2003 ◽  
Vol 40 (2) ◽  
pp. 519-526 ◽  
Author(s):  
Jongho Bae ◽  
Sunggon Kim ◽  
Eui Yong Lee
Keyword(s):  
Poisson Process ◽  
Release Rate ◽  
Average Cost ◽  
Compound Poisson Process ◽  
Water Release ◽  
Compound Poisson ◽  
Long Run ◽  
Finite Dam

We consider the policy in a finite dam in which the input of water is formed by a compound Poisson process and the rate of water release is changed instantaneously from a to M and from M to a (M > a) at the moments when the level of water exceeds λ and downcrosses τ (λ > τ) respectively. After assigning costs to the changes of release rate, a reward to each unit of output, and a cost related to the level of water in the reservoir, we determine the long-run average cost per unit time.

An embedded level crossing technique for dams and queues

1979 ◽  
Vol 16 (01) ◽  
pp. 174-186 ◽  
Author(s):  
P. H. Brill
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Release Rate ◽  
Steady State Distribution ◽  
State Distribution ◽  
Level Crossing ◽  
Alternative Approach ◽  
Stationary Set ◽  
Special Case ◽  
Instantaneous Release

The new concept of embedded level crossings is combined with the old principle of stationary set balance to produce an alternative approach for obtaining the steady-state distribution of the level in a dam with general release rule. The method yields the steady state distribution of the customer waiting time in the GI/G/1 queue as a special case. Results for a dam in which the instantaneous release rate is proportional to the level, and for the M/G/1, GI/M/1, Ek/M/1 and D/M/1 queues are derived using the new technique.

An embedded level crossing technique for dams and queues

1979 ◽  
Vol 16 (1) ◽  
pp. 174-186 ◽  
Author(s):  
P. H. Brill
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Release Rate ◽  
Steady State Distribution ◽  
State Distribution ◽  
Level Crossing ◽  
Alternative Approach ◽  
Stationary Set ◽  
Special Case ◽  
Instantaneous Release

The new concept of embedded level crossings is combined with the old principle of stationary set balance to produce an alternative approach for obtaining the steady-state distribution of the level in a dam with general release rule. The method yields the steady state distribution of the customer waiting time in the GI/G/1 queue as a special case. Results for a dam in which the instantaneous release rate is proportional to the level, and for the M/G/1, GI/M/1, Ek/M/1 and D/M/1 queues are derived using the new technique.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

A model for interaction of a Poisson and a renewal process and its relation with queuing theory

1972 ◽  
Vol 9 (2) ◽  
pp. 451-456 ◽  
Author(s):  
Lennart Råde
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Queuing Theory ◽  
Random Number ◽  
Sufficient Conditions ◽  
Stieltjes Transform ◽  
Time Intervals ◽  
Response Process ◽  
Necessary And Sufficient ◽  
Special Case

This paper discusses the response process when a Poisson process interacts with a renewal process in such a way that one or more points of the Poisson process eliminate a random number of consecutive points of the renewal process. A queuing situation is devised such that the c.d.f. of the length of the busy period is the same as the c.d.f. of the length of time intervals of the renewal response process. The Laplace-Stieltjes transform is obtained and from this the expectation of the time intervals of the response process is derived. For a special case necessary and sufficient conditions for the response process to be a Poisson process are found.

A Construction of Rigid Analytic Cohomology Classes for Congruence Subgroups of SL3(ℤ)

2009 ◽  
Vol 61 (3) ◽  
pp. 674-690 ◽  
Author(s):  
David Pollack ◽  
Robert Pollack
Keyword(s):  
Basic Method ◽  
Constructive Proof ◽  
Congruence Subgroups ◽  
Special Case

Abstract.We give a constructive proof, in the special case of GL3, of a theorem of Ash and Stevens which compares overconvergent cohomology to classical cohomology. Namely, we show that every ordinary classical Hecke-eigenclass can be lifted uniquely to a rigid analytic eigenclass. Our basic method builds on the ideas of M. Greenberg; we first form an arbitrary lift of the classical eigenclass to a distribution-valued cochain. Then, by appropriately iterating the Up-operator, we produce a cocycle whose image in cohomology is the desired eigenclass. The constructive nature of this proof makes it possible to perform computer computations to approximate these interesting overconvergent eigenclasses.

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