scholarly journals Stability and structural properties of stochastic storage networks

1996 ◽  
Vol 33 (04) ◽  
pp. 1169-1180 ◽  
Author(s):  
Offer Kella ◽  
Ward Whitt
Keyword(s):  
Structural Properties ◽  
Stability Condition ◽  
General Model ◽  
Initial Conditions ◽  
Internal Flows ◽  
Stationary Increments ◽  
Fluid Network ◽  
Storage Networks ◽  
Stochastic Fluid

We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content process is tight under the natural stability condition. The multi-dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with non-zero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.

scholarly journals Stability and structural properties of stochastic storage networks

1996 ◽  
Vol 33 (4) ◽  
pp. 1169-1180 ◽  
Author(s):  
Offer Kella ◽  
Ward Whitt
Keyword(s):  
Structural Properties ◽  
Stability Condition ◽  
General Model ◽  
Initial Conditions ◽  
Internal Flows ◽  
Stationary Increments ◽  
Fluid Network ◽  
Storage Networks ◽  
Stochastic Fluid

We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content process is tight under the natural stability condition. The multi-dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with non-zero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.

Stochastic storage networks: stationarity and the feedforward case

1997 ◽  
Vol 34 (02) ◽  
pp. 498-507 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Total Variation ◽  
Finite Time ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Input Process ◽  
Stationary Increments ◽  
Stationary Version ◽  
Storage Network ◽  
The Difference ◽  
Storage Networks

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.

Stochastic storage networks: stationarity and the feedforward case

1997 ◽  
Vol 34 (2) ◽  
pp. 498-507 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Total Variation ◽  
Finite Time ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Input Process ◽  
Stationary Increments ◽  
Stationary Version ◽  
Storage Network ◽  
The Difference ◽  
Storage Networks

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.

scholarly journals Global Existence and Blow-Up for the Classical Solutions of the Long-Short Wave Equations with Viscosity

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Jincheng Shi ◽  
Shengzhong Xiao
Keyword(s):  
Global Existence ◽  
Life Span ◽  
General Model ◽  
Wave Equations ◽  
Blow Up ◽  
Initial Conditions ◽  
Short Wave ◽  
Classical Solutions ◽  
Global Classical Solutions

We are concerned with the global existence of classical solutions for a general model of viscosity long-short wave equations. Under suitable initial conditions, the existence of the global classical solutions for the viscosity long-short wave equations is proved. If it does not exist globally, the life span which is the largest time where the solutions exist is also obtained.

Stability of feed-forward fluid networks with Lévy input

1996 ◽  
Vol 33 (2) ◽  
pp. 513-522 ◽  
Author(s):  
Haya Kaspi ◽  
Offer Kella
Keyword(s):  
Total Variation ◽  
Internal Flow ◽  
Limiting Distribution ◽  
Product Form ◽  
Initial Condition ◽  
Feed Forward ◽  
Fluid Network ◽  
Fluid Networks ◽  
Stochastic Fluid

We consider a stochastic fluid network with independent subordinator inputs to the various stations and deterministic internal flow which is of feed-forward type. We show that under suitable conditions the process of fluid contents in the station has a limiting distribution, where the limit holds in total variation and is independent of the initial condition. We also show that this limiting distribution is of product form only for trivial setups.

Pricing via anticipative stochastic calculus

1994 ◽  
Vol 26 (04) ◽  
pp. 1006-1021
Author(s):  
Eckhard Platen ◽  
Rolando Rebolledo
Keyword(s):  
Structural Properties ◽  
General Model ◽  
Stochastic Calculus ◽  
Stochastic Equations ◽  
Stochastic Integrals ◽  
Derivative Securities

The paper proposes a general model for pricing of derivative securities. The underlying dynamics follows stochastic equations involving anticipative stochastic integrals. These equations are solved explicitly and structural properties of solutions are studied.

Lyapunov Stability of Linear Fractional Systems: Part 2 — Derivation of a Stability Condition

2013 ◽  
Author(s):  
Jean-Claude Trigeassou ◽  
Nezha Maamri ◽  
Alain Oustaloup
Keyword(s):  
Stability Condition ◽  
Initial Conditions ◽  
Positive Real ◽  
Fractional Systems ◽  
Direct Derivation ◽  
Energy Part ◽  
Complex Eigenvalues ◽  
The Stability ◽  
Definition Of ◽  
Infinite State

This paper, composed of two parts, addresses the stability of linear commensurate order fractional systems, Dn (X) = A X 0 < n < 1, using the infinite state approach. Whereas Part 1 has been dedicated to the definition of fractional systems energy, Part 2 deals with the derivation of a stability condition. When the eigenvalues of A are real, the modal representation shows that system energy is the sum of independent modal energies, so the derivation of a stability condition is straightforward in this case. On the contrary, when the eigenvalues are complex with positive real parts, unusual energy dynamics depending on initial conditions prevent direct derivation of a stability condition. Thus, an indirect method is proposed to formulate a stability condition in the complex eigenvalues case.

scholarly journals Linear stochastic fluid networks

1999 ◽  
Vol 36 (01) ◽  
pp. 244-260 ◽  
Author(s):  
Offer Kella ◽  
Ward Whitt
Keyword(s):  
Infinite Server ◽  
Open Networks ◽  
Fluid Network ◽  
Stochastic Transition ◽  
Fluid Networks ◽  
Batch Sizes ◽  
Arrival Processes ◽  
Flow Through ◽  
Infinite Server Queues ◽  
Stochastic Fluid

We introduce open stochastic fluid networks that can be regarded as continuous analogues or fluid limits of open networks of infinite-server queues. Random exogenous input may come to any of the queues. At each queue, a c.d.f.-valued stochastic process governs the proportion of the input processed by a given time after arrival. The routeing may be deterministic (a specified sequence of successive queue visits) or proportional, i.e. a stochastic transition matrix may govern the proportion of the output routed from one queue to another. This stochastic fluid network with deterministic c.d.f.s governing processing at the queues arises as the limit of normalized networks of infinite-server queues with batch arrival processes where the batch sizes grow. In this limit, one can think of each particle having an evolution through the network, depending on its time and place of arrival, but otherwise independent of all other particles. A key property associated with this independence is the linearity: the workload associated with a superposition of inputs, each possibly having its own pattern of flow through the network, is simply the sum of the component workloads. As with infinite-server queueing models, the tractability makes the linear stochastic fluid network a natural candidate for approximations.

Dynamic Analysis of Three Parallel Beams With Electrostatic Force Interaction

2011 ◽  
Author(s):  
Pezhman A. Hassanpour ◽  
Patricia M. Nieva ◽  
Amir Khajepour
Keyword(s):  
Time Domain ◽  
Stability Condition ◽  
Initial Conditions ◽  
Electrostatic Force ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Stability Margin ◽  
Modal Damping ◽  
The Stability ◽  
Euler Bernoulli Beam

In this paper, the dynamics of a micro-machined structure with three parallel cantilevers is investigated. The cantilevers are electrically charged and apply electrostatic force to each other. The governing equations of motion are derived using Euler-Bernoulli beam theory and considering structural modal damping. The stability condition of the beams for various electric charges is also studied. In addition, the equations of motion are integrated to obtain the response of the beams in time-domain for a range of initial conditions. This response is used to study the behavior of the beams at the stability margin. The end application of the structure under investigation is in the device characterization. The dynamic stability condition and time-domain responses are used to investigate the reliability of the characterization. Once translated back to physical quantities, these results can be used for improving the measurements.

Stability of feed-forward fluid networks with Lévy input

1996 ◽  
Vol 33 (02) ◽  
pp. 513-522 ◽  
Author(s):  
Haya Kaspi ◽  
Offer Kella
Keyword(s):  
Total Variation ◽  
Internal Flow ◽  
Limiting Distribution ◽  
Product Form ◽  
Initial Condition ◽  
Feed Forward ◽  
Fluid Network ◽  
Fluid Networks ◽  
Stochastic Fluid

We consider a stochastic fluid network with independent subordinator inputs to the various stations and deterministic internal flow which is of feed-forward type. We show that under suitable conditions the process of fluid contents in the station has a limiting distribution, where the limit holds in total variation and is independent of the initial condition. We also show that this limiting distribution is of product form only for trivial setups.

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