Fluid Model Driven by an M/M/1 Queue with Set-Up and Close-Down Period

2014 ◽  
Vol 513-517 ◽  
pp. 3377-3380
Author(s):  
Fu Wei Wang ◽  
Bing Wei Mao
Keyword(s):  
Stationary Distribution ◽  
Solution Method ◽  
Fluid Model ◽  
Model Driven ◽  
Buffer Content ◽  
The Laplace Transform ◽  
Matrix Geometric Solution ◽  
The Mean ◽  
Joint Stationary Distribution ◽  
Set Up

The fluid model driven by an M/M/1 queue with set-up and close-down period is studied. The Laplace transform of the joint stationary distribution of the fluid model is of matrix geometric structure. With matrix geometric solution method, the Laplace-Stieltjes transformation of the stationary distribution of the buffer content is obtained, as well as the mean buffer content. Finally, with some numerical examples, the effect of the parameters on mean buffer content is presented.

scholarly journals A fluid queue with a finite buffer and subexponential input

2000 ◽  
Vol 32 (1) ◽  
pp. 221-243 ◽  
Author(s):  
A. P. Zwart
Keyword(s):  
Stationary Distribution ◽  
Fluid Model ◽  
Buffer Size ◽  
Finite Buffer ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Buffer Content ◽  
The Mean ◽  
Heavy Tailed ◽  
Finite Dam

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue established by Kella and Whitt are extended to the finite buffer case: it is shown that the stationary distribution of the buffer content is related to the stationary distribution of the finite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distribution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buffer asymptotics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic results show a significant influence of heavy-tailed input characteristics on the performance of the fluid queue.

scholarly journals A fluid queue with a finite buffer and subexponential input

2000 ◽  
Vol 32 (01) ◽  
pp. 221-243 ◽  
Author(s):  
A. P. Zwart
Keyword(s):  
Stationary Distribution ◽  
Fluid Model ◽  
Buffer Size ◽  
Finite Buffer ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Buffer Content ◽  
The Mean ◽  
Heavy Tailed ◽  
Finite Dam

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue established by Kella and Whitt are extended to the finite buffer case: it is shown that the stationary distribution of the buffer content is related to the stationary distribution of the finite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distribution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buffer asymptotics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic results show a significant influence of heavy-tailed input characteristics on the performance of the fluid queue.

scholarly journals Markov-modulated Ornstein–Uhlenbeck processes

2016 ◽  
Vol 48 (1) ◽  
pp. 235-254 ◽  
Author(s):  
G. Huang ◽  
H. M. Jansen ◽  
M. Mandjes ◽  
P. Spreij ◽  
K. De Turck
Keyword(s):  
Markov Process ◽  
Integration Theory ◽  
Background Process ◽  
Finite State ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Markov Modulated ◽  
Set Up ◽  
Functional Central Limit

Abstract In this paper we consider an Ornstein–Uhlenbeck (OU) process (M(t))t≥0 whose parameters are determined by an external Markov process (X(t))t≥0 on a finite state space {1, . . ., d}; this process is usually referred to as Markov-modulated Ornstein–Uhlenbeck. We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a system of partial differential equations (PDEs) for the Laplace transform of M(t) and the state X(t) of the background process, jointly for time epochs t = t1, . . ., tK. Then we use this PDE to set up a recursion that yields all moments of M(t) and its stationary counterpart; we also find an expression for the covariance between M(t) and M(t + u). We then establish a functional central limit theorem for M(t) for the situation that certain parameters of the underlying OU processes are scaled, in combination with the modulating Markov process being accelerated; interestingly, specific scalings lead to drastically different limiting processes. We conclude the paper by considering the situation of a single Markov process modulating multiple OU processes.

A fluid model with data message discarding

2002 ◽  
Vol 34 (02) ◽  
pp. 329-348
Author(s):  
Bin Liu ◽  
Attahiru Sule Alfa
Keyword(s):  
Stationary Distribution ◽  
Performance Measures ◽  
Fluid Model ◽  
Threshold Value ◽  
Numerical Results ◽  
Finite Buffer ◽  
Control Parameters ◽  
Level Crossing ◽  
Data Message ◽  
Buffer Content

In this paper, we study a fluid model with partial message discarding and early message discarding, in which a finite buffer receives data (or information) from N independent on/off sources. All data generated by a source during one of its on periods is considered as a complete message. Our discarding scheme consists of two parts: (i) whenever some data belonging to a message has been lost due to overflow of the buffer, the remaining portion of this message will be discarded, and (ii) as long as the buffer content surpasses a certain threshold value at the instant an on period starts, all information generated during this on period will be discarded. By applying level-crossing techniques, we derive the equations for determining the system's stationary distribution. Further, two important performance measures, the probability of messages being transmitted successfully and the goodput of the system, are obtained. Numerical results are provided to demonstrate the effect of control parameters on the performance of the system.

A fluid model with data message discarding

2002 ◽  
Vol 34 (2) ◽  
pp. 329-348 ◽  
Author(s):  
Bin Liu ◽  
Attahiru Sule Alfa
Keyword(s):  
Stationary Distribution ◽  
Performance Measures ◽  
Fluid Model ◽  
Threshold Value ◽  
Numerical Results ◽  
Finite Buffer ◽  
Control Parameters ◽  
Level Crossing ◽  
Data Message ◽  
Buffer Content

In this paper, we study a fluid model with partial message discarding and early message discarding, in which a finite buffer receives data (or information) from N independent on/off sources. All data generated by a source during one of its on periods is considered as a complete message. Our discarding scheme consists of two parts: (i) whenever some data belonging to a message has been lost due to overflow of the buffer, the remaining portion of this message will be discarded, and (ii) as long as the buffer content surpasses a certain threshold value at the instant an on period starts, all information generated during this on period will be discarded. By applying level-crossing techniques, we derive the equations for determining the system's stationary distribution. Further, two important performance measures, the probability of messages being transmitted successfully and the goodput of the system, are obtained. Numerical results are provided to demonstrate the effect of control parameters on the performance of the system.

Tissue Ki67 proliferative index expression and pathological changes in hemodialysis arteriovenous fistulae: Preliminary single-center results

2021 ◽  
pp. 112972982110154
Author(s):  
Raffaella Mauro ◽  
Cristina Rocchi ◽  
Francesco Vasuri ◽  
Alessia Pini ◽  
Anna Laura Croci Chiocchini ◽  
...  
Keyword(s):  
Morphological Changes ◽  
Hot Spot ◽  
Wall Thickening ◽  
Proliferating Cells ◽  
Ki 67 ◽  
Group A ◽  
The Mean ◽  
Set Up ◽  
Group B

Background: Arteriovenous fistula (AVF) for hemodialysis integrates outward remodeling with vessel wall thickening in response to drastic hemodynamic changes. Aim of this study is to determine the role of Ki67, a well-established proliferative marker, related to AVF, and its relationship with time-dependent histological morphologic changes. Materials and methods: All patients were enrolled in 1 year and stratified in two groups: (A) pre-dialysis patients submitted to first AVF and (B) patients submitted to revision of AVF. Morphological changes: neo-angiogenesis (NAG), myointimal thickening (MIT), inflammatory infiltrate (IT), and aneurysmatic fistula degeneration (AD). The time of AVF creation was recorded. A biopsy of native vein in Group A and of arterialized vein in Group B was submitted to histological and immunohistochemical (IHC) analysis. IHC for Ki67 was automatically performed in all specimens. Ki67 immunoreactivity was assessed as the mean number of positive cells on several high-power fields, counted in the hot spots. Results: A total of 138 patients were enrolled, 69 (50.0%) Group A and 69 (50.0%) Group B. No NAG or MIT were found in Group A. Seven (10.1%) Group A veins showed a mild MIT. Analyzing the Group B, a moderate-to-severe MIT was present in 35 (50.7%), IT in 19 (27.5%), NAG in 37 (53.6%); AD was present in 10 (14.5%). All AVF of Group B with the exception of one (1.4%) showed a positivity for Ki67, with a mean of 12.31 ± 13.79 positive cells/hot spot (range 0–65). Ki67-immunoreactive cells had a subendothelial localization in 23 (33.3%) cases, a myointimal localization in SMC in 35 (50.7%) cases. The number of positive cells was significantly correlated with subendothelial localization of Ki67 ( p = 0.001) and with NA ( p = 0.001). Conclusions: Native veins do not contain cycling cells. In contrast, vascular cell proliferation starts immediately after AVF creation and persists independently of the time the fistula is set up. The amount of proliferating cells is significantly associated with MIT and subendothelial localization of Ki67-immunoreactive cells, thus suggesting a role of Ki-67 index in predicting AVF failure.

scholarly journals The Sankara Nethralaya Tamil Nadu Essilor Myopia (STEM) Study—Defining a Threshold for Non-Cycloplegic Myopia Prevalence in Children

2021 ◽  
Vol 10 (6) ◽  
pp. 1215
Author(s):  
Aparna Gopalakrishnan ◽  
Jameel Rizwana Hussaindeen ◽  
Viswanathan Sivaraman ◽  
Meenakshi Swaminathan ◽  
Yee Ling Wong ◽  
...  
Keyword(s):  
Open Field ◽  
Tamil Nadu ◽  
Mean Difference ◽  
School Vision ◽  
Elite School ◽  
Prevalence Estimates ◽  
The Mean ◽  
Clinically Significant ◽  
Set Up ◽  
Definition Of

The aim of this study was to investigate the agreement between cycloplegic and non-cycloplegic autorefraction with an open-field auto refractor in a school vision screening set up, and to define a threshold for myopia that agrees with the standard cycloplegic refraction threshold. The study was conducted as part of the Sankara Nethralaya Tamil Nadu Essilor Myopia (STEM) study, which investigated the prevalence, incidence, and risk factors for myopia among children in South India. Children from two schools aged 5 to 15 years, with no ocular abnormalities and whose parents gave informed consent for cycloplegic refraction were included in the study. All the children underwent visual acuity assessment (Pocket Vision Screener, Elite school of Optometry, India), followed by non-cycloplegic and cycloplegic (1% tropicamide) open-field autorefraction (Grand Seiko, WAM-5500). A total of 387 children were included in the study, of whom 201 were boys. The mean (SD) age of the children was 12.2 (±2.1) years. Overall, the mean difference between cycloplegic and non-cycloplegic spherical equivalent (SE) open-field autorefraction measures was 0.34 D (limits of agreement (LOA), 1.06 D to −0.38 D). For myopes, the mean difference between cycloplegic and non-cycloplegic SE was 0.13 D (LOA, 0.63D to −0.36D). The prevalence of myopia was 12% (95% CI, 8% to 15%) using the threshold of cycloplegic SE ≤ −0.50 D, and was 14% (95% CI, 11% to 17%) with SE ≤ −0.50 D using non-cycloplegic refraction. When myopia was defined as SE of ≤−0.75 D under non-cycloplegic conditions, there was no difference between cycloplegic and non-cycloplegic open-field autorefraction prevalence estimates (12%; 95% CI, 8% to 15%; p = 1.00). Overall, non-cycloplegic refraction underestimates hyperopia and overestimates myopia; but for subjects with myopia, this difference is minimal and not clinically significant. A threshold of SE ≤ −0.75 D agrees well for the estimation of myopia prevalence among children when using non-cycloplegic refraction and is comparable with the standard definition of cycloplegic myopic refraction of SE ≤ −0.50 D.

Experiments on the flow of heat in liquid helium below 0.7 °K

1958 ◽  
Vol 246 (1246) ◽  
pp. 390-405 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Liquid Helium ◽  
Free Path ◽  
Empirical Relation ◽  
Mean Free Path ◽  
Series Of Experiments ◽  
The Mean ◽  
Set Up ◽  
Low Pressures ◽  
Measured Thermal Conductivity

A series of experiments has been performed to study the steady flow of heat in liquid helium in tubes of diameter 0.05 to 1.0 cm at temperatures between 0.25 and 0.7 °K. The results are interpreted in terms of the flow of a gas of phonons, in which the mean free path λ varies with temperature, and may be either greater or less than the diameter of the tube d . When λ ≫ d the flow is limited by the scattering of the phonons at the walls, and the effect of the surface has been studied, but when λ ≪ d viscous flow is set up in which the measured thermal conductivity is increased above that for wall scattering. This behaviour is very similar to that observed in the flow of gases at low pressures, and by applying kinetic theory to the problem it can be shown that the mean free path of the phonons characterizing viscosity can be expressed by the empirical relation λ = 3.8 x 10 -3 T -4.3 cm. This result is inconsistent with the temperature dependence of λ as T -9 predicted theoretically by Landau & Khalatnikov (1949).

scholarly journals Stochastic models for interference between searching insect parasites

1989 ◽  
Vol 30 (3) ◽  
pp. 268-277 ◽  
Author(s):  
Phil Diamond
Keyword(s):  
Stationary Distribution ◽  
Intraspecific Competition ◽  
Death Process ◽  
Confluent Hypergeometric Functions ◽  
Large Populations ◽  
The Mean ◽  
The One ◽  
Globally Stable ◽  
Insect Parasites ◽  
Birth Death

AbstractCompetition between a finite number of searching insect parasites is modelled by differential equations and birth-death processes. In the one species case of intraspecific competition, the deterministic equilibrium is globally stable and, for large populations, approximates the mean of the stationary distribution of the process. For two species, both inter- and intraspecific competition occurs and the deterministic equilibrium is globally stable. When the birth-death process is reversible, it is shown that the mean of the stationary distribution is approximated by the equilibrium. Confluent hypergeometric functions of two variables are important to the theory.

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