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.

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.

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 Fluid queues driven by a discouraged arrivals queue

2003 ◽  
Vol 2003 (24) ◽  
pp. 1509-1528 ◽  
Author(s):  
P. R. Parthasarathy ◽  
K. V. Vijayashree
Keyword(s):  
Distribution Function ◽  
Stationary Distribution ◽  
Hypergeometric Functions ◽  
Numerical Results ◽  
Fluid Queue ◽  
Confluent Hypergeometric Functions ◽  
Fluid Queues ◽  
Buffer Content ◽  
Server Queue ◽  
Stationary Distribution Function

We consider a fluid queue driven by a discouraged arrivals queue and obtain explicit expressions for the stationary distribution function of the buffer content in terms of confluent hypergeometric functions. We compare it with a fluid queue driven by an infinite server queue. Numerical results are presented to compare the behaviour of the buffer content distributions for both these models.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

The threshold for a stochastic within-host CHIKV virus model with saturated incidence rate

2021 ◽  
pp. 2150042
Author(s):  
C. Gokila ◽  
M. Sambath
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Stationary Distribution ◽  
Reproduction Number ◽  
Threshold Value ◽  
Saturated Incidence Rate ◽  
Number Formula ◽  
Saturated Incidence ◽  
Virus Model ◽  
Global Positive Solution

This paper deals with stochastic Chikungunya (CHIKV) virus model along with saturated incidence rate. We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be extinct. We also discuss about the existence of a unique ergodic stationary distribution of the model, through a suitable Lyapunov function. The stationary distribution validates the occurrence of disease; through that, we find the threshold value for prevail and disappear of disease within host. With the help of numerical simulations, we validate the stochastic reproduction number [Formula: see text] as stated in our theoretical findings.

scholarly journals Volume and duration of losses in finite buffer fluid queues

2015 ◽  
Vol 52 (3) ◽  
pp. 826-840 ◽  
Author(s):  
Fabrice Guillemin ◽  
Bruno Sericola
Keyword(s):  
Busy Period ◽  
Buffer Capacity ◽  
Exact Expression ◽  
Loss Probability ◽  
Finite Buffer ◽  
Fluid Queues ◽  
Buffer Content ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Arrival Processes

We study congestion periods in a finite fluid buffer when the net input rate depends upon a recurrent Markov process; congestion occurs when the buffer content is equal to the buffer capacity. Similarly to O'Reilly and Palmowski (2013), we consider the duration of congestion periods as well as the associated volume of lost information. While these quantities are characterized by their Laplace transforms in that paper, we presently derive their distributions in a typical stationary busy period of the buffer. Our goal is to compute the exact expression of the loss probability in the system, which is usually approximated by the probability that the occupancy of the infinite buffer is greater than the buffer capacity under consideration. Moreover, by using general results of the theory of Markovian arrival processes, we show that the duration of congestion and the volume of lost information have phase-type distributions.

scholarly journals Queuing System with Unreliable Servers and Inhomogeneous Intensities for Analyzing the Impact of Non-Stationarity to Performance Measures of Wireless Network under Licensed Shared Access

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 800 ◽  
Author(s):  
Ekaterina Markova ◽  
Yacov Satin ◽  
Irina Kochetkova ◽  
Alexander Zeifman ◽  
Anna Sinitcina
Keyword(s):  
Performance Measures ◽  
Blocking Probability ◽  
Radio Resource Management ◽  
Queuing System ◽  
Finite Buffer ◽  
Data Traffic ◽  
Multiservice Networks ◽  
Limited Frequency ◽  
The Impact

Given the limited frequency band resources and increasing volume of data traffic in modern multiservice networks, finding new and more efficient radio resource management (RRM) mechanisms is becoming indispensable. One of the implemented technologies to solve this problem is the licensed shared access (LSA) technology. LSA allows the spectrum that has been licensed to an owner, who has absolute priority on its utilization, to be used by other participants (i.e., tenants). Owner priority impacts negatively on the quality of service (QoS) by reducing the data bit rate and interrupting user services. In this paper, we propose a wireless multiservice network scheme model described as a queuing system with unreliable servers and a finite buffer within the LSA framework. The aim of this work is to analyze main system performance measures: blocking probability, average number of requests in queue, and average queue length depending on LSA frequencies’ availability.

Probabilistic Main Bearing Performance for an Internal Combustion Engine

2004 ◽  
Author(s):  
Zissimos P. Mourelatos ◽  
Nickolas Vlahopoulos ◽  
Omidreza Ebrat ◽  
Jinghong Liang ◽  
Jin Wang
Keyword(s):  
Performance Measures ◽  
Probabilistic Analysis ◽  
Combustion Engine ◽  
Random Variables ◽  
Simulation Models ◽  
Threshold Value ◽  
Oil Viscosity ◽  
Main Bearing ◽  
Structural Dynamic ◽  
Engine System

A probabilistic analysis is presented for studying the variation effects on the main bearing performance of an I.C. engine system, under structural dynamic conditions. For computational efficiency, the probabilistic analysis is based on surrogate models (metamodels), which are developed using the kriging method. An Optimum Symmetric Latin Hypercube (OSLH) algorithm is used for efficient “space-filling” sampling of the design space. The metamodels provide an efficient and accurate substitute to the actual engine bearing simulation models. The bearing performance is based on a comprehensive engine system dynamic analysis which couples the flexible crankshaft and block dynamics with a detailed main bearing elastohydrodynamic analysis. The clearance of all main bearings and the oil viscosity comprise the random variables in the probabilistic analysis. The maximum oil pressure and the percentage of time within each cycle that a bearing operates with oil film thickness below a threshold value of 0.27 μm at each main bearing constitute the system performance measures. Probabilistic analyses are first performed to calculate the mean, standard deviation and probability density function of the bearing performance measures. Subsequently, a probabilistic sensitivity analysis is described for identifying the important random variables. Finally, a Reliability-Based Design Optimization (RBDO) study is conducted for optimizing the main bearing performance under uncertainty. Results from a V6 engine are presented.

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