Asymptotic behavior of the loss rate for Markov-modulated fluid queue with a finite buffer

2010 ◽  
Vol 65 (1) ◽  
pp. 19-42 ◽  
Author(s):  
Yutaka Sakuma ◽  
Masakiyo Miyazawa
Keyword(s):  
Asymptotic Behavior ◽  
Loss Rate ◽  
Finite Buffer ◽  
Fluid Queue ◽  
Markov Modulated

scholarly journals Proof of Monotone Loss Rate of Fluid Priority-Queue with Finite Buffer

2005 ◽  
Vol 51 (1-2) ◽  
pp. 77-87
Author(s):  
Stephen L. Spitler ◽  
Daniel C. Lee
Keyword(s):  
Loss Rate ◽  
Priority Queue ◽  
Finite Buffer

Modeling and Simulation of Self-Similar Traffic in Wireless IP Networks

2011 ◽  
pp. 249-265
Author(s):  
Dimitar Radev ◽  
Izabella Lokshina ◽  
Svetla Radeva
Keyword(s):  
Network Traffic ◽  
Traffic Load ◽  
Single Server ◽  
Finite Buffer ◽  
Wide Range ◽  
Telecommunications Network ◽  
Source Models ◽  
Wireless Ip ◽  
Self Similar ◽  
Markov Modulated

The paper examines self-similar properties of real telecommunications network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Simulation with stochastic and long range dependent traffic source models is performed, and the algorithms for buffer overflow simulation for finite buffer single server model under self-similar traffic load SSM/M/1/B are explained. The algorithms for modeling fixed-length sequence generators that are used to simulate self-similar behavior of wireless IP network traffic are developed and applied. Numerical examples are provided, and simulation results are analyzed.

ON THE WORKLOAD PROCESS IN A FLUID QUEUE WITH A RESPONSIVE BURSTY INPUT AND SELECTIVE DISCARDING

2003 ◽  
Vol 17 (4) ◽  
pp. 527-543
Author(s):  
Parijat Dube ◽  
Eitan Altman
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Feedback System ◽  
Moment Generating Function ◽  
General Distribution ◽  
Finite Buffer ◽  
Fluid Queue ◽  
The Stability ◽  
The Moment ◽  
Stationary Workload

We analyze a feedback system consisting of a finite buffer fluid queue and a responsive source. The source alternates between silence periods and active periods. At random epochs of times, the source becomes ready to send a burst of fluid. The length of the bursts (length of the active periods) are independent and identically distributed with some general distribution. The queue employs a threshold discarding policy in the sense that only those bursts at whose commencement epoch (the instant at which the source is ready to send) the workload (i.e., the amount of fluid in the buffer) is less than some preset threshold are accepted. If the burst is rejected then the source backs off from sending. We work within the framework of Poisson counter-driven stochastic differential equations and obtain the moment generating function and hence the probability density function of the stationary workload process. We then comment on the stability of this fluid queue. Our explicit characterizations will further provide useful insights and “engineering” guidelines for better network designing.

Finding the Conjugate of Markov Fluid Processes

1995 ◽  
Vol 9 (2) ◽  
pp. 297-315 ◽  
Author(s):  
Michel Mandjes ◽  
Ad Ridder
Keyword(s):  
Variance Reduction ◽  
Deviant Behavior ◽  
Multiple Source ◽  
Finite Buffer ◽  
Rate Matrix ◽  
Original Process ◽  
Source Case ◽  
Fluid Process ◽  
Markov Modulated ◽  
High Level

This paper addresses characteristics of finite-buffer Markov-modulated fluid processes, particularly those related to their deviant behavior. Our aim in this paper is to find rough asymptotics for the probability of a loss cycle. Apart from that, we derive some properties of the fluid process in case of the buffer contents reaching a high level (a process we call the conjugate of the original process). Our main goal is to obtain practicable methods to find the rate matrix of this conjugate process. For this purpose we use large deviations techniques, but we consider the governing eigensystem, as well, and we discuss the relation between these two approaches. We extend the analysis to the multiple source case. Finally, we use the obtained results in simulation. We examine variance reduction by importance sampling in a multiple source example. The new statistical law of the fluid process is based on the conjugate rate matrices.

Regenerative analysis of a finite buffer fluid queue

2010 ◽  
Author(s):  
Ruslana S. Goricheva ◽  
Oleg V. Lukashenko ◽  
Evsey V. Morozov ◽  
Michele Pagano
Keyword(s):  
Finite Buffer ◽  
Fluid Queue

A second-order Markov-modulated fluid queue with linear service rate

2004 ◽  
Vol 41 (3) ◽  
pp. 758-777 ◽  
Author(s):  
Landy Rabehasaina ◽  
Bruno Sericola
Keyword(s):  
Markov Chain ◽  
Simple Expression ◽  
Second Order ◽  
Service Rate ◽  
Order Model ◽  
Fluid Queue ◽  
First Order ◽  
Linear Stochastic Differential Equation ◽  
Local Variance ◽  
Markov Modulated

We consider an infinite-capacity second-order fluid queue governed by a continuous-time Markov chain and with linear service rate. The variability of the traffic is modeled by a Brownian motion and a local variance function modulated by the Markov chain and proportional to the fluid level in the queue. The behavior of this second-order fluid-flow model is described by a linear stochastic differential equation, satisfied by the transient queue level. We study the transient level's convergence in distribution under weak assumptions and we obtain an expression for the stationary queue level. For the first-order case, we give a simple expression of all its moments as well as of its Laplace transform. For the second-order model we compute its first two moments.

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.

A matrix exponential form for hitting probabilities and its application to a Markov-modulated fluid queue with downward jumps

2002 ◽  
Vol 39 (3) ◽  
pp. 604-618 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Hiroyuki Takada
Keyword(s):  
Fluid Flow ◽  
Matrix Exponential ◽  
Alternative Proof ◽  
Fluid Queue ◽  
Exponential Form ◽  
Hitting Probabilities ◽  
Finite State ◽  
Exponent Matrix ◽  
Markov Structure ◽  
Markov Modulated

We consider a fluid queue with downward jumps, where the fluid flow rate and the downward jumps are controlled by a background Markov chain with a finite state space. We show that the stationary distribution of a buffer content has a matrix exponential form, and identify the exponent matrix. We derive these results using time-reversed arguments and the background state distribution at the hitting time concerning the corresponding fluid flow with upward jumps. This distribution was recently studied for a fluid queue with upward jumps under a stability condition. We give an alternative proof for this result using the rate conservation law. This proof not only simplifies the proof, but also explains an underlying Markov structure and enables us to study more complex cases such that the fluid flow has jumps subject to a nondecreasing Lévy process, a Brownian component, and countably many background states.

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