Accelerated buffer overflow simulation in self-similar queuing networks with long-range dependent processes and finite buffer capacity

2016 ◽  
Author(s):  
Izabella Lokshina ◽  
Thomas Wendt ◽  
Cees Lanting
Keyword(s):  
Long Range ◽  
Buffer Capacity ◽  
Buffer Overflow ◽  
Finite Buffer ◽  
Queuing Networks ◽  
Self Similar ◽  
Dependent Processes

Cell loss asymptotics for buffers fed with a large number of independent stationary sources

1999 ◽  
Vol 36 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Nikolay Likhanov ◽  
Ravi R. Mazumdar
Keyword(s):  
Local Limit ◽  
Cell Loss ◽  
Buffer Overflow ◽  
Finite Buffer ◽  
Loss Probabilities ◽  
Measure Change ◽  
Self Similar ◽  
Heavy Tailed ◽  
Overflow Probabilities ◽  
Stationary Sources

In this paper we derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the recent results of Courcoubetis and Weber on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of small buffers. Moreover we show that the results hold for a wide variety of traffic sources including ON/OFF sources with heavy-tailed distributed ON periods, which are typical candidates for so-called ‘self-similar’ inputs, showing that the asymptotic cell loss probability behaves in much the same manner for such sources as for the Markovian type of sources, which has important implications for statistical multiplexing. Numerical validation of the results against simulations are also reported.

Cell loss asymptotics for buffers fed with a large number of independent stationary sources

1999 ◽  
Vol 36 (01) ◽  
pp. 86-96 ◽  
Author(s):  
Nikolay Likhanov ◽  
Ravi R. Mazumdar
Keyword(s):  
Local Limit ◽  
Cell Loss ◽  
Buffer Overflow ◽  
Finite Buffer ◽  
Loss Probabilities ◽  
Measure Change ◽  
Self Similar ◽  
Heavy Tailed ◽  
Overflow Probabilities ◽  
Stationary Sources

In this paper we derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the recent results of Courcoubetis and Weber on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of small buffers. Moreover we show that the results hold for a wide variety of traffic sources including ON/OFF sources with heavy-tailed distributed ON periods, which are typical candidates for so-called ‘self-similar’ inputs, showing that the asymptotic cell loss probability behaves in much the same manner for such sources as for the Markovian type of sources, which has important implications for statistical multiplexing. Numerical validation of the results against simulations are also reported.

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

scholarly journals Homogeneous row-continuous bivariate markov chains with boundaries

1988 ◽  
Vol 25 (A) ◽  
pp. 237-256
Author(s):  
J. Keilson ◽  
M. Zachmann
Keyword(s):  
Data Transmission ◽  
Communication Systems ◽  
Buffer Capacity ◽  
Passage Time ◽  
Finite Buffer ◽  
Transition Rates ◽  
Boundary Problems ◽  
Ergodic Distribution ◽  
The Matrix ◽  
Voice Data

The matrix-geometric results of M. Neuts are extended to ergodic row-continuous bivariate Markov processes [J(t), N(t)] on state space B = {(j, n)} for which: (a) there is a boundary level N for N(t) associated with finite buffer capacity; (b) transition rates to adjacent rows and columns are independent of row level n in the interior of B. Such processes are of interest in the modelling of queue-length for voice-data transmission in communication systems. One finds that the ergodic distribution consists of two decaying components of matrix-geometric form, the second induced by the finite buffer capacity. The results are obtained via Green's function methods and compensation. Passage-time distributions for the two boundary problems are also made available algorithmically.

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.

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.

scholarly journals Distribution of time to buffer overflow in a finite-buffer manufacturing model with unreliable machine

2017 ◽  
Vol 112 ◽  
pp. 05005 ◽  
Author(s):  
Wojciech M. Kempa ◽  
Iwona Paprocka ◽  
Cezary Grabowik ◽  
Krzysztof Kalinowski ◽  
Damian Krenczyk
Keyword(s):  
Buffer Overflow ◽  
Finite Buffer ◽  
Unreliable Machine
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