Analysis of individual packet loss in a finite buffer queue with heterogeneous Markov modulated arrival processes: a study of traffic burstiness and priority packet discarding

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

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On Applying Evolutionary Computation Methods to Optimization of Vacation Cycle Costs in Finite-Buffer Queue

Artificial Intelligence and Soft Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-319-07173-2_41 ◽

2014 ◽

pp. 480-491 ◽

Cited By ~ 21

Author(s):

Marcin Woźniak ◽

Wojciech M. Kempa ◽

Marcin Gabryel ◽

Robert K. Nowicki ◽

Zhifei Shao

Keyword(s):

Evolutionary Computation ◽

Finite Buffer ◽

Finite Buffer Queue

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Volume and duration of losses in finite buffer fluid queues

Journal of Applied Probability ◽

10.1239/jap/1445543849 ◽

2015 ◽

Vol 52 (3) ◽

pp. 826-840 ◽

Cited By ~ 1

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.

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

Interdisciplinary and Multidimensional Perspectives in Telecommunications and Networking ◽

10.4018/978-1-60960-505-6.ch016 ◽

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.

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Finding the Conjugate of Markov Fluid Processes

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800003879 ◽

1995 ◽

Vol 9 (2) ◽

pp. 297-315 ◽

Cited By ~ 14

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.

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