On the Consecutive Customer Loss Probabilities in a Finite-Buffer Renewal Batch Input Queue with Different Batch Acceptance/Rejection Strategies Under Non-renewal Service

2018 ◽  
pp. 45-62
Author(s):  
A. D. Banik ◽  
Souvik Ghosh ◽  
M. L. Chaudhry
Keyword(s):  
Finite Buffer ◽  
Input Queue ◽  
Loss Probabilities ◽  
Batch Input

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.

Analysis of finite buffer renewal input queue with balking and multiple working vacations

OPSEARCH ◽  
2013 ◽  
Vol 50 (4) ◽  
pp. 548-565 ◽  
Author(s):  
P. Vijaya Laxmi ◽  
K. Jyothsna
Keyword(s):  
Finite Buffer ◽  
Input Queue ◽  
Multiple Working Vacations ◽  
Working Vacations

scholarly journals Fast simulation of Markov fluid models

1996 ◽  
Vol 33 (03) ◽  
pp. 786-803 ◽  
Author(s):  
Ad Ridder
Keyword(s):  
Probability Measure ◽  
Continuous Flow ◽  
Discrete Event ◽  
Empirical Measure ◽  
Finite Buffer ◽  
Fluid Models ◽  
Fast Simulation ◽  
Discrete Event Simulations ◽  
Loss Probabilities ◽  
Event Simulations

In this paper we study continuous flow finite buffer systems with input rates modulated by Markov chains. Discrete event simulations are applied for estimating loss probabilities. The simulations are executed under a twisted version of the original probability measure (importance sampling). We present a simple rule for determining a new measure, then show that the new measure matches the ‘most likely' empirical measure that we expect from large deviations arguments, and finally prove optimality of the new measure.

scholarly journals An LCFS finite buffer model with finite source batch input

1989 ◽  
Vol 26 (02) ◽  
pp. 372-380
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Queueing Systems ◽  
Length Distribution ◽  
Source Distribution ◽  
Closed Form Expression ◽  
Finite Buffer ◽  
Form Expression ◽  
Batch Arrivals ◽  
Queue Length Distribution ◽  
Recursive Computation ◽  
Batch Input

Queueing systems are studied with a last-come, first-served queueing discipline and batch arrivals generated by a finite number of non-exponential sources. A closed-form expression is derived for the steady-state queue length distribution. This expression has a scaled geometric form and is insensitive to the input distribution. Moreover, an algorithm for the recursive computation of the normalizing constant and the busy source distribution is presented. The results are of both practical and theoretical interest as an extension of the standard Poisson batch input case.

scholarly journals Fast simulation of Markov fluid models

1996 ◽  
Vol 33 (3) ◽  
pp. 786-803 ◽  
Author(s):  
Ad Ridder
Keyword(s):  
Probability Measure ◽  
Continuous Flow ◽  
Discrete Event ◽  
Empirical Measure ◽  
Finite Buffer ◽  
Fluid Models ◽  
Fast Simulation ◽  
Discrete Event Simulations ◽  
Loss Probabilities ◽  
Event Simulations

In this paper we study continuous flow finite buffer systems with input rates modulated by Markov chains. Discrete event simulations are applied for estimating loss probabilities. The simulations are executed under a twisted version of the original probability measure (importance sampling). We present a simple rule for determining a new measure, then show that the new measure matches the ‘most likely' empirical measure that we expect from large deviations arguments, and finally prove optimality of the new measure.

scholarly journals An LCFS finite buffer model with finite source batch input

1989 ◽  
Vol 26 (2) ◽  
pp. 372-380 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Queueing Systems ◽  
Length Distribution ◽  
Source Distribution ◽  
Closed Form Expression ◽  
Finite Buffer ◽  
Form Expression ◽  
Batch Arrivals ◽  
Queue Length Distribution ◽  
Recursive Computation ◽  
Batch Input

Queueing systems are studied with a last-come, first-served queueing discipline and batch arrivals generated by a finite number of non-exponential sources. A closed-form expression is derived for the steady-state queue length distribution. This expression has a scaled geometric form and is insensitive to the input distribution. Moreover, an algorithm for the recursive computation of the normalizing constant and the busy source distribution is presented. The results are of both practical and theoretical interest as an extension of the standard Poisson batch input case.

Sign in / Sign up

Export Citation Format

Share Document