Results 1 
5 of
5
Loss Probability in a Finite DiscreteTime Queue in Terms of the Steady State Distribution of an Infinite Queue
, 1999
"... Introduction We consider discretetime queueing processes fX n # n = 0# 1#:::g and fY n # n =0# 1#:::g: X n+1 =(X n ; 1) + +A n+1 # Y n+1 = min ; (Y n ; 1) + +A n+1 # N \Delta # where (x) + = max(x# 0), N is a finite positive integer representing the buffer size, and fA n # n =1# 2#:::g ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
Introduction We consider discretetime queueing processes fX n # n = 0# 1#:::g and fY n # n =0# 1#:::g: X n+1 =(X n ; 1) + +A n+1 # Y n+1 = min ; (Y n ; 1) + +A n+1 # N \Delta # where (x) + = max(x# 0), N is a finite positive integer representing the buffer size, and fA n # n =1# 2#:::g denotes a sequence of nonnegative integer random 2 Ishizaki and Takine / Loss probability in a finite discretetime queue variables representing the
Bounds for the tail distribution in a queue with a superposition of general periodic Markov sources: theory and application
, 1999
"... this paper, we consider a discretetime queue where the arrival process is a superposition of general periodic Markov sources. The general periodic Markov source is rather general since it is assumed only to be irreducible, stationary and periodic. Note also that the source model can represents mult ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
this paper, we consider a discretetime queue where the arrival process is a superposition of general periodic Markov sources. The general periodic Markov source is rather general since it is assumed only to be irreducible, stationary and periodic. Note also that the source model can represents multiple timescale correlations in arrivals. For this queue, we obtain upper and lower bounds for the asymptotic tail distribution of the queue length by bounding the asymptotic decay constant. The formulas can be applied to a queue having a huge number of states describing the arrival process. Toshow this, we consider an MPEGlike source which is a special case of general periodic Markov source. The MPEGlike source has three timescale correlations: peak rate, frame length and a group of pictures. We then apply our bound formulas to a queue with a superposition of MPEGlike sources, and provide some numerical examples to show the numerical feasibility of our bounds. Note that the number of states in a Markovchain describing the superposed arrival process is more than 1:4 \Theta 10 88 . Even for such a queue, the numerical examples show that the order of the magnitude of the tail distribution can be readily obtained. 2 Ishizaki and Takine / Bounds for the tail distribution Keywords: Tail distribution, periodic Markov source 1. Introduction Estimation of the cell loss probability has been considered as one of the most important issues in call admission and congestion controls in ATM networks. For this reason, considerable attentions have been paid to the tail distribution of queue length in ATM networks, since the cell loss probability is closely related to the tail distribution [10,12,13]. In ATM networks, the arrival process is essentially a superposition of sources whic...
Study on reduction of total bandwidth requirement by traffic dispersion
 Proceedings of International Conference on ATM and High Speed Internet 2001
, 2001
"... dispersion ..."
superposition of general periodic
, 1997
"... Bounds for the tail distribution in a queue with a ..."
unknown title
, 1997
"... Loss probability in a finite discretetime queue in terms of the steady state distribution of an infinite queue ..."
Abstract
 Add to MetaCart
(Show Context)
Loss probability in a finite discretetime queue in terms of the steady state distribution of an infinite queue