Consecutive Customer Loss Phenomenon due to Buffer Overflow in Finite Buffer Queueing System

Masaharu KOMATSU  Kozo KINOSHITA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.10   pp.1781-1789
Publication Date: 1993/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Queueing Theory
Keyword: 
modeling and simulation,  wueueing theory,  

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Summary: 
In this paper, we will clarify the problem of consecutively lost customer due to buffer overflow in an IPP, M/M/l/K queueing system including an M1, M2/M/l/K queueuing system as a special case. We define a length of a consecutive loss as the number of customers consecutively lost due to buffer overflow. And, we obtain individual distributions of the lengths of consecutive losses for the IPP- and Markov-sources. From analytical and numerical results, it is shown that either they are geometrical or they can be approximated by a geometric distribution. Also, from numerical examples, we show some properties of the length of consecutive customer loss.