On Overflow Processes for a Trunk Group with Trunk Reservation

Fumiaki MACHIHARA 

Publication
IEICE TRANSACTIONS (1976-1990)  Vol.E65  No.5  pp.249-256
Publication Date: 1982/05/20
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Switching Systems
Keyword: 


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Summary: 
This paper reports on the overflow process for a trunk reservation system which has two kinds of Poisson inputs. The Laplace-Stieltjes transforms of the interoverflow distributions for each of priority calls and ordinary calls are derived, respectively. The overflow process for priority calls is renewal. The Laplace-Stieltjes transform of the interoverflow distribution for priority calls is represented by the recurrences, and the variance of overflow traffic can be easily obtained by the theory of GI/M/ model. The overflow process for ordinary calls is semi-Markovian, since it depends on the number of busy trunks. The Laplace-Stieltjes transform for the semi-Markovian kernel, depending on the number of busy trunks, is derived. The variance can be obtained by the theory of semi-Markovian inputs model, SM/M/. The total overflow process for both priority and ordinary calls is also derived, but in this case the semi-Markovian kernel is more complicated than that for the overflow process for ordinary calls. The variance of the total overflow traffic being analyzed, the covariance for the two kinds of overflow traffic can be easily obtained. Moreover, some numerical results are shown and characteristics of the overflow traffic are discussed.