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On Level Crossing Analysis of Queues
Author(s) -
Shanthikumar J. G.
Publication year - 1981
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1981.tb00796.x
Subject(s) - queue , steady state (chemistry) , burke's theorem , mathematics , state (computer science) , queueing theory , computer science , queue management system , fork–join queue , statistics , algorithm , computer network , chemistry
Summary In this note we introduce a new level crossing analysis and using it derive an integral equation for the steady state waiting time in the GI/G /1 Queue. For the GI/M /1 queue we derive the rates of up‐ and down‐crossings of the virtual delay process and two integral equations, one for the steady state time spent in the system and the other for the steady state waiting time in the queue. Also, the steady state probability distributions of the time spent in the system and the waiting time in the queue are obtained by solving these integral equations.