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Journals ACM SIGMETRICS Performance Evaluation Review Volume 36 Issue 2

Busy Period Analysis of Finite QBD Processes Chaitanya Garikiparthi — Appie van de Liefvoort Dept. Computer Science Electrical Engineering University of Missouri “ Kansas City Kansas City, Missouri, USA Ken Mitchell Dept. Computer Science Electrical Engineering University of Missouri “ Kansas City Kansas City, Missouri, USA Microsoft Redmond, Washington, USA Chaitanya.Garikiparthi @microsoft.com ABSTRACT appie@umkc.edu mitchellke@umkc.edu 2. MODEL DESCRIPTION A nite QBD process is a Markov process with in nitesi˜ mal generator Q, given by ¹ ® B0 A 0 º ¯ B1 A 1 A 0 º ¯ º ¯ A2 A1 A0 º ¯ ˜ (1) Q= ¯ º. .. .. .. º ¯ . . . º ¯ ° A 2 A 1 C0 » A 2 C1 In the particular system we study, B 1 = A2 , re ‚ecting that the service process is suspended if no customers are present without a €ecting the internal state of the service process. De ne the embedding operators H a re ‚ecting an arrival event occurring before the service and H s representing a service event occurring before the arrival by unconditioning on the initial state of the system by: Ha Hs = ( ’A1 ) ’1

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Busy period analysis of finite QBD processes

Garikiparthi, Chaitanya; van de Liefvoort, Appie; Mitchell, Ken
ACM SIGMETRICS Performance Evaluation Review , Volume 36 (2)
Association for Computing Machinery – Aug 31, 2008

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