Open AccessTransient analysis of a fluid queue driven by a birth and death process suggested by a chain sequence
Author(s) -
P.R. Parthasarathy,
Bruno Séricola,
K. V. Vijayashree
Publication year - 2005
Publication title -
international journal of stochastic analysis
Language(s) - English
Resource type - Journals
eISSN - 2090-3340
pISSN - 2090-3332
DOI - 10.1155/jamsa.2005.143
Subject(s) - queue , sequence (biology) , transient (computer programming) , mathematics , birth–death process , stationary distribution , chain (unit) , fraction (chemistry) , measure (data warehouse) , distribution (mathematics) , process (computing) , simple (philosophy) , statistics , markov chain , mathematical analysis , computer science , physics , chromatography , chemistry , demography , population , biochemistry , philosophy , epistemology , astronomy , database , sociology , programming language , operating system
We analyse the transient behaviour of a fluid queue driven by abirth and death process (BDP) whose birth and death rates aresuggested by a chain sequence. For the BDP suggested by a chainsequence, the stationary probabilities do not exist andhence the stationary buffer content distribution for fluid queues driven by such BDP does not exist.However, their transient distribution is obtained in a simpleclosed form by two different approaches: the first isthe continued fraction approach and the second is an approachin terms of recurrence relation by an analysis similarto that of Sericola (1998). The probability for thebuffer content to be empty at an arbitrary time is also studied.The variations in this performance measure are revealed in theform of graphs. Numerical illustrations are included
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