A FLUID MODEL DRIVEN BY AN M/M/1 QUEUE
WITH CATASTROPHE AND RESTORATION TIME
T. Vijayalakshmi1, V. Thangaraj2
1,2Ramanujan Institute for Advanced Study in Mathematics
University of Madras
Chepauk, Chennai, 600 005, INDIA
Abstract. In this paper, we discuss a fluid queue driven by an M/M/1 queue with catastrophe and restoration. Using the continued fraction technique, we derive the Laplace transform of the transient state probability distribution of the buffer content, transient solution for this fluid queue and the corresponding steady state results explicitly. Also we analyze the queue when there are no catastrophes and no restoration.
AMS Subject classification: 60K25, 11Y65
Keywords and phrases: fluid queue, M/M/1 with catastrophe, restoration time, three-term recurrence relation, Laplace transform, inverse Laplace transform


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DOI: 10.12732/ijam.v26i2.1

Volume: 26
Issue: 2
Year: 2013