Exact transient solution of an M/M/1 driven fluid queue

Abstract

The transient solution of a fluid queue driven by an M/M/1 queue is obtained explicitly using continued fractions. The probability that the buffer is empty at a specified time is also determined and illustrated graphically.

Keywords:

• Catalan numbers
• Continued fractions
• Recurrence relation

Acknowledgements

The authors P. R. Parthasarathy and K. V. Vijayashree wish to thank Av Humboldt Stiftung and the National Board of Higher Mathematics (NBHM) respectively for the financial assistance during the preparation of the paper.