Probability in the Engineering and Informational Sciences



BOUNDS FOR FLUID MODELS DRIVEN BY SEMI-MARKOV INPUTS


N.  Gautam a1, V. G.  Kulkarni a2 1 , Z.  Palmowski a3 2 and T.  Rolski a3 3
a1 Department of Industrial Engineering, Pennsylvania State University, University Park, Pennsylvania 16802
a2 Department of Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599
a3 Mathematical Institute, Wroclaw University, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland

Abstract

In this paper we consider an infinite buffer fluid model whose input is driven by independent semi-Markov processes. The output capacity of the buffer is a constant. We derive upper and lower bounds for the limiting distribution of the stationary buffer content process. We discuss examples and applications where the results can be used to determine bounds on the loss probability in telecommunication networks.



Footnotes

1 This author was partially supported by NSF Grant No. NCR-9406823.

2 This author was partially supported by KBN Grant No. 2 P03 A 024 14.

3 This author was partially supported by NSF Grant No. 2 P03 A 049 15.