Stationarity of some processes in transport protocols

Authors:
Teunis J. Ott;Jason Swanson
Affiliations:
Ott Associates, Chester, NJ;Univ Wisconsin, Madison, Wisc.
Venue:
ACM SIGMETRICS Performance Evaluation Review
Year:
2006

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Abstract

This note establishes stationarity of a number of stochastic processes of interest in the study of Transport Protocols. For many of the processes studied in this note stationarity had been established before, but for one class the result is new. For that class, it was counterintuitive that stationarity was hard to prove. This note also explains why that class offered such stiff resistance.The stationarity is proven using Liapunov functions, without first proving tightness by proving boundedness of moments. After the 2006 MAMA workshop simple conditions for existence of such moments were obtained and were added to this note.