The input-output map of a monotone discrete-time quasireversible node [queueing theory]

Author

Anantharam, Venkat

Author_Institution

Sch. of Electr. Eng., Cornell Univ., Ithaca, NY, USA

Volume

39

Issue

2

fYear

1993

fDate

3/1/1993 12:00:00 AM

Firstpage

543

Lastpage

552

Abstract

A class of discrete-time quasi-reversible nodes called monotone, which includes discrete-time analogs of the ./M/∞ and ./M/1 nodes, is considered. For stationary ergodic nonnegative integer valued arrival processes, the existence and uniqueness of stationary regimes are proven when a natural rate condition is met. Coupling is used to prove the contractiveness of the input-output map relative to a natural distance on the space of stationary arrival processes that is analogous to Ornstein´s d¯ distance. A consequence is that the only stationary ergodic fixed points of the input-output map are the processes of independent and identically distributed Poisson random variables meeting the rate condition

Keywords

discrete time systems; information theory; queueing theory; Poisson random variables; communication networks; contractiveness; ergodic fixed points; i.i.d. random variables; input-output map; monotone discrete-time quasireversible node; queueing networks; stationary arrival processes; stationary regimes; Communication networks; Computer networks; Distributed computing; H infinity control; Helium; Performance analysis; Queueing analysis; Random variables; Space stations;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.212284

Filename

212284