Performance analysis of sequential tests between Poisson processes

Author

DeLucia, James ; Poor, H. Vincent

Author_Institution

IDA Center for Commun. Res., Princeton, NJ, USA

Volume

43

Issue

1

fYear

1997

fDate

1/1/1997 12:00:00 AM

Firstpage

221

Lastpage

238

Abstract

The problem of performance computation for sequential tests between Poisson processes is considered. The average sample numbers and error probabilities of the sequential probability ratio test (SPRT) between two homogeneous Poisson processes are known to solve certain delay-differential equations (DDEs). Exact, numerically stable solutions to these DDEs are developed here, and their asymptotic properties are explored. These solutions are seen to be superior to earlier solutions of Dvoretsky, Kiefer, and Wolfowitz (1953), which suffer from severe numerical instability in some ranges of parameters of interest in applications. The application of these results is illustrated in the problem of performance approximation for the cumulative sum (CUSUM) quickest detection procedure

Keywords

Poisson distribution; asymptotic stability; delay systems; delay-differential systems; numerical stability; stochastic processes; testing; CUSUM quickest detection procedure; Poisson processes; SPRT; asymptotic properties; average sample numbers; cumulative sum quickest detection procedure; delay-differential equations; error probabilities; exact numerically stable solutions; exit statistics; homogeneous Poisson processes; performance computation; sequential probability ratio test; sequential test; Control charts; Delay; Error probability; Performance analysis; Poisson equations; Sequential analysis; Statistics; Telecommunication traffic; Testing; Traffic control;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.567689

Filename

567689