On the diffusion approximation to two parallel queues with processor sharing

Author

Knessl, Charles

Author_Institution

Dept. of Math., Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA

Volume

36

Issue

12

fYear

1991

fDate

12/1/1991 12:00:00 AM

Firstpage

1356

Lastpage

1367

Abstract

A two-dimensional queuing model is considered in which the server in the second queue helps the server in the first queue during periods when the second queue is empty. The system is analyzed in the heavy traffic limit and explicit approximate solutions are obtained to the resulting diffusion equations using singular perturbation methods. Approximate asymptotic formulas are obtained for the stationary distribution of the number of customers as well as for some first-passage-time problems associated with the busy period. It is shown that these formulas reduce to the asymptotic expansions of the exact solutions, when the latter are available

Keywords

probability; queueing theory; approximate asymptotic formulas; busy period; diffusion approximation; first-passage-time problems; heavy traffic limit; parallel queues; processor sharing; singular perturbation methods; two-dimensional queuing model; Difference equations; Integral equations; Mathematics; Partial differential equations; Perturbation methods; Queueing analysis; Statistics; Traffic control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.106152

Filename

106152