An application of the reflection principle to the transient analysis of the  M / M /1 queue | Zendy

Towsley Don | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

An application of the reflection principle to the transient analysis of the M / M /1 queue

Author(s) -

Towsley Don

Publication year - 1987

Publication title -

naval research logistics (nrl)

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.665

H-Index - 68

eISSN - 1520-6750

pISSN - 0894-069X

DOI - 10.1002/1520-6750(198706)34:3<451::aid-nav3220340310>3.0.co;2-8

Subject(s) - reflection (computer programming) , transient (computer programming) , interval (graph theory) , queueing theory , burke's theorem , queue , reflection principle (wiener process) , mathematics , queueing system , mathematical analysis , combinatorics , discrete mathematics , computer science , queue management system , statistics , fork–join queue , operating system , knowledge management , diffusion process , innovation diffusion , geometric brownian motion , programming language

This paper applies the well‐known reflection principle for random walks to the analysis of the transient M/M/ 1 queueing system. A closed‐form solution is obtained for the probability that exactly i arrivals and j departures occur over an interval of length t in an M/M/ 1 queueing system that contains n users at the beginning of the interval. The derivation of this probability is based on the calculation of the number of paths between two points in a two‐dimensional −y coordinate system that lie above the x axis and touch the x axis exactly r times. This calculation is readily performed through the application of the reflection principle.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research