Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/158844

Title

The asymptotic variance rate of the output process of finite capacity birth-death queues

Author(s)

Nazarathy, Yoni;  Weiss, Gideon

Abstract

We analyze the output process of finite capacity birth-death Markovian queues. We develop a formula for the asymptotic variance rate of the form λ *+σvi where λ * is the rate of outputs and v i are functions of the birth and death rates. We show that if the birth rates are non-increasing and the death rates are non-decreasing (as is common in many queueing systems) then the values of v i are strictly negative and thus the limiting index of dispersion of counts of the output process is less than unity. In the M/M/1/K case, our formula evaluates to a closed form expression that shows the following phenomenon: When the system is balanced, i.e. the arrival and service rates are equal, σvi\λ* is minimal. The situation is similar for the M/M/c/K queue, the Erlang loss system and some PH/PH/1/K queues: In all these systems there is a pronounced decrease in the asymptotic variance rate when the system parameters are balanced.

Publication type

Journal article

Source

Queueing Systems: Theory and Applications, Vol. 59, no. 2 (Jun 2008), pp. 135-156

Publication year

2008

FOR Code(s)

0102 Applied Mathematics;  0103 Numerical and Computational Mathematics;  0104 Statistics

Keyword(s)

Asymptotic variance rate;  BRAVO;  Loss systems;  M/M/1/K;  MAP;  Queueing theory

Publisher

Springer

ISSN

0257-0130

Publisher URL

http://dx.doi.org/10.1007/s11134-008-9079-4

Copyright

Copyright © 2008 Springer Science+Business Media, LLC.

Peer reviewed