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

Nazarathy, Yoni and Weiss, Gideon (2008) The asymptotic variance rate of the output process of finite capacity birth-death queues. Queueing Systems, 59 2: 135-156. doi:10.1007/s11134-008-9079-4


Author Nazarathy, Yoni
Weiss, Gideon
Title The asymptotic variance rate of the output process of finite capacity birth-death queues
Journal name Queueing Systems   Check publisher's open access policy
ISSN 0257-0130
1572-9443
Publication date 2008-06
Sub-type Article (original research)
DOI 10.1007/s11134-008-9079-4
Volume 59
Issue 2
Start page 135
End page 156
Total pages 22
Place of publication Secaucus, NJ, United States
Publisher Springer
Language eng
Formatted 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.
Keyword Queueing theory
Loss systems
M/M/1/K
MAP
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Thu, 10 May 2012, 16:31:35 EST by Kay Mackie on behalf of Mathematics