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Home List of Titles The asymptotic variance rate of the output process of finite capacity birth-death queues
Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/158844
- The asymptotic variance rate of the output process of finite capacity birth-death queues
- Nazarathy, Yoni; Weiss, Gideon
- 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
- Queueing Systems: Theory and Applications, Vol. 59, no. 2 (Jun 2008), pp. 135-156
- Publication year
- FOR Code(s)
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; 0104 Statistics
- Asymptotic variance rate; BRAVO; Loss systems; M/M/1/K; MAP; Queueing theory
- Publisher URL
- Copyright © 2008 Springer Science+Business Media, LLC.
- Peer reviewed