Abstract
The time tau(n) of first passage from queue length x to queue lengthn > x in a many-server queue with both the arrival process and service intensities governed by a finite Markov process is considered. The mean and the Laplace transform are computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being far more efficient for large n.
Original language | English |
---|---|
Pages (from-to) | 249-270 |
Journal | Queueing Systems |
Volume | 46 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 2004 |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- Levy process
- transform
- Laplace
- Kella-Whitt martingale
- heterogeneous servers
- passage problem
- first
- exponential martingale
- birth-death process
- buffer overflow
- MMM/MMM/c queue
- Markov additive process
- optional stopping