Heavy traffic analysis of a Markov-modulated queue with finite capacity and general service times
- Univ. of Illinois, Chicago, IL (United States). Dept. of Mathematics, Statistics and Computer Science
The authors consider a set of N independent sources, each of which alternates between ``on`` and ``off`` states. When a source is on, it generates a Poisson arrival stream to a finite-capacity queue with a general server. They derive the balance equations satisfied by the joint steady-state distribution of the queue length and the number of ``on`` sources. Then they analyze the problem in the heavy traffic limit where N {yields} {infinity} and the average arrival rate is nearly equal to the mean service rate. The capacity is scaled to be O({radical}N). The first two terms in the asymptotic series are characterized as solutions to elliptic partial differential equations (PDEs) with appropriate boundary conditions. The authors then develop numerical and asymptotic methods for solving these PDEs. The analysis makes use of singular perturbation techniques and special functions.
- Sponsoring Organization:
- National Science Foundation, Washington, DC (United States); USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG02-93ER25168
- OSTI ID:
- 616169
- Journal Information:
- SIAM Journal of Applied Mathematics, Vol. 58, Issue 1; Other Information: PBD: Feb 1998
- Country of Publication:
- United States
- Language:
- English
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