Research
List of Research Papers
This research has been generously funded by NSF Grants
DMS-93-00136 and DMS-99-28950
and DOE Grants DE-FG02-93ER25168 and
DE-FG02-93ER25168
PIs: Charles Knessl
and Charles Tier
The research program on the above grants developed new
asymptotic and
perturbation methods for approximating the performance of
queueing systems. This involved obtaining approximations to equations
such as integral equations and difference equations. The approximations
lead to highly accurate formulas for the performance measures of the systems.
The models considered include large queueing networks, transient
behavior of queues, processor-sharing queues and first passage times in
Jackson networks. Queueing models of these types arise in the analysis
of computer and communications systems which are applications in
the HPCC Program.
In addition, the methods developed in the proposal were
also found to be applicable to applied stochastic models, such as those
arising in computer science, risk theory,
and conservation biology.
Below we describe some areas of recent research and
provide abstracts of the publications. Postscript versions of the
entire manuscripts are also available.
Selected References
- Survey Paper
C. Knessl and C. Tier,
Applications of singular perturbation methods in
queueing ,
Advances in Queueing: Theory, Methods and Open Problems,
edited by J.H. Dshalalow, CRC Press, 1995, 311-336.
- Large Queueing Networks
C. Knessl and C. Tier, Asymptotic expansions for large closed
queueing networks, J. Assoc. Comput. Mach.
37, 1990, 144-174.
C. Knessl and C. Tier, Asymptotic expansions for large closed
queueing networks with multiple job classes,
IEEE Trans. on Computers
41, 1992, 480-488.
F.B. Hanson, J.D. Mei, C. Tier and H. Xu, PDAC: A data parallel
algorithm for the performance of closed queueing networks, Parallel
Computing 19, 1993, 1345-1358.
J.D. Mei and C. Tier, Asymptotic approximations for a queueing
network with multiple classes, SIAM J. Applied Math.
54, 1994, 1147-1180.
C. Knessl and C. Tier,
Asymptotic approximations and bottleneck analysis
in product form queueing networks with large populations ,
Performance Evaluation
41, 1992, 480-488.
- Buildup and emptying of queues
C. Knessl and C. Tier, Asymptotic Properties of first passage times
for Jackson networks I: buildup of large queue lengths,
Commun. Statist. Stochastic Models 11, 1995, 133-162.
C. Knessl and C. Tier,
Mean time for the development of large
workloads and large queue lengths in the GI/G/1 queue ,
Journal of Applied Mathematics and Stochastic Analysis
9,1996, 107-142.
C. Knessl and C. Tier, Asymptotic Properties of first passage times
for two tandem queues: time to empty the system
Commun. Statist. Stochastic Models 12, 1996, 633-672.
- Models relating to ATM Networks
D.I. Choi, C. Knessl and C. Tier,
A queueing system with queue length dependent service times, with
application to cell discarding in ATM networks ,
Journal of Applied Mathematics and Stochastic Analysis ,
to appear.
- Tandem Queues
Last Modified: Tuesday, 19-Jun-2007 21:18:52 CDT
by Charles Tier
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