Analyses are addressed for a number of problems in queueing systems and
stochastic modeling that arose due to an investigation into techniques that could
be used to approximate general closed networks.
In Chapter II, a method is presented to calculate the system size distribution at
an arbitrary point in time and at departures for a (n)/G/1/N queue. The analysis
is carried out using an embedded Markov chain approach. An algorithm is also
developed that combines our analysis with the recursive method of Gupta and Rao.
This algorithm compares favorably with that of Gupta and Rao and will solve some
situations when Gupta and Rao's method fails or becomes intractable.
In Chapter III, an approach is developed for generating exact solutions of the
time-dependent conditional joint probability distributions for a phase-type renewal
process. Closed-form expressions are derived when a class of Coxian distributions
are used for the inter-renewal distribution. The class of Coxian distributions was
chosen so that solutions could be obtained for any mean and variance desired in the
inter-renewal times.
In Chapter IV, an algorithm is developed to generate numerical solutions for
the steady-state system size probabilities and waiting time distribution functions of
the SM/PH/1/N queue by using the matrix-analytic method. Closed form results are also obtained for particular situations of the preceding queue. In addition, it
is demonstrated that the SM/PH/1/N model can be implemented to the analysis
of a sequential two-queue system. This is an extension to the work by Neuts and
Chakravarthy.
In Chapter V, principal results developed in the preceding chapters are employed
for approximate analysis of the closed network of queues with arbitrary service
times. Specifically, the (n)/G/1/N queue is applied to closed networks of a
general topology, and a sequential two-queue model consisting of the (n)/G/1/N
and SM/PH/1/N queues is proposed for tandem queueing networks.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-1016 |
| Date | 15 May 2009 |
| Creators | Sun, Feng |
| Contributors | Feldman, Richard M., Curry, Guy L., Larson, David R., Peters, Brett A. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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