The nonstationary Erlang loss model is a queueing system consisting of a finite number of servers and no waiting room with a nonstationary arrival process or a time-dependent service rate. The Erlang loss model is commonly used to model and evaluate many communication systems. Often, these types of service systems encounter a change in the arrival rate over time while the service rate remains either constant or changes very little over time. In view of this, the focus in this research is the nonstationary Erlang loss queues and network with time-dependent arrival rate and constant service rate. We developed an iterative scheme referred to as the fixed point approximation (FPA) in order to obtain the time-dependent blocking probability and other measures for a single-class nonstationary Erlang loss queue and a nonstationary multi-rate Erlang loss queue. The FPA method was compared against exact numerical results, and two other methods, namely, MOL and PSA, for various nonstationary Erlang loss queues with sinusoidal arrival rates. Although we used sinusoidal functions to model the time-dependent arrival rate, the solution can be obtained for any arrival rate function. Experimental results demonstrate that the FPA algorithm provides an exact solution for nonstationary Erlang loss queue. The FPA algorithm was also applied to the case of multi-rate nonstationary Erlang loss queues and the results obtained were compared with simulation. We generalized the FPA algorithm for networks of nonstationary Erlang loss queues with Markovian branching, and compared its accuracy to simulation. Finally, FPA was used to analyze networks of nonstationary Erlang loss queues with population constraints. Numerical results showed that FPA provides a good approximation.
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-04222004-192735 |
| Date | 23 April 2004 |
| Creators | Alnowibet, Khalid Abdulaziz |
| Contributors | William Stewart, Thomas Reiland, Yannis Viniotis, Harry Perros |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-04222004-192735/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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