Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2005
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/9631 |
| _version_ | 1811087279882502144 |
|---|---|
| author | Escobar Fernández de la Vega, Marcos |
| author2 | Amedeo R. Odoni. |
| author_facet | Amedeo R. Odoni. Escobar Fernández de la Vega, Marcos |
| author_sort | Escobar Fernández de la Vega, Marcos |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998. |
| first_indexed | 2024-09-23T13:42:55Z |
| format | Thesis |
| id | mit-1721.1/9631 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:42:55Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/96312020-07-14T22:06:47Z Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management Escobar Fernández de la Vega, Marcos Amedeo R. Odoni. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Electrical Engineering and Computer Science Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998. Includes bibliographical references (p. 209-213). This thesis is concerned with approximations of certain M(t)/G(t)/n(t)/n(t) + q queueing systems. More specifically, we are interested in such systems under very general conditions such as time-varying demand and capacity, and high utilization, including occasional oversaturation. Conditions such as these cannot be addressed with existing methodologies. We focus on M(t)/G(t)/n(t)/n(t) + q systems that can be approximated fairly well by M(t)/E&(t)/n(t)/n(t) + q systems. The latter have a large number of system states, that increase with the system parameters k, n, q and the utilization ratio, and involve complicated state transition probabilities. We propose numerical methods to solve the corresponding Chapman-Kolmogorov equations, exactly and approximately We first describe the exact solution technique of M(t)/Ek(t)/n(t)/n(t) + q queueing systems. Then, we develop two heuristic solution techniques of M(t)/E&(t)/ndt)/n(t) + q queueing systems, and provide the corresponding complete state descriptions. We compare the exact and approximate results to validate our heuristics and to select the heuristic that best approximates the exact results in steady-state and under stationary conditions. We also propose two algorithms to vary the number of servers in the system, since many real-life problems involve such changes in response to variations in demand. Further results using our ELC heuristic show that our practical approach behaves well under nonstationary conditions, including varying capacity, and during the transient period to steady-state. We conclude that our heuristic approach is an excellent alternative for studying and analyzing M(t)/E&(t)/n(t)/n(t)+q models and, as a by-product, many M(t)/G(t)/n(t)/n(t) +q systems that arise in practice. Finally, we present an application of the M(t)/E&(t)/n(t)/n(t) + q queueing model in the context of Air Traffic Management. This model appears to be a reasonable approach to estimating delays and congestion in an en-route sector in the air traffic system and can be used as an important building block in developing an analytical model of the entire Air Traffic Management system. by Marcos Escobar Fernández de la Vega. Ph.D. 2005-08-19T19:03:52Z 2005-08-19T19:03:52Z 1998 1998 Thesis http://hdl.handle.net/1721.1/9631 42333551 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 213 p. 14115772 bytes 14115532 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science Escobar Fernández de la Vega, Marcos Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management |
| title | Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management |
| title_full | Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management |
| title_fullStr | Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management |
| title_full_unstemmed | Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management |
| title_short | Approximate solutions for multi-server queuing systems with Erlangian service times and an application to air traffic management |
| title_sort | approximate solutions for multi server queuing systems with erlangian service times and an application to air traffic management |
| topic | Electrical Engineering and Computer Science |
| url | http://hdl.handle.net/1721.1/9631 |
| work_keys_str_mv | AT escobarfernandezdelavegamarcos approximatesolutionsformultiserverqueuingsystemswitherlangianservicetimesandanapplicationtoairtrafficmanagement |