On the Convergence of Multiclass Queueing Networks in Heavy Traffic
The subject of this paper is the heavy traffic behavior of a general class of queueing networks with first-in-first-out (FIFO) service discipline. For special cases which require various assumptions on the network structure, several authors have proved heavy traffic limit theorems to justify the app...
| Main Authors: | , |
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| Format: | Working Paper |
| Language: | en_US |
| Published: |
Massachusetts Institute of Technology, Operations Research Center
2004
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| Online Access: | http://hdl.handle.net/1721.1/5410 |
| _version_ | 1826217903189393408 |
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| author | Dai, I. G. Nguyen, Viên |
| author_facet | Dai, I. G. Nguyen, Viên |
| author_sort | Dai, I. G. |
| collection | MIT |
| description | The subject of this paper is the heavy traffic behavior of a general class of queueing networks with first-in-first-out (FIFO) service discipline. For special cases which require various assumptions on the network structure, several authors have proved heavy traffic limit theorems to justify the approximation of queueing networks by reflected Brownian motions (RBM's). Based on these theorems, some have conjectured that the Brownian approximation may in fact be valid for a more general class of queueing networks. In this paper, we prove that the Brownian approximation does not hold for such a general class of networks. Our findings suggest that studying Brownian models of non-FIFO queueing networks may perhaps be more fruitful. |
| first_indexed | 2024-09-23T17:10:52Z |
| format | Working Paper |
| id | mit-1721.1/5410 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:10:52Z |
| publishDate | 2004 |
| publisher | Massachusetts Institute of Technology, Operations Research Center |
| record_format | dspace |
| spelling | mit-1721.1/54102019-04-10T10:36:21Z On the Convergence of Multiclass Queueing Networks in Heavy Traffic Dai, I. G. Nguyen, Viên The subject of this paper is the heavy traffic behavior of a general class of queueing networks with first-in-first-out (FIFO) service discipline. For special cases which require various assumptions on the network structure, several authors have proved heavy traffic limit theorems to justify the approximation of queueing networks by reflected Brownian motions (RBM's). Based on these theorems, some have conjectured that the Brownian approximation may in fact be valid for a more general class of queueing networks. In this paper, we prove that the Brownian approximation does not hold for such a general class of networks. Our findings suggest that studying Brownian models of non-FIFO queueing networks may perhaps be more fruitful. 2004-06-01T16:43:14Z 2004-06-01T16:43:14Z 1992-10 Working Paper http://hdl.handle.net/1721.1/5410 en_US Operations Research Center Working Paper;OR 270-92 1077456 bytes application/pdf application/pdf Massachusetts Institute of Technology, Operations Research Center |
| spellingShingle | Dai, I. G. Nguyen, Viên On the Convergence of Multiclass Queueing Networks in Heavy Traffic |
| title | On the Convergence of Multiclass Queueing Networks in Heavy Traffic |
| title_full | On the Convergence of Multiclass Queueing Networks in Heavy Traffic |
| title_fullStr | On the Convergence of Multiclass Queueing Networks in Heavy Traffic |
| title_full_unstemmed | On the Convergence of Multiclass Queueing Networks in Heavy Traffic |
| title_short | On the Convergence of Multiclass Queueing Networks in Heavy Traffic |
| title_sort | on the convergence of multiclass queueing networks in heavy traffic |
| url | http://hdl.handle.net/1721.1/5410 |
| work_keys_str_mv | AT daiig ontheconvergenceofmulticlassqueueingnetworksinheavytraffic AT nguyenvien ontheconvergenceofmulticlassqueueingnetworksinheavytraffic |