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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Atar, R. Mandelbaum, A. Zviran, A. |
| Copyright Year | 2012 |
| Description | Author affiliation: Faculty of Electrical Engineering, Technion, Haifa 32000, Israel (Atar, R.) || Faculty of Industrial Engineering and Management, Technion Haifa 32000, Israel (Mandelbaum, A.; Zviran, A.) |
| Abstract | A Fork-Join Network (FJN) is a natural model for a queueing system in which customers, or rather tasks associated with customers, are processed both sequentially and in parallel. In this paper we analyze a network that, in addition, accommodates feedback of tasks. An example of a FJN is an assembly operation, where parts are first produced and then assembled to ultimately create a final product. Another example is an emergency department, where a patient “forks” into, say, a blood test and an X-ray, which must then “join” the patient as a prerequisite for a doctor examination. There is a fundamental difference between the dynamics of these two examples: In an assembly network, parts are exchangeable while, in an emergency department, tasks are associated uniquely with patients. They are thus nonexchangeable in the sense that one cannot combine/join tasks associated with different customers. In single-server feed-forward FJNs, FCFS processing maintains a fully synchronized flow of tasks. Probabilistic feedback, however, introduces flow disruptions that give rise to task delays and ultimately a decrease in throughput rate. Nevertheless, we show that a simple flow control of tasks can render this decrease of performance asymptotically negligible (though it is not absolutely negligible). More specifically, we analyze a concrete FJN, with nonexchangeable tasks and Markovian feedback, in the conventional heavy-traffic (diffusion) regime. We prove asymptotic equivalence between this network and its corresponding assembly network (exchangeable tasks), thus establishing asymptotic throughput-optimality of our control. The analysis also reveals further interesting properties, such as state-space collapse of synchronization queues. |
| Starting Page | 823 |
| Ending Page | 830 |
| File Size | 693782 |
| Page Count | 8 |
| File Format | |
| ISBN | 9781467345378 |
| e-ISBN | 9781467345392 |
| DOI | 10.1109/Allerton.2012.6483303 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2012-10-01 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Process control Throughput Synchronization Servers Assembly Queueing analysis Load modeling |
| Content Type | Text |
| Resource Type | Article |
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