The Trouble With Diversity Fork Join Networks With Heterogeneous Customer Popul
The Trouble With Diversity Fork Join Networks With Heterogeneous Customer Popul
Vin Nguyen
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One can interpret the presence of additional faces as articulations of synchronization constraints embodied in the fork and join constructs. In this paper, we show that the heavy traffic limit of certain processes associated with hetero- geneous fork-join networks can also be expressed as c/-dimensional SRBM's with polyhedral state space. However, the polyhedral region typically has many more faces than its homogeneous coun- terpart, and the description of the state space becomes vastly more co...mplicated in this setting. This result is surprising when compared to those a. Ssociated with conventional queueing networks, where the form of the limiting process does not change with the presence of multiple customer types (this is a result of the "state-space collapse" phenomenon) [19, 21]. One can interpret the proliferation of additional faces in heterogeneous fork-join networks as results of the disordering effects that occur when jobs fork and join in their sojourns through the network. Processing systems that are characterized by parallel as well as sequential processing exist in many industrial settings.
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