Abstract
A class of open processing networks operating under a maximum pressure policy is considered in the heavy traffic regime. We prove that the diffusion-scaled workload process for a network with several bottleneck resources converges to a semimartingale reflecting Brownian motion (SRBM) living in a polyhedral cone. We also establish a state space collapse result that the queue length process can be lifted from the lower-dimensional workload process.
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Ata, B., Lin, W. Heavy traffic analysis of maximum pressure policies for stochastic processing networks with multiple bottlenecks. Queueing Syst 59, 191–235 (2008). https://doi.org/10.1007/s11134-008-9082-9
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DOI: https://doi.org/10.1007/s11134-008-9082-9
Keywords
- Maximum pressure policy
- Heavy traffic analysis
- Multiple bottlenecks
- Semimartingale
- Brownian motion in a convex cone