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- W3176116543 abstract "Consider N stations interconnected with links, each of capacity K, forming a complete graph. Calls arrive to each link at rate λ and depart at rate 1. If a call arrives to a link xy, connecting stations x and y, which is at capacity, then a third station z is chosen uniformly at random and the call is attempted to be routed via z: if both links xz and zy have spare capacity, then the call is held simultaneously on these two; otherwise the call is lost. We analyse an approximation of this model. We show rigorously that there are three phases according to the traffic intensity α:=λ/K: for α∈(0,αc)∪(1,∞), the system has mixing time logarithmic in the number of links n:=N2; for α∈(αc,1) the system has mixing time exponential in n, the number of links. Here αc:=13(5 10−13)≈0.937 is an explicit critical threshold with a simple interpretation. We also consider allowing multiple rerouting attempts. This has little effect on the overall behaviour; it does not remove the metastability phase. Finally, we add trunk reservation: in this, some number σ of circuits are reserved; a rerouting attempt is only accepted if at least σ+1 circuits are available. We show that if σ is chosen sufficiently large, depending only on α, not K or n, then the metastability phase is removed." @default.
- W3176116543 created "2021-07-05" @default.
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- W3176116543 date "2022-04-01" @default.
- W3176116543 modified "2023-09-23" @default.
- W3176116543 title "Metastability in loss networks with dynamic alternative routing" @default.
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- W3176116543 doi "https://doi.org/10.1214/21-aap1711" @default.
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