METASTABILITY IN LOSS NETWORKS WITH DYNAMIC ALTERNATIVE ROUTING
成果类型：
Article
署名作者：
Olesker-Taylor, Sam
署名单位：
University of Bath
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/21-AAP1711
发表日期：
2022
页码：
1362-1399
关键词：
摘要：
Consider N stations interconnected with links, each of capacity K, forming a complete graph. Calls arrive to each link at rate lambda 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 alpha := lambda/K: for alpha is an element of (0, alpha(c)) boolean OR (1, infinity), the system has mixing time logarithmic in the number of links n := ((N)(2)); for alpha is an element of (alpha(c), 1) the system has mixing time exponential in n, the number of links. Here alpha(c) := 1/3(5 root 10 - 13) approximate to 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 sigma of circuits are reserved; a rerouting attempt is only accepted if at least sigma + 1 circuits are available. We show that if sigma is chosen sufficiently large, depending only on alpha, not K or n, then the metastability phase is removed.
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