Stability of Decentralized Queueing Networks Beyond Complete Bipartite Cases
Gaitonde and Tardos recently studied a model of queueing networks where queues compete for servers and re-send returned packets in future rounds. They quantify the amount of additional processing power that guarantees a decentralized system's stability, both when the queues adapt their strategi...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
14.10.2022
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Subjects | |
Online Access | Get full text |
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Summary: | Gaitonde and Tardos recently studied a model of queueing networks where
queues compete for servers and re-send returned packets in future rounds. They
quantify the amount of additional processing power that guarantees a
decentralized system's stability, both when the queues adapt their strategies
from round to round using no-regret learning algorithms, and when they are
patient and evaluate the utility of a strategy over long periods of time. In
this paper, we generalize Gaitonde and Tardos's model and consider scenarios
where not all servers can serve all queues (i.e., the underlying graph is an
incomplete bipartite graphs) and, further, when packets need to go through more
than one layer of servers before their completions (i.e., when the underlying
graph is a DAG). For the bipartite case, we obtain bounds comparable to those
by Gaitonde and Tardos, with the factor slightly worse in the patient queueing
model. For the more general multi-layer systems, we show that straightforward
generalizations of the utility function and servers' priority rules in Gaitonde
and Tardos's model may lead to unbounded gaps between centralized and
decentralized systems when the queues use no regret strategies. We define a new
utility and a service priority rule that are aware of the queue lengths, and
show that these suffice to restore the bounded gap between centralized and
decentralized systems observed in bipartite graphs. |
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DOI: | 10.48550/arxiv.2210.07632 |