Some Classical Diophantine Equations

Andreescu, Titu; Andrica, Dorin; Cucurezeanu, Ion

doi:10.1007/978-0-8176-4549-6_2

Cited by 2 publications

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“…In addition, the solution always includes an indeterminate parameter. In a wider sense, the target system can be said to be the Diophantine problem 48 . Meanwhile, in the case of α = 0 , the second term in the curly braces in Eq.…”

Section: Methodsmentioning

confidence: 99%

Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

Tsuzuki

Yanagisawa

Nishinari

2022

Sci Rep

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This study elucidates the effect of congestion avoidance of agents given congestion information on optimizing traffic in a star topology in which the central node is connected to isolated secondary nodes with different preferences. Each agent at the central node stochastically selects a secondary node by referring to the declining preferences based on the congestion rate of the secondary nodes. We investigated two scenarios: (1) repeated visits and (2) a single visit for each node. For (1), we found that multivariate statistics describe well the nonlinear dependence of agent distribution on the number of secondaries, demonstrating the existence of the number of secondaries that makes the distribution the most uniform. For (2), we discovered that congestion avoidance linearizes the travel time for all agents visiting all nodes; in contrast, the travel time increases exponentially with secondaries when not referring to congestion information. Health examination epitomizes this finding; by allowing patients to be preferentially selected for examination in vacant examination sites, we can linearize the time it takes for everyone to complete their examination. We successfully described the optimization effect of congestion avoidance on the collective dynamics of agents in star topologies.

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Section: Methodsmentioning

confidence: 99%

Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

Tsuzuki

Yanagisawa

Nishinari

2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In addition, the solution always includes an indeterminate parameter. In a wider sense, the target system can be said to be the Diophantine problem [41]. Meanwhile, in the case of α = 0, the second term in the curly braces in Eq.…”

Section: Agent Distributionmentioning

confidence: 99%

Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

Tsuzuki¹,

Yanagisawa²,

Nishinari³

2022

Preprint

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The importance of fundamental research on network topologies is widely acknowledged. This study aims to elucidate the effect of congestion avoidance of agents given congestion information on optimizing traffic in a network topology. We investigated stochastic traffic networks in a star topology with a central node connected to isolated secondary nodes with different preferences. Each agent at the central node selects a secondary node by referring to the declining preferences based on the congestion rate of the secondary nodes. We examined two scenarios: 1) Each agent can repeatedly visit the central and secondary nodes. 2) Each agent can access each secondary node only once. For 1), we investigated the uniformity of the agent distribution in a stationary state, and for 2), we measured the travel time for all agents visiting all nodes. When agents repeatedly visit central and other nodes, the uniformity of agent distribution has been found to show three types of nonlinear dependence on the increase in nodes. We found that multivariate statistics describe these characteristic dependences well, suggesting that the balance between the equalization of network usage by avoiding congestion and the covariance caused by mutual referral to congestion information determines the uniformity. We discovered that congestion-avoidance linearizes the travel time, which increases exponentially with the number of nodes, notwithstanding the degree of reference to the congestion information. Consequently, we successfully described the optimization effect of congestion-avoidance on the collective dynamics of agents in star topologies. Our findings are useful in many areas of network science.

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Some Classical Diophantine Equations

Cited by 2 publications

References 0 publications

Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

Effect of congestion avoidance due to congestion information provision on optimizing agent dynamics on an endogenous star network topology

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