Internet Data Packet Transport: From Global Topology to Local Queueing Dynamics

Lee, H. K.; Goh, K.-I.; Kahng, B.; Kim, D.

doi:10.1142/s0218127407018555

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…2b). Moreover, for the hub-node, the mean waiting time τ O,hub of O-tasks diverges with the exponent α < 2, similarly to the Poisson queue placed on the hubs in scale-free networks [25]. For other tasks, P (τ ) with α < 2 for large N is accompanies by the peak at τ = 1, rendering the average waiting time finite.…”

Section: Priority-queue Network With Or-type Protocolmentioning

confidence: 85%

Waiting time dynamics of priority-queue networks

2009

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We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A 388, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.PACS numbers: 89.75. Da, 02.50.Le, 89.65.Ef In the last century, queueing theory has proved useful for various problems ranging from operations research to telecommunications [1]. There is a recent resurgence of interest for the queueing theory among the statistical physics community with the application to the problems in human dynamics. Specifically, various queueing models based on the prioritization of tasks, or the priority queue models to be short, have been introduced to account for the heavy-tailed distributions observed in the waiting time and response time distributions [2,3,4,5,6,7,8]. The priority queue model is grounded on the assumption that the human dynamics is the result of an inherent decision-making process of the individual, with implicit priorities assigned for every tasks in his/her task queue, according to which he/she decides which task to execute next.To be specific, the priority queue model by Barabási [2] consists of a single fixed-length queue, filled with tasks each of which is assigned a priority value drawn randomly when it enters into the queue. Every step the task with the highest priority is executed and is replaced by a new task with random priority value. Upon execution, the waiting time τ , that is, how long the task has sat (waited) on the queue, is measured. Waiting time distribution P (τ ) of the Barabási model has been shown to exhibit a power-law tail for large τ aswith the exponent α = 1 [2, 3], conforming to the behaviors observed for the e-mail, library loan, and website visitation records [2,9,10,11]. Besides the human dynamics, however, due to the extremal nature of its dynamics the priority queue model would bear implications also to disparate problems in extremal dynamics, such as the Bak-Sneppen model for biological evolution [12] and invasion percolation [4]. * Email: kgoh@korea.ac.krBarabási model purposefully simplified many aspects of potential importance in realistic human dynamics, serving as a starting framework on which various detailed factors can be embedded [13,14,15,16,17]. One important factor that was not been accounted for is the human interaction...

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Section: Priority-queue Network With Or-type Protocolmentioning

confidence: 85%

Waiting time dynamics of priority-queue networks

2009

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“…protocol [16]. This is because, when µ ≫ n λ (1 − x), tasks are executed upon its arrival in the steady state so that the priority-based protocol can be regarded as the FIFO-based one.…”

Section: The Queue-length Distributionmentioning

confidence: 99%

Priority queues with bursty arrivals of incoming tasks

2009

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Recently increased accessibility of large-scale digital records enables one to monitor human activities such as the interevent time distributions between two consecutive visits to a web portal by a single user, two consecutive emails sent out by a user, two consecutive library loans made by a single individual, etc. Interestingly, those distributions exhibit a universal behavior,where τ is the interevent time, and δ ≃ 1 or 3/2. The universal behaviors have been modeled via the waiting-time distribution of a task in the queue operating based on priority; the waiting time follows a power law distribution P w (τ ) ∼ τ −α with either α = 1 or 3/2 depending on the detail of queuing dynamics. In these models, the number of incoming tasks in a unit time interval has been assumed to follow a Poisson-type distribution. For an email system, however, the number of emails delivered to a mail box in a unit time we measured follows a powerlaw distribution with general exponent γ. For this case, we obtain analytically the exponent α, which is not necessarily 1 or 3/2 and takes nonuniversal values depending on γ. We develop the generating function formalism to obtain the exponent α, which is distinct from the continuous time approximation used in the previous studies.

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“…In the (N, r)-model, the mean I-task waiting time is finite but the variance diverges for r < N (α I < 3). For the O-task, not only the variance but also the mean waiting time diverge (α 2), implying the lack of characteristic scale in the waiting times dynamics [21].…”

Section: Resultsmentioning

confidence: 99%

Generalized priority-queue network dynamics: Impact of team and hierarchy

et al. 2010

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We study the effect of team and hierarchy on the waiting-time dynamics of priority-queue networks. To this end, we introduce generalized priority-queue network models incorporating interaction rules based on team-execution and hierarchy in decision making, respectively. It is numerically found that the waiting-time distribution exhibits a power law for long waiting times in both cases, yet with different exponents depending on the team size and the position of queue nodes in the hierarchy, respectively. The observed power-law behaviors have in many cases a corresponding single or pairwise-interacting queue dynamics, suggesting that the pairwise interaction may constitute a major dynamic consequence in the priority-queue networks. It is also found that the reciprocity of influence is a relevant factor for the priority-queue network dynamics.

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Internet Data Packet Transport: From Global Topology to Local Queueing Dynamics

Cited by 4 publications

References 31 publications

Waiting time dynamics of priority-queue networks

Waiting time dynamics of priority-queue networks

Priority queues with bursty arrivals of incoming tasks

Generalized priority-queue network dynamics: Impact of team and hierarchy

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