Hierarchical Dynamics, Interarrival Times, and Performance

Kleban, S.D.; Clearwater, Scott H.

doi:10.1145/1048935.1050179

Cited by 19 publications

(19 citation statements)

References 17 publications

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“…2). Time intervals between consecutive tasks arriving at a server computer [10,11,12,13] and between a user's hypertext markup language (HTML) requests [5], which are closely related to the number of incoming tasks per unit time, also show similar patterns. The origin of such nonuniform numbers of incoming tasks is not known yet, but may be consequences of multiple correspondences with multiple people or self-similar patterns in the number of data packets arriving at a given router [14].…”

Section: Introductionmentioning

confidence: 94%

“…Such bursty arrivals of tasks may significantly change the behavior of priority queue systems. For example, a more skewed distribution of the number of incoming tasks per unit time may result in a more skewed waiting-time distribution of a task P w (τ ), as briefly suggested in [12]. In this paper, we study the waiting-time distribution of a task in the queue for the case of heterogeneous numbers of incoming tasks.…”

Section: Introductionmentioning

confidence: 96%

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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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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 96%

Priority queues with bursty arrivals of incoming tasks

2009

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“…Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes [1,2,3]. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity [4,5,6,7,8]. Here we show that the bursty nature of human behavior is a consequence of a decision based queuing process [9,10]: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experience very long waiting times.…”

Section: Introductionmentioning

confidence: 99%

“…Measurements capturing the distribution of the time differences 2 between consecutive instant messages sent by individuals during online chats [5] show a similar pattern. Professional tasks, such as the timing of job submissions on a supercomputer [6], directory listings and file transfers (FTP requests) initiated by individual users [7], or the timing of printing jobs submitted by users [13] were also reported to display non-Poisson features. Similar patterns emerge in the time interval distribution between individual trades in currency futures [8].…”

mentioning

confidence: 99%

The origin of bursts and heavy tails in human dynamics

Barabási

2005

Nature

1,994

1,883

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The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes [1,2,3]. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity [4,5,6,7,8]. Here we show that the bursty nature of human behavior is a consequence of a decision based queuing process [9,10]: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experience very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. These findings have important implications from resource management to service allocation in both communications and retail.1 Humans participate on a daily basis in a large number of distinct activities, ranging from electronic communication, such as sending emails or making phone calls, to browsing the web, initiating financial transactions, or engaging in entertainment and sports. Given the number of factors that determine the timing of each action, ranging from work and sleep patterns to resource availability, it appears impossible to seek regularities in human dynamics, apart from the obvious daily and seasonal periodicities. Therefore, in contrast with the accurate predictive tools common in physical sciences, forecasting human and social patterns remains a difficult and often elusive goal.Current models of human activity are based on Poisson processes, and assume that in a dt time interval an individual (agent) engages in a specific action with probability qdt, where q is the overall frequency of the monitored activity. This model predicts that the time interval between two consecutive actions by the same individual, called the waiting or inter-event time, follows an exponential distribution ( Fig. 1, a-c [4]. Yet, an increasing number of recent measurements indicate that the timing of many human actions systematically deviate from the Poisson prediction, the waiting or inter-event times being better approximated by a heavy tailed or Pareto distribution (Fig. 1, d-f). The differences between Poisson and heavy tailed behavior is striking: a Poisson distribution decreases exponentially, forcing the consecutive events to follow each other at relatively regular time intervals and forbidding very long waiting times. In contrast, the slowly decaying heavy tailed processes allow for very long periods of inactivity that separate bursts of intensive activity (Fig. 1).To provide direct evidence for non-Poisson activity patterns in individual h...

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“…In fact, this dataset was the main example used to demonstrate various ways to quantify selfsimilarity and long-range dependence in Section 7.4. In particular, interarrival times are not exponentially distributed, but rather tend to have a longer tail, fitting a lognormal or Weibull distribution [404]. The arrival of individual jobs is also affected by feedback from the system's performance and the session dynamics, as discussed in Section 8.…”

Section: Arrivalsmentioning

confidence: 99%

Workload Modeling for Computer Systems Performance Evaluation

Feitelson

2015

197

131

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Reliable performance evaluations require the use of representative workloads. This is no easy task since modern computer systems and their workloads are complex, with many interrelated attributes and complicated structures. Experts often use sophisticated mathematics to analyze and describe workload models, making these models difficult for practitioners to grasp. This book aims to close this gap by emphasizing the intuition and the reasoning behind the definitions and derivations related to the workload models. It provides numerous examples from real production systems, with hundreds of graphs. Using this book, readers will be able to analyze collected workload data and clean it if necessary, derive statistical models that include skewed marginal distributions and correlations, and consider the need for generative models and feedback from the system. The descriptive statistics techniques covered are also useful for other domains.

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Hierarchical Dynamics, Interarrival Times, and Performance

Cited by 19 publications

References 17 publications

Priority queues with bursty arrivals of incoming tasks

Priority queues with bursty arrivals of incoming tasks

The origin of bursts and heavy tails in human dynamics

Workload Modeling for Computer Systems Performance Evaluation

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