Priority queues with bursty arrivals of incoming tasks
N. Masuda, J. S. Kim, and B. Kahng

TL;DR
This paper analyzes how bursty, power-law distributed arrivals of tasks affect priority queue waiting times, deriving a new analytical relationship for the waiting time distribution exponent based on the arrival distribution.
Contribution
It introduces a generating function approach to determine the waiting time exponent for priority queues with power-law task arrivals, extending previous models that assumed Poisson arrivals.
Findings
Derived the exponent for waiting time distribution based on power-law arrival rates.
Showed that the waiting time exponent is nonuniversal and depends on the power-law exponent b3 of arrivals.
Provided analytical results that differ from previous models assuming Poisson arrivals.
Abstract
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 is the interevent time, and 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 with either 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…
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