A large-deviations analysis of the GI/GI/1 SRPT queue

We consider a GI/GI/1 queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times. Our interest is focused on the tail behavior of the sojourn-time distribution. We obtain a general expression for its large-deviations decay rate. The value of this decay rate critically depends on whether there is mass in the endpoint of the service-time distribution or not. An auxiliary priority queue, for which we obtain some new results, plays an important role in our analysis. We apply our SRPT-results to compare SRPT with FIFO from a large-deviations point of view.Comment: 22 page

Hidden scaling patterns and universality in written communication

The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agent's `proper time' measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bi-modal character, which is empirically borne out by our new years-long data on email. These novel perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, emergency handling.Comment: 27 pages, 10 figure

Queues and risk models with simultaneous arrivals

We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue) we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline how the two-dimensional risk model with a general two-dimensional claim size distribution (hence without ordering of claim sizes) is related to a known Riemann boundary value problem

A first passage time problem for spectrally positive Lévy processes and its application to a dynamic priority queue

We study a first passage time problem for a class of spectrally positive Lévy processes. By considering the special case where the Lévy process is a compound Poisson process with negative drift, we obtain the Laplace–Stieltjes transform of the steady-state waiting time distribution of low-priority customers in a two-class M/GI/1 queue operating under a dynamic non-preemptive priority discipline. This allows us to observe how the waiting time of customers is affected as the policy parameter varies