9 research outputs found
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
The preemptive repeat hybrid server interruption model
We analyze a discrete-time queueing system with server interruptions and a hybrid preemptive repeat interruption discipline. Such a discipline encapsulates both the preemptive repeat identical and the preemptive repeat different disciplines. By the introduction and analysis of so-called service completion times, we significantly reduce the complexity of the analysis. Our results include a.o. the probability generating functions and moments of queue content and delay. Finally, by means of some numerical examples, we assess how performance measures are affected by the specifics of the interruption discipline
Analysis of Two Stage M[X1],M[X2]/G1,G2/1 Retrial G-queue with Discretionary Priority Services, Working Breakdown, Bernoulli Vacation, Preferred and Impatient Units
In this paper, we study M[X1] , M[X2] /G1 ,G2 /1 retrial queueing system with discretionary priority services. There are two stages of service for the ordinary units. During the first stage of service of the ordinary unit, arriving priority units can have an option to interrupt the service, but, in the second stage of service it cannot interrupt. When ordinary units enter the system, they may get the service even if the server is busy with the first stage of service of an ordinary unit or may enter into the orbit or leave the system. Also, the system may breakdown at any point of time when the server is in regular service period. During the breakdown period, the interrupted priority unit will get the fresh service at a slower rate but the ordinary unit can not get the service and the server will go for repair immediately. During the ordinary unit service period, the arrival of negative unit will interrupt the service and it may enter into an orbit or leave the system. After completion of each priority unitâs service, the server goes for a vacation with a certain probability. We allow reneging to happen during repair and vacation periods. Using the supplementary variable technique, the Laplace transforms of time-dependent probabilities of system state are derived. From this, we deduce the steady-state results. Also, the expected number of units in the respective queues and the expected waiting times, are computed. Finally, the numerical results are graphically expressed
Performance analysis of priority queueing systems in discrete time
The integration of different types of traffic in packet-based networks spawns the need for traffic differentiation. In this tutorial paper, we present some analytical techniques to tackle discrete-time queueing systems with priority scheduling. We investigate both preemptive (resume and repeat) and non-preemptive priority scheduling disciplines. Two classes of traffic are considered, high-priority and low-priority traffic, which both generate variable-length packets. A probability generating functions approach leads to performance measures such as moments of system contents and packet delays of both classes
Discrete-time queues with discretionary priorities
In this paper, we consider a discrete-time two-class discretionary priority queueing model with generally distributed service times and per slot i.i.d. structured inputs in which preemptions are allowed only when the elapsed service time of a lower-class customer being served does not exceed a certain threshold. As the preemption mode of the discretionary priority discipline, we consider the Preemptive Resume, Preemptive Repeat Different, and Preemptive Repeat Identical modes. We derive the Probability Generating Functions (PGFs) and first moments of queue lengths of each class in this model for all the three preemption modes in a unified manner. The obtained results include all the previous works on discrete-time priority queueing models with general service times and structured inputs as their special cases. A numerical example shows that, using the discretionary priority discipline, we can more subtly adjust the system performances than is possible using either the pure non-preemptive or the preemptive priority disciplines.Queueing Discretionary priority General service times