Journal of Applied Probability

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On the optimality of static priority policies in stochastic scheduling on parallel machines
Journal of Applied Probability - Tập 24 Số 2 - Trang 430-448 - 1987
Thomas Kämpke
n jobs are to be preemptively scheduled for processing on n machines. The machines may have differing speeds and the jobs have processing requirements which are distributed as independent exponential random variables with different means. Holding cost g(U) is incurred per unit time that the set of uncompleted jobs is U and it is desired to minimize the total expected holding cost which is incurred... hiện toàn bộ
Scheduling tasks with exponential service times on parallel processors
Journal of Applied Probability - Tập 16 Số 3 - Trang 685-689 - 1979
K. D. Glazebrook
We consider the problem of how to schedule n tasks on to several identical processors to meet the objective of minimising the expected flow-time. The strategy which always serves those tasks whose processing-time distributions have the highest hazard rates is shown to be optimal when these distributions are all exponential.
Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime
Journal of Applied Probability - Tập 23 Số 3 - Trang 841-847 - 1986
Richard Weber, Pravin Varaiya, Jean Walrand
A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling ... hiện toàn bộ
Inequalities and bounds for the scheduling of stochastic jobs on parallel machines
Journal of Applied Probability - Tập 22 Số 3 - Trang 739-744 - 1985
Michael Pinedo, Zvi Schechner
Consider n jobs and m machines. The m machines are identical and set up in parallel. All n jobs are available at t = 0 and each job has to be processed on one of the machines; any one can do. The processing time of job j is Xj, a random variable with distribution Fj. The sequence in which the jobs start with their processing is predetermined and preemptions are not allowed. We investigate the effe... hiện toàn bộ
Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions
Journal of Applied Probability - Tập 17 Số 1 - Trang 187-202 - 1980
Gideon Weiss, Michael Pinedo
We consider preemptive scheduling of N tasks on m processors; processors have different speeds, tasks require amounts of work which are exponentially distributed, with different parameters. The policies of assigning at every moment the task with shortest (longest) expected processing time among those not yet completed to the fastest processor available, second shortest (longest) to the second fast... hiện toàn bộ
Scheduling jobs by stochastic processing requirements on parallel machines to minimize makespan or flowtime
Journal of Applied Probability - Tập 19 Số 1 - Trang 167-182 - 1982
Richard Weber
A number of identical machines operating in parallel are to be used to complete the processing of a collection of jobs so as to minimize either the jobs' makespan or flowtime. The total processing required to complete each job has the same probability distribution, but some jobs may have received differing amounts of processing prior to the start. When the distribution has a monotone hazard rate t... hiện toàn bộ
Limit theorem for continuous-time random walks with two time scales
Journal of Applied Probability - Tập 41 Số 2 - Trang 455-466 - 2004
Peter Becker–Kern, Mark M. Meerschaert, Hans‐Peter Scheffler
Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations tha... hiện toàn bộ
The estimation of frequency
Journal of Applied Probability - Tập 10 Số 3 - Trang 510-519 - 1973
E. J. Hannan
Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequency θ0, is in fact 0 or ... hiện toàn bộ
Tail Asymptotics for the Queue Size Distribution in an M/G/1 Retrial Queue
Journal of Applied Probability - Tập 44 Số 4 - Trang 1111-1118 - 2007
Jerim Kim, Bara Kim, Sung‐Seok Ko
We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.
Exponential spectra as a tool for the study of server-systems with several classes of customers
Journal of Applied Probability - Tập 15 Số 1 - Trang 162-170 - 1978
Julian Keilson
For a single-server system having several Poisson streams of customers with exponentially distributed service times, busy period densities, waiting time densities, and idle state probabilities are completely monotone. The exponential spectra for such densities are of importance for understanding the transient behavior of such systems. Algorithms are given for the computation of such spectra. Appli... hiện toàn bộ
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