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 t...... 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 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 sh...... 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 hazar...... 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 equat...... 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 <it is shown that the estimate, hiện toàn bộ
On New Classes of Extreme Shock Models and Some Generalizations
Journal of Applied Probability - Tập 48 Số 01 - Trang 258-270 - 2011
Ji Hwan, Maxim Finkelstein
In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. A shock model which combines these two types is called a ‘combined shock model’. In this paper we study new classes of extreme shock models and, based on the obtained results and model int...... hiện toàn bộ
Approximations in finite-capacity multi-server queues by Poisson arrivals
Journal of Applied Probability - Tập 15 Số 4 - Trang 826-834 - 1978
Shirley A. Nozaki, Sheldon M. Ross
An approximation for the average delay in queue of an entering customer is presented for the M/G/K queuing model with finite capacity. The approximation is obtained by means of an approximation relating a joint distribution of remaining service time to the equilibrium service distribution.
Analysis of the Luria–Delbrück distribution using discrete convolution powers
Journal of Applied Probability - Tập 29 Số 2 - Trang 255-267 - 1992
W. T., G. Sandri, Sahotra Sarkar
The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency:p0=... hiện toàn bộ
Advances in Complete Mixability
Journal of Applied Probability - Tập 49 Số 2 - Trang 430-440 - 2012
Giovanni Puccetti, Bin Wang, Ruodu Wang
The concept of complete mixability is relevant to some problems of optimal couplings with important applications in quantitative risk management. In this paper we prove new properties of the set of completely mixable distributions, including a completeness and a decomposition theorem. We also show that distributions with a concave density and radially symmetric distributions are completely...... hiện toàn bộ
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