scholarly journals Mean and Variance of Time to Recruitment in A Two Graded Manpower System with Correlated Inter-Decision Times Involving Depletion Having Independent and Non-Identically Distributed Random Variables

2017 ◽  
Vol 13 (03) ◽  
pp. 18-23
Author(s):  
S. Jenita ◽  
S.Sendhamizh Selvi
Keyword(s):  
Random Variables ◽  
Manpower System ◽  
Mean And Variance ◽  
Decision Times

On the number of leaves of a euclidean minimal spanning tree

1987 ◽  
Vol 24 (4) ◽  
pp. 809-826 ◽  
Author(s):  
J. Michael Steele ◽  
Lawrence A. Shepp ◽  
William F. Eddy
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Random Variables ◽  
Minimal Spanning Tree ◽  
Absolutely Continuous ◽  
Mean And Variance ◽  
Number Of Leaves ◽  
The Mean ◽  
Vertex Degrees ◽  
Minimal Spanning Trees

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi, , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n–1Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.

On the number of leaves of a euclidean minimal spanning tree

1987 ◽  
Vol 24 (04) ◽  
pp. 809-826 ◽  
Author(s):  
J. Michael Steele ◽  
Lawrence A. Shepp ◽  
William F. Eddy
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Random Variables ◽  
Minimal Spanning Tree ◽  
Absolutely Continuous ◽  
Mean And Variance ◽  
Number Of Leaves ◽  
The Mean ◽  
Vertex Degrees ◽  
Minimal Spanning Trees

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi , , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n –1 Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.

The Largest Missing Value in a Sample of Geometric Random Variables

2014 ◽  
Vol 23 (5) ◽  
pp. 670-685 ◽  
Author(s):  
MARGARET ARCHIBALD ◽  
ARNOLD KNOPFMACHER
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Missing Value ◽  
Asymptotic Expressions ◽  
Mean And Variance ◽  
The Mean ◽  
Special Case

We consider samples of n geometric random variables with parameter 0 < p < 1, and study the largest missing value, that is, the highest value of such a random variable, less than the maximum, that does not appear in the sample. Asymptotic expressions for the mean and variance for this quantity are presented. We also consider samples with the property that the largest missing value and the largest value which does appear differ by exactly one, and call this the LMV property. We find the probability that a sample of n variables has the LMV property, as well as the mean for the average largest value in samples with this property. The simpler special case of p = 1/2 has previously been studied, and verifying that the results of the present paper coincide with those previously found for p = 1/2 leads to some interesting identities.

Limit theorems for general size distributions

1981 ◽  
Vol 18 (1) ◽  
pp. 139-147 ◽  
Author(s):  
Wen-Chen Chen
Keyword(s):  
Limit Theorems ◽  
Local Limit Theorem ◽  
Random Variables ◽  
Local Limit ◽  
Negative Integer ◽  
Urn Model ◽  
Special Cases ◽  
Mean And Variance ◽  
Bose Einstein ◽  
General Size

Let X1, X2, · ··, Xn, · ·· be independent and identically distributed non-negative integer-valued random variables with finite mean and variance. For any positive integer n and m we consider the random vector i.e., L has the same distribution as the conditional distribution of (X1, · ··, Xm) given the condition It is easy to see that our model includes the classical urn model, the Bose–Einstein urn model and the Pólya urn model as special cases. For any non-negative integer s define G(s) = the number of Li′s such that Li = s, and U = the number of Li′s such that Li is an even number; in this paper we study the asymptotic behaviour of the random variables considered above. Some central limit theorems and a multinormal local limit theorem are proved.

scholarly journals Time to Recruitment for a Two Grade Manpower System by Max Policy of Recruitment

2018 ◽  
Vol 7 (4.10) ◽  
pp. 755
Author(s):  
K. Parameswari ◽  
P. Rajadurai ◽  
S. Venkatesh
Keyword(s):  
Policy Decisions ◽  
Manpower System ◽  
Mean And Variance ◽  
System Characteristics

In this paper an organization with two different grades, the grade wise depletion of manpower occurs due to its policy decisions is considered. Using max policy of recruitment the system characteristics namely mean and variance of time to recruitment are obtained by considering two different forms of wastages. The influence of the nodal parameters on the system characteristics is studied. 

AN EFFICIENT JOB SCHEDULING ALGORITHM IN PARTITIONABLE MESH CONNECTED SYSTEMS

2001 ◽  
Vol 12 (06) ◽  
pp. 763-773 ◽  
Author(s):  
KEQIN LI
Keyword(s):  
Job Scheduling ◽  
Scheduling Algorithm ◽  
Random Variables ◽  
Multiprocessor Scheduling ◽  
Performance Ratio ◽  
Task Execution ◽  
Average Case ◽  
Mean And Variance ◽  
Special Case ◽  
And Task

In this paper, we consider the problem of scheduling independent jobs in partitionable mesh connected systems. The problem is NP-hard, since it includes the multiprocessor scheduling problem as a special case when all jobs request for one processor. We analyze a simple approximation algorithm called A m. In particular, we show that if the sizes of submeshes requested by jobs are independent and identically distributed (i.i.d.) random variables uniformly distributed in the range [1..M1]×[1..M2], where M1×M2 is the size of a partitionable mesh connected system, and task execution times are i.i.d. random variables with finite mean and variance, then the average-case performance ratio E( A m(L))/E( OPT (L)) is asymptotically bounded from above by 1.6637594…. The average-case performance ratio improves significantly when jobs request for square submeshes or small submeshes.

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