scholarly journals On an extremal property of Doob’s class

1979 ◽  
Vol 252 ◽  
pp. 393-393
Author(s):  
J. S. Hwang
Keyword(s):  
Extremal Property

An extremal property of the hypersphere

1951 ◽  
Vol 47 (1) ◽  
pp. 245-247 ◽  
Author(s):  
A. M. Macbeath
Keyword(s):  
Convex Body ◽  
Extremal Property ◽  
Plane Case ◽  
Simple Application ◽  
Plane Convex ◽  
Plane Convex Body

It was shown by Sas (1) that, if K is a plane convex body, then it is possible to inscribe in K a convex n-gon occupying no less a fraction of its area than the regular n-gon occupies in its circumscribing circle. It is the object of this note to establish the n-dimensional analogue of Sas's result, giving incidentally an independent proof of the plane case. The proof is a simple application of the Steiner method of symmetrization.

On Twisted Odd Graphs

2000 ◽  
Vol 9 (3) ◽  
pp. 227-240
Author(s):  
M. A. FIOL ◽  
E. GARRIGA ◽  
J. L. A. YEBRA
Keyword(s):  
Automorphism Group ◽  
Extremal Property ◽  
Involutive Automorphism ◽  
Basic Properties

The twisted odd graphs are obtained from the well-known odd graphs through an involutive automorphism. As expected, the twisted odd graphs share some of the interesting properties of the odd graphs but, in general, they seem to have a more involved structure. Here we study some of their basic properties, such as their automorphism group, diameter, and spectrum. They turn out to be examples of the so-called boundary graphs, which are graphs satisfying an extremal property that arises from a bound for the diameter of a graph in terms of its distinct eigenvalues.

An extremal property of outer functions

1971 ◽  
Vol 10 (1) ◽  
pp. 456-458 ◽  
Author(s):  
B. I. Korenblyum
Keyword(s):  
Extremal Property

A conservation law for single-server queues and its applications

1991 ◽  
Vol 28 (1) ◽  
pp. 198-209 ◽  
Author(s):  
Genji Yamazaki ◽  
Hirotaka Sakasegawa ◽  
J. George Shanthikumar
Keyword(s):  
Conservation Law ◽  
Extremal Property ◽  
Service Discipline ◽  
Single Server ◽  
Processor Sharing ◽  
Equilibrium Equations ◽  
Common Mean ◽  
The Mean ◽  
Mean Queue Length ◽  
Basic Equations

We establish a conservation law for G/G/1 queues with any work-conserving service discipline using the equilibrium equations, also called the basic equations. We use this conservation law to prove an extremal property of the first-come firstserved (FCFS) service discipline: among all service disciplines that are work-conserving and independent of remaining service requirements for individual customers, the FCFS service discipline minimizes [maximizes] the mean sojourn time in a G/G/1 queue with independent (but not necessarily identical) service times with a common mean and new better [worse] than used (NBUE[NWUE]) distributions. This extends recent results of Halfin and Whitt (1990), Righter et al. (1990) and Yamazaki and Sakasegawa (1987a,b). In addition we use the conservation law to obtain an approximation for the mean queue length in a GI/GI/1 queue under the processor-sharing service discipline with finite degree of multiplicity, called LiPS discipline. Several numerical examples are presented which support the practical usefulness of the proposed approximation.

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