MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C3E6A6.F551E350" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C3E6A6.F551E350 Content-Location: file:///C:/226BB24E/Objectivefunction.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" In

 In my paper, Z.I. Flikop “Some Problems with a Design of Hierar= chical Management Systems” [in Russian],  Mehanizatcia i avtomatizatcia ypravlenia, 1971 # 5,  I have proposed the criterion for t= he evaluation efficiency  of  multiphase queuing systems that con= sist of different type of servers and provide service to different type of eleme= nts (customers).  I do not have th= is paper, however I have a book A. L. = Lifshitc, E.A. Maltc = “Statistical Modeling of Queuing System” [in Russian], Mos= cow, 1971 that cited  this crit= erion from my paper.

 

The criterion is:

 

 

where:

 

 - is a cost= (per unit of time) associated with a waiting time in the queue of a customer of = an l type;

k – is a number of customer types;

=  - is a numb= er of l type customers, that currently a= re servicing by the system and also        =   being in all queues of all phases of a system;

=  - is a probability that m customers of= an l type currently are servicing by = all phases of the system and also  being in all queues of all phases of the system;

=  

 - is a cost= (per unit of time) associated with idling of a j type server;

&n= bsp;

n – is a number of server ty= pes;

&n= bsp;

 - is a cost= (per unit of time) associated with a servicing of a customer by a server of a   j type;

&n= bsp;

 - is a numb= er of servers of j type;

&n= bsp;

 -is a numbe= r of idling servers of a j type;

&n= bsp;

- is a probability that customer is being served by a j type server;

&n= bsp;

 - is a probability that j type server = is idle;

&n= bsp;

 - is cost associated with time that customers spend in the system;

&n= bsp;

- is a cost associated with idling of servers;

 

- is a cost associated with usage of a servicing system.<= /p>

 

In addition to the criterion, A.L.  Lifshitc and E.A. Maltc  in theirs book gave the fol= lowing explanation:

  - is an av= erage number of customers of type l t= hat are in the system;

 

 - is an ave= rage number of idling servers of type j<= /i>;

 

- is an average numbers of working servers of type j;

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