Skip to main content

Permutation: Computer-Oriented


Suppose we have two Jobs A and B. A and B carry data of size 1 Kilo Byte each. Data carried by Jobs A and B has to be processed. 

Let us further suppose that there are two slots ( Slot I and Slot II ) available. The important condition is that processing of Jobs A and B can occur, only if they appear in Slot I. When these jobs appear in Slot II, they are not processed. 

____________

Case I:

____________

The permutations of Jobs A and B are as:


_________________

            Slot I        Slot II

Perm I         A         B


Perm II        B           A              

________________

//Permutation- A Great Fun//

//Titbits Under the Sun//

____________________

Clearly job A would be in Slot I for once.  Job B too would be in Slot I for once.

Let us suppose the  data processing speed of our imaginary Processor is 1 Kilo Byte ( 1 KB ) per second ( 1 KB/s ). Job A whose size is 1 KB would be completely processed in 1 second. Equally sized Job B ( of 1 KB ) would also be finished in 1 second. Slot I is occupied once each by Job A and Job B in the twin possible permutations of A and B. Total time dedicated to Slot I by the Processor is 2 seconds. 

_______________

Case II:

_______________



Now, Jobs A, B, and C are with us. Job C is new.  So, the three Jobs produce permutations. There is a restriction.  Now, we would consider only two jobs at a time.The following permutations are possible:

______________________________

Slot I                           Slot II

____________________________

Job                              Job

____________________________

A                                      B

A                                      C

B                                       A

B                                       C

C                                       A :Ignore

C                                     B :Ignore

____________________


_______________________

//Permutations Tutored to Permit//

//The Crispy Cakewalk- Boys Admit//

_______________________

The permutations show that Slot I is occupied by Job C in the last two rows. Job C is not under consideration. So, the last two rows are ignored.

In the new permutations, we see that Job A appears twice in Slot I. Job B too appears twice in Slot I. As mentioned before, we are interested in Job A and Job B. From the start, we have considered only these two ( A and B ).

The same imaginary Processor having a data processing speed of 1 Kilo Byte per second is used. The same number of Bytes- 1 Kilo Byte each-  is associated with Job A and Job B.

Number appearances of Job A and Job B, in Slot I, is two for both ( Look at the given Permutations of Job A, Job B, and Job C listed above ).  So, the size of data brought by Job A in Slot I is ( 1 KB + 1 KB  = ) 2 KB. Similarly, the size of data that is handed over to the Processor by Job B is ( 1 KB + 1 KB = ) 2 KB. Total data to be processed is:

 Job A ------> 1 KB + 1 KB = 2 KB


Job B ------->  1 KB + 1 KB = 2 KB

______________________________

Total Size of Data         = 4 KB   

_______________________________

The data processing speed of the Processor is  1 KB/second . Requirement of time is 4 seconds to process the data carried by Job A and Job B in Slot I. 




__________________________

Observation: 

Permutations of two unique objects ( Job A and Job B ) puts each of them in the high priority slot ( Slot I ) only once. 

So, Requirement of Processor Time = 2 Seconds

***************

Permutations of three unique objects ( Job A, Job B, Job C ) puts Job A and Job B twice in the high priority slot ( Slot I ). 

So, Requirement of Processor Time = 4 Seconds 

____________________________

********

********

Conclusion: Requirement of Processor's time may depend on permutations of tasks.

*********

*********

____________________________

_____________________________







Labels:

Comments

Post a Comment

Popular posts from this blog

Local-Area Networks

Local-Area Networks ( LANs ) are restricted to a small area. Such Networks may be established within a building. Computers that are part of Local-Area Networks are Personal Computers ( PCs ) or microcomputers. These Computers are connected to each other. Simple communication lines connect these Pers Networks bring people together. When people join  hands teamwork becomes possible. The structural composition of LANs simplifies teamwork. In other words, LAN hardware supports teams having similar processing requirements. LAN Computers readily support personalization of tasks allocated to professionals.  Office staff can work together and share information. This improves the efficiency of the entire workforce. It has been noted that here all the Networked Computers are Personal Computers. They are of equal capacity. Mostly LAN users have similar tasks. If situations allow, a user is independent to access any Computer to serve his purpose. LAN users can exercise the option of secu...
Post a Comment
Read more

Computers - An Introduction

Computers are man made machines. They are made to work very fast. Working fast they can solve  big and small problems.  Modern science has given us these computers. They are very popular. Computers affect and change lives. They keep us happy.The happiness grows. Computers are quick and smart. Great problem solvers and simplifiers are our computers. They can do our work without stopping. Focus is on doing only what is needed. Not needed, not done.  Computers are  life-less servants. They cannot think or make decisions on their own. They are empowered to work. They are given each and every thing so that they carry out our orders. Orders are respected by computers. The manner in which computers work is wholly dependent on man.  The quality of service provided by computers is remarkable. They are loved by human beings. Computers are known for smart and quick service. Computers do not give wrong results. Correct answers are always given. Questions which are difficult...
Post a Comment
Read more

Euclid's Algorithm

The Greatest Common Divisor ( GCD ) of  two numbers is a number. The number ( GCD ) causes division of the two numbers. This number ( GCD ) is the greatest number that is possible. This divisor partially forms the two numbers. Adding  the divisor successively may result in formation of the two numbers. One can note that when the divisor is the greatest, the division of the dividend is the sharpest. The division operation is very effective. When the Greatest Common Divisor of two numbers is considered, we think of a number that can cause division of both the numbers. Here the two numbers are unequal. The Greatest Common Divisor causes divisions of the two numbers differently. This is clear from the two different quotient values.  The GCD value is very interesting to note. It relates very well with the two numbers. The GCD of two even numbers is also an even number. The GCD of two odd numbers is an odd number. So, we can say that GCD is an abstraction of the two numbers in ...
1 comment
Read more