## Efficiency vs. number of processors, Computer Networking

Assignment Help:

Efficiency:-

The other main metric used for performance measurement is efficiency of parallel computer system i.e. how the resources of the parallel systems are being utilized. This is known as degree of effectiveness and the efficiency of a program on a parallel computer with k processors can be defined as the ratio of the relative speed up achieved as shifting the load from one processor machine to k processor machine where the multiple processors are being used for achieving the result in a parallel computer. This is denoted by E(k).

Ek is defined as follows:

E(k) = S (k )/ k

The value of E (k) is directly proportional to S (k) and inversely proportional to number of processors employed for performing the computation. The relation between E (k) vs. Number of processors is shown in Figure. Efficiency vs. Number of Processors

Assuming we have the multiplication problem as discussed above with k processors, then the efficiency is as under:

E(k) = T(1)/T(n)*K = N/log n*N

E(n) =1/log(n)

Now, supposing we have X processors i.e. X < K and we have to multiply n numbers, in such a condition the processors may be overloaded or might have a few overheads. Then the efficiency is as under:

E(X)= T(1)/T(X)*X

Now, the value of T(X) has to be computed. As we have n numbers, and we have X processors, thus firstly each processor will multiply n/X numbers and consequently process the X partial results on the X processors according to the method discussed in Figure. The time complexity is equal to the sum of the time to compute multiplication of k/X numbers on every processor i.e., O(k/X) and time to compute the answer of partial results i.e. log (X)

E(X) =K/(K/X +log(X))*X

E(X) = (K/X)/(K/X +log(X))

Dividing by X/K we get

E(X) = 1/ (1+(X/K)* log(X))

It can be concluded from the above statement that if N is fixed then the efficiency i.e. E(X) will reduces as the value of X increases and becomes equivalent to E(N) in case X=N.  Likewise, if X is fixed then the efficiency i.e., E(X) will increase as the value of X i.e. the number of computations increases.

The other performance metrics engage the standard metrics like MIPS and Mflops. The term MIPS (Million of Instructions Per Second) shows the instruction execution rate. Mflops (Million of Floating Point Operations per Second) shows the floating-point execution rate.

#### Determine the concept of placing antenna on hieght, Determine the concept o...

Determine the concept of placing antenna on hieght First, starting deployment simply placed cells in regions where there was high density of vehicle or human population. Once t

#### State sonet frame, SONET Frame Can be viewed as a matrix of nine rows ...

SONET Frame Can be viewed as a matrix of nine rows of 90 octets every for a total of 810 octets.  A few used for control they aren't positioned at the beginning or end of the

#### Hardware difficulty of benz network, Hardware difficulty of Benz Network: -...

Hardware difficulty of Benz Network: - Benz network uses smaller switches and it gives excellent connectivity.  To find hardware difficulty of Benz network let us presume that

#### Which applications of computer network can be categorized, What are the mai...

What are the main categories based on which applications of computer network can be categorized? The major areas under which the applications for computer network can be divide

#### Mime the multipurpose internet mail extensions, MIME The Multipurpose Inter...

MIME The Multipurpose Internet Mail Extensions While  the message  headers described in are satisfactory for sending  ordinary  ASCII text they are  not sufficiently Reich for

#### Which protocol is used for booting diskless workstations, Reverse Address R...

Reverse Address Resolution Protocol - RARP is ARP's counterpart, but it resolves IP addresses to MAC addresses typically on diskless workstations.

#### Enumerate the various internetworking facility, Enumerate the various inter...

Enumerate the various internetworking facility 1.) Give a link among networks. At minimum, a physical and link control connection is required.   (2) Provide for the routing

#### Operating system for server, Operating system for Server Since 1994, w...

Operating system for Server Since 1994, when the original pair of web servers - NCSA HTTPd and CERN HTTPd , were proposed, dozens of commercial and shareware programs have

#### What is groupware, What is Groupware Groupware are a collection of sof...

What is Groupware Groupware are a collection of software tools that encompass a broad range of applications. Even though groupware broadly consists of applications like calend  