Efficiency vs. number of processors, Computer Networking

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.

1947_Efficiency vs. Number of Processors.png

   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.

Posted Date: 3/4/2013 6:00:29 AM | Location : United States







Related Discussions:- Efficiency vs. number of processors, Assignment Help, Ask Question on Efficiency vs. number of processors, Get Answer, Expert's Help, Efficiency vs. number of processors Discussions

Write discussion on Efficiency vs. number of processors
Your posts are moderated
Related Questions
Assign switch ports to VLANs. Refer to the port assignment table at the starting of the lab to assign ports to the VLANs. Use the interface range command to make simpler this

PING - Packet Internet Gopher A utility that shows connections to one or more remote hosts. The ping command uses the ICMP echo request and echo reply packets to verify whether

QUESTION a) Security is a very crucial component in a Distributed System. Describe three properties of a secure channel. b) During packet transmission, messages are subdivid

Medium Earth Orbiting satellite is an orbit which is located just above the few hundred miles to a few thousands above the earth surface. It is of higher advantage than Low orbit s

What are the concerns of the Physical Layer? Physical layer coordinates the functions needed to transmit a bit stream over a physical medium. a. Physical characteristics of in

What do you mean by Protocol? In the context of data networking, a protocol is a formal set of rules and conventions that governs how computers exchange information over a netw

Question: a) Consider the following MIP scenario. Quite a few enterprise networks use private addresses and NAPT for the communication to the Internet. i. Discu

What is Proxy Sever and Firewall Proxy Sever Also known as a proxy or application level gateway. It is an application that breaks the connection among sender and receiver.

Consider a subnet with subnet prefix 101.101.101/24  a)  If you subdivide the subnet into four equal size subnets, what are their prefixes? Give all four prefixes in the form a.

I have a project on Information Communication Technology(I.C.T). So sir I want to know that what is internet? and how it works?