# Numerical Problem on Processor Pool Model

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1. Nov 18, 2015

### 22990atinesh

Consider the case of a distributed computing system based on the processor-pool model that has $P$ processors in the pool. In this system, suppose a user start a computing job that involves compilation of a program consisting of $F$ source file $(F < P)$. Assume that at this time the user is the only user using the system. What maximum gain in speed can be hoped for this job in this systems compared to its execution on a single processor system ? What factors might cause the gain in speed to be less than this maximum ?

Attempt:
Let 't' secs are required by each processor in processor pool model to complete the job. Hence overall 't' secs will be needed as in processor pool model as all processor are running in parallel.

In case of single processor system time required will be = Ft s

Hence gain in speed is = (Ft - t)/Ft

is it correct or I'm assuming sth wrong. Can anybody help.

2. Nov 23, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Nov 23, 2015

### Staff: Mentor

Your reasoning is fine if you make the assumption that every file requires the same time to compile, that there is no linking and loading of the compiled modules into a single runtime image, and that there are no resources that are competed for. In this case you have found an expression for the maximum, best case speedup.

In a real-world situation there's likely to be a range of compile times and library requirements, and the link/load step would require access to all the compiled modules after compilation.

The compilations would then be finished when the longest module is done, and linking could only start when that is complete. Linking and creating/writing the load image would likely involve some irreducible serial activity. Refer to Amdahl's law.