Question

if you have Mathematica; 25 if you must write your own code.] Suppose Peter Piper of Puerile Publications, Example 6.3.3, discovers that he must add 10 more workstations to their system (business is booming at Puerile). Use his model to do the following: (a) Calculate $\lambda$ and $W$ for the current system with 10 more workstations, that is, $N=40$. (b) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server that has $D_1=0.1, D_2=0.4$, and $D_3=0.2$ (all values in seconds). (c) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server consisting of the original CPU but a single $I / O$ device, that is much faster because of caching and a faster disk drive so that $D_1=0.3$ seconds and $D_2=0.02$ seconds.

   if you have Mathematica; 25 if you must write your own code.] Suppose Peter Piper of Puerile Publications, Example 6.3.3, discovers that he must add 10 more workstations to their system (business is booming at Puerile). Use his model to do the following:
(a) Calculate $\lambda$ and $W$ for the current system with 10 more workstations, that is, $N=40$.
(b) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server that has $D_1=0.1, D_2=0.4$, and $D_3=0.2$ (all values in seconds).
(c) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server consisting of the original CPU but a single $I / O$ device, that is much faster because of caching and a faster disk drive so that $D_1=0.3$ seconds and $D_2=0.02$ seconds.

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Arnold O. Allen 2nd Edition

Chapter 6, Problem 10

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Peter Piper's system is modeled as a closed queuing network with $N$ workstations and a file server. The file server consists of three components: a CPU, a disk, and a network. Each component has a service demand $D_i$ (in seconds). The total number of jobs Show more…

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if you have Mathematica; 25 if you must write your own code.] Suppose Peter Piper of Puerile Publications, Example 6.3.3, discovers that he must add 10 more workstations to their system (business is booming at Puerile). Use his model to do the following: (a) Calculate $\lambda$ and $W$ for the current system with 10 more workstations, that is, $N=40$. (b) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server that has $D_1=0.1, D_2=0.4$, and $D_3=0.2$ (all values in seconds). (c) Calculate $\lambda$ and $W$ with $N=40$ for an upgraded file server consisting of the original CPU but a single $I / O$ device, that is much faster because of caching and a faster disk drive so that $D_1=0.3$ seconds and $D_2=0.02$ seconds.

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