Question

Interactive Systems has a transaction processing computer system that processes two kinds of transactions. The analysts at Interactive feel they can model their system as an open multiclass model described in Section 6.3.2.1 with one CPU and two $I / O$ devices. The service demands and arrival rates are described in the table below. Calculate $W_1, W_2, L_1$, and $L_2$. $$ \begin{array}{cccc} c & k & D_{c k} & \lambda_c \\ \hline 1 & 1 & 0.2 & 1.0 \\ 1 & 2 & 0.3 & - \\ 1 & 3 & 0.4 & - \\ 2 & 1 & 0.4 & 1.5 \\ 2 & 2 & 0.3 & - \\ 2 & 3 & 0.2 & - \\ \hline \end{array} $$

   Interactive Systems has a transaction processing computer system that processes two kinds of transactions. The analysts at Interactive feel they can model their system as an open multiclass model described in Section 6.3.2.1 with one CPU and two $I / O$ devices. The service demands and arrival rates are described in the table below. Calculate $W_1, W_2, L_1$, and $L_2$.
$$
\begin{array}{cccc}
c & k & D_{c k} & \lambda_c \\
\hline 1 & 1 & 0.2 & 1.0 \\
1 & 2 & 0.3 & - \\
1 & 3 & 0.4 & - \\
2 & 1 & 0.4 & 1.5 \\
2 & 2 & 0.3 & - \\
2 & 3 & 0.2 & - \\
\hline
\end{array}
$$

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

Arnold O. Allen 2nd Edition

Chapter 6, Problem 11

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Step 1

The table provided gives us the service demands $ D_{ck} $ and arrival rates $ \lambda_c $ for two classes of transactions (c = 1, 2) processed by three devices (k = 1 for CPU, k = 2 and k = 3 for I/O devices). $ D_{ck} $ is the service demand of class c Show more…

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Interactive Systems has a transaction processing computer system that processes two kinds of transactions. The analysts at Interactive feel they can model their system as an open multiclass model described in Section 6.3.2.1 with one CPU and two $I / O$ devices. The service demands and arrival rates are described in the table below. Calculate $W_1, W_2, L_1$, and $L_2$. $$ \begin{array}{cccc} c & k & D_{c k} & \lambda_c \\ \hline 1 & 1 & 0.2 & 1.0 \\ 1 & 2 & 0.3 & - \\ 1 & 3 & 0.4 & - \\ 2 & 1 & 0.4 & 1.5 \\ 2 & 2 & 0.3 & - \\ 2 & 3 & 0.2 & - \\ \hline \end{array} $$

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