Question 10.69: Analyzing congestion at a shrinkwrap machine Unit loads arri...

The operating characteristics are obtained using Equations $10.172$ through $10.175$ by letting $\lambda=15, \mu=24, \sigma^{2}=0$, and $\rho=0.625$.

$L=\rho+\frac{\lambda^{2} \sigma^{2}+\rho^{2}}{2(1-\rho)}$     (10.172)

$L_{q}=\frac{\lambda^{2} \sigma^{2}+\rho^{2}}{2(1-\rho)}$     (10.173)

$W=\frac{1}{\mu}+\frac{\lambda\left(\sigma^{2}+\frac{1}{\mu^{2}}\right)}{2(1-\rho)}$     (10.174)

$W_{q}=\frac{\lambda\left(\sigma^{2}+\frac{1}{\mu^{2}}\right)}{2(1-\rho)}$     (10.175)

$L=0.625+\frac{(15)^{2}(0)+(0.625)^{2}}{2(1-0.625)}=1.1458$ unit load

$L_{q}=\frac{(15)^{2}(0)+(0.625)^{2}}{2(1-0.625)}=0.5208$ unit load

$W=\frac{L}{\lambda}=0.07639$ hour per unit load

$=4.583$ minutes per unit load

$W_{q}=W-\frac{1}{\mu}=2.083$ minutes per unit load