Consider two waiting line systems, each with an arrival rate of $2$ customers per minute. The first system is a Pooled$-$Queue system with two servers and each server takes $0\mathrm{.}9$ minutes to serve a customer. The second system is a Faster$-$Service system with one server that serves each customer in $0\mathrm{.}45$ minutes. Assume that the notation used corresponds to the lecture media $/$ text for a$,$ p$,$ CVa, CVp$,$ and m$.$ Unless otherwise stated, assume that all coefficients of variation $($e$.$g$.,$ CVa, CVp$)$ are one, corresponding to moderate variability. We seek to compare performance in these two systems. Pick all options below that are correct.

Note: This can be a challenging question. Use of a Waiting Line spreadsheet calculator, available on Canvas Module $3,$ can be beneficial.

Group of answer choices

When there is no variability, both systems will have zero time in queue, Tq$.$

Both systems will satisfy I $=(1/$a$)$ T$,$ Iq $=(1/$ a$)$ Tq$.$

Both systems will have the same average inventory at the servers, Ip$.$

The two$-$server system will be better than the faster$-$server system in terms of the four waiting line metrics, Tq$,$ T$,$ Iq$,$ and I.

On average, the two$-$server system will be busier $($have higher utilization$)$ than the faster$-$server system

Flow time T will be higher in the two$-$server system, but Tq will be higher in the faster$-$server system.

When the variability is really high $($much bigger than CVa $=$ CVp $=1),$ we expect the two$-$server system to perform better than the faster$-$server system.