Consider the loan application office example we modeled in lab classes. There are $4$ different processes

which are

Credit check

Preparing the loan covenant

Pricing the loan

Disbursement of funds

Bank manager should decide whether to have specialized serial or generalized parallel workers when

processing involves the above tasks. There are $4$ workers. The performance measure that bank manager

considered is mean response time per customer. In order to find difference between two processing, two

models are run with the service times that are generated with independent random numbers, common

random numbers with synchronization and common random numbers without synchronization. The

average service time for serial and parallel workers models are given below as Model $1$ and Model $2$

respectively.

Replication Average Response Time for Model $($minutes$)$ Model $1$ Model $2$ IRN

Model $2$ CRN w$/$ Sync

Model $2$ CRN w$/$o Sync$.$

$24\mathrm{.}8217\mathrm{.}118\mathrm{.}6322\mathrm{.}79244\mathrm{.}2815\mathrm{.}679\mathrm{.}8624\mathrm{.}23327\mathrm{.}314\mathrm{.}0816\mathrm{.}4121\mathrm{.}24419\mathrm{.}4211\mathrm{.}368\mathrm{.}9015\mathrm{.}72534\mathrm{.}9411\mathrm{.}7119\mathrm{.}6322\mathrm{.}54646\mathrm{.}7111\mathrm{.}6617\mathrm{.}5717\mathrm{.}78745\mathrm{.}8917\mathrm{.}4218\mathrm{.}3220\mathrm{.}69831\mathrm{.}312\mathrm{.}5813\mathrm{.}1313\mathrm{.}77926\mathrm{.}779\mathrm{.}810\mathrm{.}4623\mathrm{.}771022\mathrm{.}7917\mathrm{.}1513\mathrm{.}6223\mathrm{.}85$

a$.$ Compare the serial and parallel loan application processing using independent sampling and CRN where R$=$R$\_(1)=$R$\_(2).$ Please comment about the results you find.

b$.$ Determine how many replications are needed if it is important to detect difference of $4$ minutes per customer. $,$ I want to step by step. Especially, b$)$ choise.