## Assignment 8 Answer Checker

This assignment repeats most of 7A's questions. Comparing the two, you can see what difference it makes to add a second server who works in parallel with the first.

Before we do the questions, let's check the preliminaries (unless you'd rather skip to question 2):

What is lambda?
(For these answers, use hours as the units of time.)

What is mu?

What is M?

What is rho?

To calculate the answers to questions 2, 3, and 4, you need to first calculate the the probability that, at any particular time, no one will be in the system. What is that probability of 0 in the system?

Next you need Lq, because the other quantities' formulas are based on it. What did you get for Lq?

Now you're ready to do the problems.

2. What is the average number of patients in the ER (waiting or being served?)

3. What is the average length of time that a patient spends from the time they enter the ER to the time they leave?

4. The waiting area is separate from the examining/treatment room. How many chairs should there be in the waiting area to reduce the probability that someone will have no chair to less than 0.01? (No fractions of chairs, please.)

5. Suppose the hospital has announced, as part of a TQM policy, that it will discount each patient's bill by \$6.00 per hour that the patient waits in the ER waiting area. How much will this discount cost the hospital per hour on the average? (Note that patients get paid only for waiting time, not for service time. Also note that patients get paid proportionally for fractions of hours spent waiting.)

6. Suppose a physician costs \$30 per hour. If the \$6.00 per hour waiting penalty is in effect, does it pay to add the second physician? You must compare the situation when you have one physician with the situation when you have two.

7. Regardless of the answer to question 6, which gives you shorter waits overall, one ER with two physicians or two separate ER's with one physician in each one, each serving half as many patients on the average? Based on this comparison alone, is it better to have centralized or decentralized ER facilities in a city?

Help with question 7: The rest of the applets lead you through answering question 7. Use them if you would like help with that question.

Back to question 7.

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