utilization of the computers doesn't exceed $90$ percent. At least how many computers do

they need to have?

A small call center normally has five employees answering calls while open. On aver$-$

age, five calls arrive every four minutes. Under normal operating conditions, each

employee on average handles each call in $3\mathrm{.}5$ minutes. But today, one employee has

the flu, so the center needs to operate with four employees during this time. The man$-$

ager is nervous that it may be supply$-$constrained and so she directs her employees

to hurry up their processing of calls today. What is the maximum average process$-$

ing time $($in minutes$)$ for each call that they need to achieve today so that they have a

stable queue?

Experience the Tour de France $($ETF$)$ is a specialty travel agent. It arranges vacations

for amateur cyclists who want to experience the Tour de France by riding through one

or more stages in the race. It has four people who take calls from clients. Each call lasts

$30$ minutes, on average, with a standard deviation of $60$ minutes. A call arrives, on aver$-$

age, every $20$ minutes, with a standard deviation of $20.$ On average, how many minutes

does a caller wait before talking to an agent?

CloudRack provides web hosting services on its five servers. When a person requests

a page from one of its hosted websites, the server must find the page and send it to the

person's browser. These requests arrive at the rate of $400$ per second. The coefficient of

variation of the interarrival times is two. The processing time for a server is $0\mathrm{.}01$ second

with a coefficient of variation of one. On average, how much time $($in seconds$)$ does a

request take to be filled $($i$.$e$.,$ include time waiting for a server and the actual processing

by the server$)?$

Huduko operates with a utilization of $30$ percent. The interarrival time of jobs is

$8$ milliseconds $(0\mathrm{.}008$ second$)$ with a coefficient of variation of $1\mathrm{.}5.$ On average, there

are $20$ jobs waiting in the queue to be served and $60$ jobs in process $($i$.$e$.,$ being pro$-$

cessed by a server rather than waiting to be sent to a server for processing$).$ How many

servers does it have in this system?

L$016-4$

A pediatric practice has five physicians. Historically, patients were assigned to one

physician and these patients always were treated by the same physician. For example,

Alice's patients always visited her $($for "well visits" and "sick visits"$)$ and never inter$-$

acted with the other physicians. However, the practice has decided to change how

it sees patients. Now patients will be seen by whoever is available $($i$.$e$.,$ not treating

patients$).$ Based on our discussion of queuing theory, which of the following three out$-$

comes is$/$are likely to occur due to this change?

i$.$ The coefficient of variation of patient interarrival times will increase.

ii$.$ The utilization of the physicians will increase.

iii. The average number of patients actually with a physician $($that is$,$ "inventory in pro$-$

cess"$)$ will increase.

a$.$ I only

b$.$ II only

c$.$ III only

d$.$ I and II only

e$.$ I and III only

f$.$ II and III only

g$.$ All of them $($I$,$ II$,$ and III$)$

h$.$ None of them $($neither I, II$,$ nor III$)$