om470

Name: ___________

Individual take-home assignment: WSJ on Queuing analysis

Please type. Submit your completed assignment on Canvas before it is due.

Instructions:

1. Read the WSJ article titled “The Science Behind Your Long Wait in Line” and answer the following questions. You can ignore the Appendix in that article.

2. Download this file and insert/type your response after each question. Do keep the original problem statements as well as everything else (e.g., header, footer, etc.). The only thing you change is to add your responses in. After you finish, upload your completed file on Canvas before the due day/time.

[Note] I will recommend you skimming through Chapter 5 as it will be helpful in answering some of the questions too. 1 point per question unless otherwise noted.

Question 1: What is queuing theory? Three key parameters of queuing theory are arrival rate, service rate (i.e., number of customers can be served within a time period) and average length (in terms of time) to pass through a queuing system. Why is queuing theory important for planning a retail operation? [This question sets the foundation for our term project.]

Question 2: What innovative techniques can retailers use to shorten waiting times or the perception of their length? Are any of those techniques commonly applicable to both online vs. in-store shopping? In answering the second question mark, be specific and give an example each that can be applied to both online and in-store shopping vs. that can only be applied to one but not the other.

Question 3: Three key parameters of queuing theory are arrival rate, service rate and average length (in terms of time) to pass through a queuing system. The article mentions that the queuing theory originated in a Danish phone company and various forms a queue can take, some are trivial like a line at an ATM, others may be serious like a list of people waiting for an organ transplant. Please specify what each of the three key parameters are in each of these three different queuing system respectively by filling in the table below. Your responses have to be context specific. To begin with, I’ve filled in the arrival rate in the phone company queuing system to demonstrate; in this context, the word “callers” is specific to the phone company context. (1pt per row; see the point breakdown in the table header)

Context of the queuing system	Arrival rate (λ) (0.3pt)	Service rate (μ): (0.3pt)	Average length in terms of time: i.e., time spent in the queuing system (W) (o.4pt)
1. phone company (you can think of this as a call center too if it helps)	Number of callers (within a period of time)
2. ATM
3. organ transplant

(OM470 W21 Chen) individual take-home assignment (WA1)

OM470. Chen

(Waiting line analysis. Little’s Law (B)) 1

The Science Behind Your Long Wait in Line
by: Jo Craven McGinty

Oct 08, 2016

Click here to view the full article on WSJ.com

You’ve probably participated in this familiar dance: Given a choice of checkout lines, you’ve

somehow picked the slowest.

You could wait it out. You could chassé to another queue. Or you could bail out altogether. After

all, no one likes to wait. But are the other lines really faster?

When parallel lines feed multiple cashiers, you may not be in the slowest one, but chances are,

you also are not in the fastest.

Bill Hammack, a professor at the University of Illinois at Urbana-Champaign and YouTube’s

“Engineer Guy,” explained it like this:

Imagine three lines feeding three cash registers. Some shoppers will have more items than others,

or there may be a delay for something like a price check. The rate of service in the different lines

will tend to vary. If the delays are random, there are six ways three lines could be ordered from

fastest to slowest—1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-1-2 or 3-2-1. Any one of the three (including the

one you picked) is quickest in only two of the permutations, or one-third of the time.

There are two sources of variability, according to Linda V. Green, a professor of health-care

management at the Columbia University Business School who specializes in mathematical

models of service systems.

“When the demands for service come in and how long it takes the servers to process them,” she

said. “That inevitably causes temporary mismatches between supply and demand and hence

backups, delays and congestion.”

http://www.wsjsmartkit.com/wsj_redirect.asp?key=OM20161013-03&mod=djem_jiewr_OM_domainid

http://www.wsjsmartkit.com/wsj_redirect.asp?key=OM20161013-03&mod=djem_jiewr_OM_domainid

https://www.youtube.com/user/engineerguyvideo

OM470. Chen (Waiting line analysis. Little’s Law (B)) 2

Luckily, most service providers take steps to manage the wait. A supermarket with parallel lines

reserves some registers for customers with fewer items. Airline security uses a single serpentine

line to feed multiple agents to mitigate bottlenecks at individual checkpoints. Emergency rooms

and 911 dispatchers give priority to those whose needs are most urgent.

Each approach is based on queuing theory, or the mathematical study of lines.

Queues can be trivial, like a line at an ATM, or they can be serious, like a list of people waiting

for an organ transplant, said Richard Larson, director of Massachusetts Institute of Technology’s

Center for Engineering Systems and an expert on queuing, but the fundamentals are the same: A

basic queue funnels clients demanding service to one or more servers who respond. If the servers

are busy, other demands must wait.

The clients may include a line of people, a series of 911 calls, or a string of commands issued

over a computer network (think of a printer queue). The servers are the cashiers, the dispatchers

or the devices that respond.

Queuing theory helps untangle the mess of requests, or at least smooth it out, by estimating the

number of servers needed to meet demand over a given period and designing rules for advancing

the queue.

The best system depends on the situation. “First come, first served” is most familiar, and people

often prefer it because it seems fair. But most also accept that a heart attack should take

precedence over a sprained ankle or someone with five items shouldn’t have to wait behind a

procession of brimming shopping carts.

Queuing theory originated in 1908 when a Danish scientist named Agner Krarup Erlang went to

work for the Copenhagen Telephone Company and set about trying to determine how many

telephone trunks, or lines, were needed to serve callers.

The company could have provided a trunk for each telephone, Dr. Hammack said, but that would

have been wasteful because not everyone calls at the same time. It could have provided enough

trunks to handle the average number of calls, but too many would be blocked when the average

was exceeded.

“Think of it like a bike wheel,” said Dr. Larson. “The switchboard is the hub. Each spoke is a

wire coming in from a home to a human operator who can connect your wire to some other

spoke in the wheel. What should the capacity be? If it’s too big, you’ll spend too much money on

capital investments. If it’s too small customers won’t be able to be connected reliably.”

https://plus.maths.org/content/agner-krarup-erlang-1878-1929

OM470. Chen (Waiting line analysis. Little’s Law (B)) 3

Customers waited in line to check out at an
Ikea store in New York City in September. PHOTO: MICHAEL NAGLE/BLOOMBERG NEWS

Erlang’s basic formula included three parameters: the number of trunks, the number of calls per

hour and their average length. Adjusting the number of trunks in the formula raised or lowered

the probability that a call would be blocked during the busiest hour.

Since then, retail stores, banks, call centers, emergency rooms, manufacturing plants, computer

networks and all variety of queuing environments have used Erlang’s formulas or related models

to figure out how to manage their lines.

Meanwhile, clients—at least the human variety—can’t help but wonder if there isn’t a way to

game the system.

Raj Jain, a computer-science and engineering professor at Washington University in St. Louis

takes an analytical approach: When he’s in line, he times the service. “Then I count the number

of people ahead of me, and I know how much time I am to wait.”

Dr. Larson takes a different approach. “I just strike up a conversation with an adjacent queue

dweller,” he said, “and wait.”

http://www.radio-electronics.com/info/telecommunications_networks/erlang/erlang-b.php

OM470. Chen (Waiting line analysis. Little’s Law (B)) 4

Appendix:

Erlang B & Erlang B Formula

– details & tutorial describing the Erlang B unit, and Erlang B formula developed from the basic

Erlang unit to handle blocked calls into the calculations.

ERLANG TUTORIAL INCLUDES

 Erlang telecommunications tutorial



Erlang B

 Erlang C

The Erlang B is used to work out how many lines are required from a knowledge of the traffic figure during
the busiest hour. The Erlang B figure assumes that any blocked calls are cleared immediately. This is the
most commonly used figure to be used in any telecommunications capacity calculations.

Erlang B

It is particularly important to understand the traffic volumes at peak times of the day. Telecommunications
traffic, like many other commodities, varies over the course of the day, and also the week. It is therefore
necessary to understand the telecommunications traffic at the peak times of the day and to be able to
determine the acceptable level of service required. The Erlang B figure is designed to handle the peak or
busy periods and to determine the level of service required in these periods.

Essentially, the Erlang B traffic model is used by telephone system designers to estimate the number of
lines required for PSTN connections or private wire connections. The three variables involved are Busy
Hour Traffic (BHT), Blocking and Lines.

Busy Hour Traffic (in Erlangs) is the number of hours of call traffic there are during the busiest hour of
operation of a telephone system.

Blocking is the failure of calls due to an insufficient number of lines being available. E.g. 0.03 mean 3 calls
blocked per 100 calls attempted.

Lines is the number of lines in a trunk group.

The Extended Erlang B is similar to Erlang B, but it can be used to factor in the number of calls that are
blocked and immediately tried again.

Erlang B formula

Where:
B=Erlang B loss probability
N=Number of trunks in full availability group
A=Traffic offered to group in Erlangs

http://www.radio-electronics.com/info/telecommunications_networks/erlang/what-is-erlang-telecommunications-unit-tutorial.php

http://www.radio-electronics.com/info/telecommunications_networks/erlang/erlang-b.php

http://www.radio-electronics.com/info/telecommunications_networks/erlang/erlang-c.php