The Gender Inequity in Restroom Facilities Queues
Combining queues is not the only contribution management science has made
to comfort and convenience. Ahn Tran, an undergraduate Engineering student
at Cornell, observed that lines form more often and are usually longer
at women's rest rooms than at men's. As part of a summer job with the Washington
State Department of Transportation, she collected data showing that women
take an average time of about 79 seconds to use the facilities, while
men take only 45 seconds.
Consider this time a "service time" for queuing analysis. Consider
a rest stop on the New York State Throughway with 5 units for each sex.
During holiday weekends, the average arrival rate is 200 people of
each sex per hour, or 3.33 per minute. Since these people are coming
out of New York City, assume an infinite source of patrons.
HINT: Be sure to put everything in terms of minutes and calculate separate
models for men and women before comparison. Don't combine the queues.
Remember, the average service rate (m) is the inverse
of service time, so the service rate for males would be 1.33 per minute,
and for females, service rate would be 0.76 per minute. Arrival rate
for each is 3.33 per minute.
a) For each--what would the average length (Lq) of each line be
c) On average, how much longer would a woman spend in the system
(Ws) than a man?
d) Many places had laws requiring adjacent facilities to be equal in
number for both sexes. Does this study support the reasonableness
of those laws? Has Management Science triumphed again?
r = 3.33/1.33 = 2.50
Lq (table) = 0.13
Ws=Lq/l + 1/m
=0.13/3.33 + 1/1.33 = 0.79 minutes
r = 3.33/0.76= 4.38
Lq (table) = 5.3
Ws=Lq/l + 1/m
= 5.3/3.33 + 1/0.76 = 2.91 minutes
|Since women spend over 2 minutes more than males do, equal is not equitable
in this case. Although management science has not yet prevailed in
all areas, studies such as this one are being used to get things changed.
Management science pervades all aspects of our lives. Management
Science is more than just a way to make a living, it's a way of living