Complete problem D.15 at the end of Module D of your textbook . Document your calculations/solutions in a Word doc and submit your assignment here. No PDFs please. I will attach the grading rubric as well
The typical subway station in Washington, DC, has
six turnstiles, each of which can be controlled by the station manager to be used for either entrance or exit control—but never for
both. The manager must decide at different times of the day how
many turnstiles to use for entering passengers and how many to
use for exiting passengers.
At the George Washington University (GWU) Station, passengers enter the station at a rate of about 84 per minute between the
hours of 7 a.m. and 9 a.m. Passengers exiting trains at the stop reach
the exit turnstile area at a rate of about 48 per minute during the
same morning rush hours. Each turnstile can allow an average of
30 passengers per minute to enter or exit. Arrival and service times
have been thought to follow Poisson and negative exponential distributions, respectively. Assume riders form a common queue at both
entry and exit turnstile areas and proceed to the first empty turnstile.
The GWU station manager, Gerald Aase, does not want the
average passenger at his station to have to wait in a turnstile line
for more than 6 seconds, nor does he want more than 8 people in
any queue at any average time
a) How many turnstiles should be opened in each direction every
morning?
b) Discuss the assumptions underlying the solution of this problem using queuing theory