Problem 1
Dr. Ahmed Ali practices dentistry in Gaza, Palestine. Dr. Ali tries hard to schedule
appointments so that patients do not have to wait beyond their appointment time.
His October 20 schedule is shown in the following table.
SCHEDULED APPOINTMENT AND TIME
Amin
9:30 A.M.
Bader
9:45 A.M.
Carmen
10:15 A.M.
Dalal
10:30 A.M.
Eyad
10:45 A.M.
Fady
11:15 A.M.
Ghaleb
11:30 A.M.
Huda
11:45 A.M.
EXPECTED TIME NEEDED
15
20
15
10
30
15
20
15
Unfortunately, not every patient arrives exactly on schedule, and expected times to
examine patients are just that—expected. Some examinations take longer than
expected, and some take less time.
Problem 1 (continued)
Dr. Ali experience dictates the following:
(a) 20% of the patients will be 20 minutes early.
(b) 10% of the patients will be 10 minutes early.
(c) 40% of the patients will be on time.
(d) 25% of the patients will be 10 minutes late.
(e) 5% of the patients will be 20 minutes late.
He further estimates that
(a) 15% of the time he will finish in 20% less time than expected.
(b) 50% of the time he will finish in the expected time.
(c) 25% of the time he will finish in 20% more time than expected.
(d) 10% of the time he will finish in 40% more time than expected.
Dr. Ali has to leave at 12:15 P.M. on October 20 to catch a flight to a dental
convention in Dubai. Assuming that he is ready to start his workday at 9:30 A.M.
and that patients are treated in order of their scheduled exam (even if one late
patient arrives after an early one), will he be able to make the flight? Comment
on this simulation.
Simulation of a queueing problem
R1= 60, 08, 19, 29, 36, 72, 30, 27
R2= 80, 45, 86, 99, 02, 34, 87, 08
Simulation of a queueing problem
Expected Expected
Arrival
Time
9:30 A.M
15
9:45 A.M
20
10:15 A.M
15
10:30 A.M
10
10:45 A.M
30
11:15 A.M
15
11:30 A.M
20
11:45 A.M
15
Problem 2
The manager of Bank of Palestine is attempting to determine how many tellers are
needed at the tellers area. As a general policy, the manager wishes to offer service
such that average customer waiting time does not exceed 2 minutes. The first
customer will enter the system after 2 minutes of the opening time (Open time
9:00AM). Given the existing service levels, as shown in the following data, does the
drive-in window meet this criterion?
Simulation of a queueing problem