HP 12c Platinum - Page 140

140 Miscellaneous
If the number of servers is limited to one, with other conditions remaining the same
(unlimited queue, Poisson arrival, exponential service), the average queue length can be
readily calculated without reference to tables:
RPN Mode:
1.
Key in the arrival rate, λ and press
?1.
2.
Key in the service rate, µ and press
?2
z\\2q~ 1~-z to calculate the average number of customers
waiting in queue at any one time.
3.
Press
:1z to calculate the average waiting time.
4.
Press
:2y+ to calculate the average total time the customer spends in the
system.
5.
Press
:1§ to calculate the average number of customers in the system.
ALG Mode:
1.
Key in the arrival rate, λ and press
?1z.
2.
Key in the service rate, µ and press
?2³y-g’~³y to calculate
the average number of customers waiting in queue at any one time.
3.
Press
z:1+ to calculate the average waiting time.
4.
Press
:2y§ to calculate the average total time the customer spends in the
system.
5.
Press
:1³ to calculate the average number of customers in the system.
Example 2: A small grocery store has but a single check-out counter. Customers arrive at
a rate of 1 every 2 minutes (λ
= .5) and, on the average, customers can be checked out at a
rate of .9 per minute (µ). What is the average number of customers in the waiting line at
any time? The average waiting time? What is the average total time for a customer to wait
and be checked out? The average number of customers in the system?
12c platinum / 12C
RPN Keystrokes
12c platinum
ALG Keystrokes
Display Comments
.5?1 .5?1z
0.50
.9?2z\ .9?2
\2q~
³
0.56
(intensity factor, ρ)
1~
y-g’
-z ~³y
0.69
Average # customers waiting in
queue.
:1z z:1+
1.39
Average waiting time.
:2y+ :2y§
2.50
Average total time in the
system.
:1§ :1³
1.25
Average # customers in system.