HP 12c Platinum Reference Manual page 139

ALG Mode:
1. Key in the arrival rate of customers, λ, and press z .
2. Key in the service rate, µ, and press z to calculate ρ, the intensity factor . (Note ρ
must be less than n for valid results, otherwise the queue will lengthen without limit).
3. Key in n, the number of servers and press ³ to calculate ρ/n.
4. For a given n and ρ/n find the mean waiting time as a multiple of mean service time
from the table. Key it in and press z .
5. Calculate the average waiting time in the queue by keying in the service rate, µ, and
pressing ? 1 +? 2.
6. Calculate the average waiting time in the system by pressing : 1 y³ .
7. Key in λ and press §: 2 + to calculate the average queue length .
8. Key in ρ, the intensity factor (from step 2 above) and press ³ to calculate the
average number of customers in the system .
Reference:
Richard E Trueman, "An Introduction to Quantitative Methods for Decision Making,"
Holt, Rinehart and Winston, New York, 1977
Example 1: Bank customers arrive at a bank on an average of 1.2 customers per minute.
They join a common queue for three tellers. Each teller completes a transaction at the rate
of one customer every 2 minutes (0.5 customers per minute). What is the average waiting
time in the queue? In the system? What is the average number of customers in the queue?
In the system?
12c platinum / 12C
RPN Keystrokes
1.2\
.5z
3z
From Table 12.2, page 512 of the reference, the mean waiting time as a multiple of mean
service time for n = 3, ρ/n = 0.8 is 1.079. (Note S is used instead of n in the reference's
notation).
12c platinum / 12C
RPN Keystrokes
1.079\
.5?1z?2
:1y+
1.2:2§
2.4+
12c platinum
ALG Keystrokes
1.2z
.5z
3³
12c platinum
ALG Keystrokes
1.079z
.5?1+?2
:1y³
1.2§:2+
2.4³
Display
1.20
ρ, intensity factor.
2.40
ρ / n
0.80
Display
1.08
Average wait in queue (min).
2.16
Average wait in system (min).
4.16
Average queue length.
2.59
Average # of customers in
4.99
system.
Miscellaneous
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