Page 498 -

478 CHAPTER 11 QUEUING MODELS

Figure 11.5 Worksheet for the Kolkmeyer Two-Channel Machine Repair Problem

EXCEL file
KOLKMEYER

(11.33) makes the computations involved somewhat cumbersome. Confirm for
yourself that Equation (11.33) provides the value of P 0 ¼ 0.4845. The calculations
for the other operating characteristics are:

0:05 þ 0:50
L q ¼ 6 ð1 0:4845Þ¼ 0:3297 machine
0:05
L ¼ 0:3295 þð1 0:4845Þ¼ 0:8451 machine
0:3295
W q ¼ ¼ 1:279 hours
ð6 0:845Þ0:50
1
W ¼ 1:279 þ ¼ 3:279 hours
Operating characteristics 0:50
of an M/M/1 waiting line P w ¼ 1 P 0 ¼ 1 0:4845 ¼ 0:5155
with a finite calling
population are
considered in Finally, Equation (11.39) can be used to calculate the probabilities of any number of
Problem 20. machines being in the repair system.
As with other waiting line models, the operating characteristics provide the
An Excel worksheet manager with information about the operation of the waiting line. In this case, the
template on the online
platform that fact that a machine breakdown waits an average of W q ¼ 1.279 hours before main-
accompanies this text or tenance begins and the fact that more than 50 per cent of the machine breakdowns
The Management must wait for service, P w ¼ 0.5155, indicates a two-channel system may be needed to
Scientist software may improve the machine repair service.
be used to analyze the
two-channel finite calling Calculations of the operating characteristics of a multiple-channel finite calling
population model. population queuing system are more complex than those for the single-channel
model. A computer solution is virtually mandatory in this case. The Excel worksheet
for the Kolkmeyer two-channel machine repair system is shown in Figure 11.5. With
two repair personnel, the average machine breakdown waiting time is reduced to
W q ¼ 0.0834 hours or five minutes and only 10 per cent, P w ¼ 0.1036, of the
machine breakdowns wait for service. Thus, the two-channel system significantly

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.