MODULE D
DISCUSSION QUESTIONS
2.
The assumptions underlying the standard waiting line or queuing model are:
n
Arrivals are served on a “first come, first served” (FCFS, or FIFO) basis; and every arrival
waits to be served regardless of the length of the line or queue.
n
All arrivals are independent of preceding arrivals, and the average number of arrivals per unit
time (arrival rate) does not change over time.
n
Arrival rates are described by a Poisson probability distribution, and arrivals come from an
infinite or very large source.
n
Service times vary from one customer to another and are independent of one another, but their
average rate is known.
n
Service times are described by a negative exponential probability distribution.
n
The effective service rate is faster than the arrival rate.
4.
If the service rate is not greater than the arrival rate, the line will increase in length indefinitely.
12.
This deals with the interesting issue of the value of waiting time. Some service organizations
place a very low value on your time, leading to a good classroom discussion.
15.
Supermarkets simply do not have enough space to set up a common line, so they use a separate
queue for each checkout station.
16.
The
cost tradeoffs
in queuing are waiting cost versus service cost.
ENDOFMODULE PROBLEMS
D.1
(a)
ρ
λ
μ
=
=
=
40
60
2
3
(b)
L
q
=

(
29
=

=
(
29
(
29
μμ
2
2
40
60 60
40
4
3
(c)
L
s
=

=

=
40
60
40
2
(d)
W
q
=

(
29
=

=
=
(
29
40
60 60
40
0 033
2
.
hours
minutes
(e)
W
s
=

=

=
=
1
1
60
40
1
20
3
hour
minutes
=
40/hour,
=
60
/hour
D.2
(a)
=
=
=
40
90
0 44
44%
.
(b)
L
q
=

=
(
29
(
29
40
90 90
40
0 356
2
.
(c)
L
s
=

=
40
90
40
0 8
.
(d)
W
q
=

=
=
=
(
29
40
90 90
40
0 0089
0 533
.
.
hours
minutes
32 seconds
(e)
W
s
=

=
=
=
1
90
40
1
50
12
hour
minutes
72 seconds
.
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 Winter '03
 JamesCampbell
 Harshad number, average number, Solutions Manual t/a, Manual t/a Operations

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