Page 299 - Schaum's Outlines - Probability, Random Variables And Random Processes

292 QUEUEING THEORY [CHAP. 9

A1 = = & and p1 = 3. Then, from Eq. (9.16),
3 -
10
Wq = ---- = 27 min
I
4(4 - 6)
For external jobs, 1, = = $ and p2 = 5, and
1
;I
Wq2 ---- - 9 min
-
=
+(3 - $1
(b) When two computers handle both types of jobs, we model the computing service as an M/M/2
queueing system with

Now, substituting s = 2 in Eqs. (9.20), (9.22), (9.24), and (9.25), we get

Thus, from Eq. (9.54), the average waiting time per job when both computers handle both types of jobs
is given by

2(%)
mu - (%)21
%= 11 = 6.39 min
From these results, we see that it is more efficient for both computers to handle both types of jobs.

9.14. Derive Eqs. (9.27) and (9.28).
From Eqs. (9.26) and (9.1 O), we have

From Eq. (9.1 I), p, is obtained by equating

Using the summation formula

we obtain

Note that in this case, there is no need to impose the condition that p = Alp < 1.

9.15. Derive Eq. (9.30).