Page 298 - Schaum's Outlines - Probability, Random Variables And Random Processes

CHAP. 91 QUEUEING THEORY

Equation (9.21) can be rewritten as

Then the average number of customers in the system is

" - ' (spy'
n = 0 n = 0
Using the summation formulas,

and Eq. (9.20), we obtain

Next, using Eqs. (9.21) and (9.50), the average number of customers in the queue is

9.13. A corporate computing center has two computers of the same capacity. The jobs arriving at the
center are of two types, internal jobs and external jobs. These jobs have Poisson arrival times
with rates 18 and 15 per hour, respectively. The service time for a job is an exponential r.v. with
mean 3 minutes.

(a) Find the average waiting time per job when one computer is used exclusively for internal
jobs and the other for external jobs.
(b) Find the average waiting time per job when two computers handle both types of jobs.
(a) When the computers are used separately, we treat them as two M/M/1 queueing systems. Let W,, and
W,, be the average waiting time per internal job and per external job, respectively. For internal jobs,