Question

7. In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds.

a. What is λ?

b. What is μ?

c. Find probability of no units in the system.

d. Find average number of units in the system.

e. Find average time in the waiting line.

f. Find average time in the system.

g. Find probability that there is one person waiting.

h. Find probability an arrival will have to wait.

Answer 1

A) Given  

Arrival rate = 2 per min

service tima = 18 seconds

a)

= 2

b)

= 3.333

c)

The probability of no units in the system is calculated below:

P0=1−λ/μ

=1−2/3.33 =0.399

d)

The average number of units (Ls)(Ls)in the system is:

Ls=λ/(μ−λ)

=2/(3.33-2) = 1.503

e)

The average time ((Wq) in the waiting line will be:

Wq=λ /μ(μ−λ)

=2 / 3.33(3.33−2))

=2/3.33(1.33) =2/4.429

=0.4516

So, the average time in the waiting line is 0.4516.

g)

The probability that there is one person waiting in the system is as follows:

Pn=(1−λμ)×(λμ)n

P1=(1−λ / μ)×(λ / μ)

=(1−0.600)×(0.600) = 0.399*0.600

=0.2396

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