Question

In a waiting line situation, arrivals occur at a rate of 3 per minute, and the service times average 12 seconds. Assume the Poisson and exponential distributions.

a.	What is λ?   What is μ?
b.	Find average number of units in the system.
c.	Find average time in the waiting line.
d.	Find probability that there is one person waiting.
e.	Find probability an arrival will have to wait.

Answer 1

Answer:-

Given That:-

In a waiting line situation, arrivals occur at a rate of 3 per minute, and the service times average 12 seconds. Assume the Poisson and exponential distributions.

The assumptions in single-server queue theory include: -

Unlimited calling population may enter the queue

Arrivals are random and independent but average number of arrival does not change.

Single waiting line and arriving customers are patient customers who can wait in the queue before they can be served regardless of the length of the line.

Arrivals are served on FIFO basis

Service time of one customer may vary from that of another customer.

Single server and service time is as per the negative exponential probability distribution.

Average service rate is greater than average arrival rate.

a. What is λ? What is μ?

b. Find average number of units in the system.?

or

c. Find average time in the waiting line.?

or

d. Find probability that there is one person waiting.?

e. Find probability an arrival will have to wait.?