Question

A super market has a single cashier. During the

peak hours, customers arrive at a rate of

20 customers per hour. The average number of

customers that can be processed by the cashier is

24 per hour. Calculate

(a) Probability that cashier is idle.

(b) Average number of customers queueing

system.​

Answer 1

Answer:

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Answer 2

Given:

Arrival Rate = 20 customer/hr

Processed customers = 24/hr

To Find:

(a) Probability that cashier is idle.

(b) Average number of customers queueing

Solution:

Arrival Rate = (λ) = 20 customers / hour

Service Rate (μ) = 24 customers / hour

a. Probability that the cashier is idle

P0 = 1 - λ/μ

Substituting the values -

= 1 - 20/24

= 24-20/24

= 4/24

= 1/6

= 0.17

b. Average number of customers in the queuing system:

Ls = λ/μ - λ

Substituting the values -

= 20/24 - 20

= 20/4

= 5

Answer: The probability is 0.17 and the customers that are  queued are 5.