Poisson process 1 10 At a small store the customers arrive

Poisson process (

1. (10%) At a small store, the customers arrive at an average rate of 1.2 per minute in the peak hour and at the rate of 0.4 per minute in the off hours.

Assuming 3 clerks, compute the probability of a waiting line

(a)in the peak hour

(b)in the off hours

(c)Suppose the store management hires one extra temporary clerk in the peak hour, compute the probability of a waiting line.

(d)What do you observe or conclude from the results above? Do you think the store management needs to hire more than one temporary clerk in the peak hour to have the same or lower probability of waiting line as the off hours?

Solution

a) since in peak hours rate is 1.2 per minute

that is 72 per hour.

3 clerks are there so each clerk has to handle 24 person in an hour

which means each clerk has got 24/60 = 0.4 person per minute..

so there will no probability of waiting line.

b) as rate of person is low so from above probability will be 0.

c)again 0 from a)

d) i think there is only 1 clerk required to handle the shop.