Question

 A small auto parts store has a single counter with one employee. Customers arrive at the counter at the rate of 10 per hour according to a Poisson distribution. The employee can handle 20 customers per hour and service times are exponentially distributed. Calculate

 (A) The probability that a customer finds an empty counter in the auto parts store (no customers waiting or being served) (B) The average number of customers waiting in the que at the auto parts store (i.e., waiting, not yet being served)

 (C) The average total number of customers in the auto parts store system (i.e., waiting plus being served)

 (D) The average total time that customers spend in the auto parts store system (i.e., waiting and being served)

 (E) The average time it takes for customers to wait in line at the auto parts store system (before being served)

 (F) If there are three other auto parts stores in town, is one employee adequate for this store?

Answer 1

arrivals/time period =			λ=	10
served/time period=			μ=	20

a)

probability of n=0 people wating in system =

(1-λ/μ)*(λ/μ)n      =

0.5

b)

average number of customers in queue Lq =

λ2/(μ(μ-λ))=

0.50

c)

average number of customers in system L =

λ/(μ-λ)=

1

d)

average time spend in system W                   =

1/(μ-λ)=

0.1 Hours

e)

average time spend in queue Wq                   =

λ/(μ(μ-λ))=

0.05 Hours

f)

Yes as servce rate is greater then arrival rate