Question

In: Statistics and Probability

Paul is the pharmacist at RiteAid pharmacy where customers arrive on average every 10 minutes (Exponential...

Paul is the pharmacist at RiteAid pharmacy where customers arrive on average every 10 minutes (Exponential distribution). Paul can serve on average 8 customers per hour (Poisson distribution).

Using Queuing theory, calculate

a. the average number of customers waiting in line

b. the average waiting time in line

c. the average waiting time in the system (line + order filling)

d. the system utilization

e. the probability that no customers are in the pharmacy

Expert Solution

arrivals/time period =			λ=	6
served/time period=			μ=	8

a)

average number of customers in queue L_q =

λ²/(μ(μ-λ))=

2.25

b)

average time spend in queue W_q =

λ/(μ(μ-λ))=

0.38

c)

average time spend in system W =

1/(μ-λ)=

0.5

d)

utilization factor = ρ =

λ/μ =

0.75

e)

probability that no customers are in the pharmacy =1-utilization =1-0.75 =0.25

orchestra answered 1 year ago

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