If service time is exponentially distributed with a mean of 20 per hour, determine

a) Percentage utilization of capacity

b) Probability that there are at least 3 customers in the queue

c) average time spent in the system

d) Average number of customers waiting in the line

e) Probability that there are 5 customers in the system?

Mumbai University > Mechanical Engineering > Sem 7 > Operations Research

Marks: 10 Marks

λ=16 per hour μ=20 per hour

a. Percentage utilization of capacity

ρ=λ/μ=16/20

ρ=0.8

b. Probability that there are at least 3 customers in queue :

p(≥n)=(λ/μ)^n=(16/20)^3

p(≥n)=0.512

c. Average time spent in the system:

W_s=1/(μ-λ)=1/(20-16)

W_s=0.25 hour

d. Average number of customers waiting in the line:

W_q=λ/μ 〖.W〗_s=16/20.0.25

W_q=0.2 hour

e) Probability that there are 5 customer in system:

P_n = (λ/μ)^n (1-λ/μ) = (16/20)^5 (1-16/20) = 0.0655