Answers
arrival rate lambda = 2.9 per hour
service rate mu = 60/10 =6 per hour
utilisation rho =lambda /mu = 2.9/6 = 0.4833
Lq = (lambda)^2/ mu ( mu-lambda)
= 2.9x2.9 /6x3.1 =0.4521
Wq = Lq /lambda = 0.4521/2.9 =0.1559 hours =9.358 minutes
L = lambda /mu-lambda = 2.9/3.1 =0.9354
W = 1/mu-lambda = 1/3.1 =0.3225 hours =19.358 min.
(ii)Waiting time os 9.358 minutes hence the goal of 6 min is not met.
new service rate to meet the target of 6 min ( or 1/10 hour)
0.1 = lambda / mu ( mu-lambda)
0.1 = 2.9 /mu ( mu-2.9)
mu^2-2.9*mu-29=0
mu = [2.9+ (2.9)^2 + 4*29]/2
= 7.026
(iii) If W=8 minutes that is mu = 7.5 per customer, the new values
Wq = lambda / mu ( mu-lambda) = 2.9 /7.5(7.5-2.9) = 0.084 hours = 5.04 min
The service goals will be met.
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