9. Raymond and Rose were working with exponents.
1 answer:
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Answer:
Step-by-step explanation:
Arrival rate of guests: R = 15 per hour.
Number of concierge services: c =1, mean = 3 min, Standard deviation = 3 min , so
Rp = c/Tp = 1/3 per min or 20 per hour.
U= R/Rp = 15/20= 0.75
Average service time: Tp = 3 min
Standard deviation of service time: Sp = 3 min
Coefficient of variation for service time: Cp = Sp /Tp = 3/3 =1
Average inter-arrival time: Ta = 1/R = 1/15 hr = 4 min
Ca=0.5
Considering the formula, for M/G/1 queue which is attached to this solution.
B ) Putting the values in the formula , we get I = 2.875 – Number of customers in the waiting line
How long a customer wait in the concierge line?
RT=I, rate of arrival x time = Number of customers in the waiting line
15xT=2.875, solving for T
T=2.875*60/15= 11.5 minutes
c) the number of service = C= 2
Number of concierge services: c =1, mean = 3 min, Standard deviation = 3 min, so
Rp = c/Tp = 2/3 per min or 40 per hour.
U= R/Rp = 15/40= 0.375
Average service time: Tp = 3 min
Standard deviation of service time: Sp = 3 min
Coefficient of variation for service time: Cp = Sp /Tp = 3/3 =1
Average inter-arrival time: Ta = 1/R = 1/15 hr = 4 min
Ca=0.5
Considering the formula, for M/G/2 queue ,
Substituting values in above equation,
I = 0.769 , Number of customers in the waiting line. Also,
RT=I, rate of arrival x time = Number of customers in the waiting line
15xT=0.769, solving for T
T=0.769*60/15= 3.07 minutes , so the wait time reduces , as evident
