Asked by Jamie Walker on Jun 18, 2024
Verified
A waiting-line problem that cannot be modelled by standard distributions has been simulated. The table below shows the result of a Monte Carlo simulation. (Assume that the simulation began at 8:00 a.m. and there is only one server.
Customer Number Arrival Time Service Time Service Ends 18:0628:0828:07108:1838:12108:2848:24118:3958:3058:44\begin{array} { | c | c | c | c | } \hline \text { Customer Number } & \text { Arrival Time } & \text { Service Time } & \text { Service Ends } \\\hline 1 & 8 : 06 & 2 & 8 : 08 \\\hline 2 & 8 : 07 & 10 & 8 : 18 \\\hline 3 & 8 : 12 & 10 & 8 : 28 \\\hline 4 & 8 : 24 & 11 & 8 : 39 \\\hline 5 & 8 : 30 & 5 & 8 : 44 \\\hline\end{array} Customer Number 12345 Arrival Time 8:068:078:128:248:30 Service Time 21010115 Service Ends 8:088:188:288:398:44 a. What is the average waiting time in line?
b. What is the average time in the system?
Monte Carlo Simulation
A computational algorithm that uses repeated random sampling to obtain numerical results, often used in physical and mathematical problem-solving.
Average Waiting Time
calculates the average duration customers or items wait before being serviced, often used in queue management to assess performance.
- Understand how to compose probability distributions, cumulative distributions, and random number intervals.
- Comprehend the idea of time compression within simulation contexts and its pragmatic effects.
Verified Answer
AH
Alana HoblinJun 23, 2024
Final Answer :
(a) Waiting time is 0 + 1 + 6 + 4 + 9 = 20. Average waiting time is 20/5 = 4.0 min; (b) Total time in system is 2 + 11 + 16 + 15 + 14 = 58. Average time in system is 58/5 = 11.6 min.
Learning Objectives
- Understand how to compose probability distributions, cumulative distributions, and random number intervals.
- Comprehend the idea of time compression within simulation contexts and its pragmatic effects.
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