Serving customers from a single line.

A. Consider a system with two servers in parallel who serve customers from a single line. Customers are served in a First-Come First-Served fashion. If both servers are available, customers always go to server 1 first.
Given the inter-arrival times and service time for the following five customers, complete the tables below.
Customer # Inter-arrival time (min) Service Time (min)
1 – 5.82
2 3.35 5.26
3 1.65 3.02
4 3.52 5.51
5 2.27 2.05

Entity Time of arrival (arrival time) (minutes) Wait time (minutes) Service time (minutes) Time of Departure (minutes) Total time in the system (minutes)
1 0.00
2
3
4
5

Clock System State Future Event List Comments Cumulative Statistics
Servers 1 and 2 (B1 and B2 respectively) Busy Time
LQ(t) LS(t) B1 B2
0.00


B. From the hand simulation you just did, calculate the following metrics:

  1. Proportion of server busy time for each teller (also known as utilization)
  2. Average time a customer spends in the system
  3. Average waiting time for a customer
  4. Average wait time of those who wait
  5. Probability a customer has to wait

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