Customers arrive randomly to a checkout counter with tickets at an electronics s

Question

Customers arrive randomly to a checkout counter with tickets at an electronics store for the items they want to purchase. Inter-arrival times to registration are as in below table (2^nd column). There are two identical cash register stations that can serve the customers - processing times are also given in the table (3^rd column). The two registers share a common queue - customers at the front of the line go to which ever register opens up first. After paying at the register, the customer proceeds with their stamped tickets to a "pickup" window where they collect the item they just purchased. Processing times for this window are also given in the table (4^th column). There is only one server at the pickup window. Simulate this process through time 20 manually, drawing the WIP plot for the two servers. Calculate the average flow time for all completed customers, the average queue length for each queue, and the average server utilization for each server during the simulation period. Develop a Simio simulation model for the same operation as in Q#1. Assume arrival times, register processing times, and pickup windows times are all exponential with rates 14 arrivals per hour, 10 per hour, and 16 per hour respectively. Run 20 replications of 20 minutes each and collect the same statistics as in Q#1. No need to submit the Simio file.

Explanation / Answer

1) Since Customer No.4 can’t leave the store, we consider Customer No.1 – 3

  Customer No.1’s flow time = 5

Customer No.2’s flow time = 7

Customer No.3’s flow time = 8

Average flow time = (5 + 7 + 8) / 3 = 20/3

Average queue length of registration = 0 / 20 = 0

Average queue length of pick-up = 0 / 20 = 0

Server utilization of registration = (18 / 40) = 0.45

Server utilization of pick-up = 8 / 20 = 0.4

2)

Arrival flow rate = 1 hour / 14 arrivals , avg. interarrival time = 1/rate * 60 (min) = 4.29

Processing rate (registration) = 1 hour / 10 arrivals ,avg. processing time = 1/rate * 60 (min) = 6

Processing rate (pick-up) = 1 hour / 16 arrivals, avg. processing time = 1/rate * 60 (min) = 3.75

From your Pivot Grid tab, AVG. Customer Flowtime = ModelEntity , DefaultEntity ,FlowTime ,TimeInSystem , Average(hours)

AVG. queue length of registration = Server Registration ,InputBuffer , Content , NumberInSystem ,Average.

AVG. queue length of Pick_up = Server ,Pick_up,InputBuffer, Content , NumberInSystem , Average

Server utilization of registration = Server Registration ,Processing ,Content,NumberInSystem ,Average (this number should be divided by

. Server utilization of pick_up = Server , Pick_up ,Processing ,Content , NumberInSystem , Average

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