Simulation and Modeling Lab Assignment
Assignment 1-
Question 1: The following is the number of incoming calls (each hour for 80 successive hours) to a call center setup for serving customers of a certain internet service provider. Use Stat::Fit to analyze the data and fit an appropriate discrete distribution. What are the parameters for this distribution?
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12
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12
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11
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13
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12
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16
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11
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10
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9
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13
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14
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10
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14
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9
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13
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12
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12
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12
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11
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13
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12
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16
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11
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10
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10
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8
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17
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12
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10
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7
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13
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11
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11
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11
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12
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8
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15
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14
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15
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13
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9
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13
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14
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10
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14
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9
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13
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12
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12
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12
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11
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13
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12
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16
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11
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10
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10
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8
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17
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12
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10
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7
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13
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11
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11
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10
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13
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10
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11
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12
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14
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15
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10
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8
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17
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12
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10
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7
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13
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11
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Question 2: Customers visit the neighborhood barber shop fantastic Dan for a haircut. Among the customers are 30 percent children, 50 percent women and 20 percent men. The customer inter-arrival time is triangularly distributed with a minimum, mode and maximum of 8, 11 and 14 minutes, respectively. The hair cut time (in minutes) depends on the type of customer as shown in the Table below.
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Uniform distribution
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Haircut Mean
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Time (min) Half-width
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Children
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8
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2
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Women
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12
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3
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Men
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10
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2
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The initial signing and greetings in take Normal (2,0.2) minutes, and the transaction of money at the end of the haircut takes Normal (3.0.3) minutes. Run the simulation for 2000 hrs. (250 - 8hr days)
a) About how many of each type of customer does Dan process per day?
b) What is the average number of customers of each type waiting to get a haircut? What is the maximum?
c) What is the average time spent by a customer of each type in the salon? What is the maximum?
You will need to create attributes and variables. This model can be created 2 ways, results will differ.
Question 3: Two types of jobs (regular and high priority) arrive at two identical assembly machines. Regular jobs arrive according to an exponential distribution with a mean inter-arrival time of 10 minutes. High priority jobs arrive according to an exponential distribution with a mean inter-arrival time of 20 minutes. One of two machines is selected by turn. Processing either entity is uniformly U(8, 2) minutes. Upon completion, jobs are sent to a third machine where they wait for final assembly, which requires 5 minutes normally distributed with a standard deviation of 2 minutes. Jobs are selected from the waiting line for assembly based on the estimated assembly time (jobs with shorter assembly times having a high priority over jobs with longer assembly times). Completed jobs are promptly shipped to the customer.
The final assembly machine is unreliable. It fails at intervals that may be described by an exponential distribution with a mean of 60 minutes. Repair time is uniformly distributed over the range 10 to 20 minutes. The high priority jobs have higher priority over regular jobs in terms of processing on the three assembly machines. The processing times are identical for both types of jobs. Simulate for 2,000 hours and determine:
a) Utilization of the three machines.
b) Average time in the shop for both types (average and max values).
c) Average number of jobs (regular and high priority) processed per hour.
Assignment 2 -
Question 1: An average of 100 customers per hour arrive to the Picayune Mutual Bank. It takes a teller an average of two minutes to serve a customer. Inter-arrival and service times are exponentially distributed. The bank currently has four tellers working. Bank manager Rick Gold wants to compare the following two systems with regard to the average time customers spend in the bank.
(Arrival rate: e(?)hr (Use hr unit) what is the value in the brackets)? It should be used for both models.
System 1
A separate queue is provided for each teller. Assume that customers choose the shortest queue when entering the banks, and that customer cannot jockey between queues (jump to another queue).
System 2
A single queue is provided for customers to wait for the first available teller.
Assume that there is no move time within the queues. Run 15 replications of an eight hour simulation to complete the following:
a) For each system, record the 90% confidence interval using a 0.10 level of significance for the average time customers spend in the bank. (Your data is from the statistics tab. Look at average time in system).
b) Estimate the number of replications needed to reduce the half width of each confidence interval by 25 percent. Run the additional, replications for each system and compute new confidence intervals using 0.10 level of significance. (Use equation show in the lab book page 170).
c) Based on the results from part 'b', would you recommend one system over the other? Explain.
Assignment 3 -
Question: Increase the capacity of the Pickup_Q location in the Spuds-n-More3 model from three to six. Call this Model Spuds-n-More4. Using the Common Random Numbers (CRN) technique with ProModel Streams 1,2,3 and 4 assigned as in Figure L9.3, see if spuds-n-More4 processes more customers per day on average than does Spuds-n-More3. Use a paired-t confidence interval with a 0.02 significance level. Run each model simulation model for 25 replications.