Project #11121 - simulation

Please use word equation tool or excel drawing chart/graph tool if necessary. Problems must be complete and easy to understand.

 

Problem

During the dinner hour, the distribution of the inter-arrival time of customers at a restaurant is estimated to be as shown below.  The mode of payment and the service times of the cash and credit card customers are shown in the following tables. Complete the tables and simulate the system for 20 customer arrivals and determine the average time a cash and credit card customer must wait in line before paying the cashier.

 

Use Column A of the given random number table to determine the customer inter-arrival time. For the arrival time, please start at 0 seconds, and increments in seconds from the results you get from decoding of the random numbers. As an example, the first random number is 6320, which equates to 60 seconds of inter-arrival time. So, your first customer arrival time is 60 seconds. For your second customer, the random number is 4630, which also equates to 60 seconds of inter-arrival time. As a result, your second customer arrival time will be 120 seconds, and so on. Please keep your results in seconds for all customers.

 

Use Column B to determine whether the customer pays with cash or credit, and Column C to determine the service time.

 

Inter-arrival time

Inter-arrival Time

Probability

Cumulative Probability

Random Number Interval

30 seconds

0.45

 

 

60 seconds

0.25

 

 

90 seconds

0.15

 

 

120 seconds

0.10

 

 

150 seconds

0.05

 

 

 

Mode of Payment

Payment Mode

Probability

Cumulative Probability

Random Number Interval

Cash

0.6

 

 

Credit Card

0.4

 

 

 

Cash Service Time

Service Time

Probability

Cumulative Probability

Random Number Interval

20 seconds

0.35

 

 

40 seconds

0.30

 

 

60 seconds

0.25

 

 

80 seconds

0.10

 

 


 

 

 

Credit Card Service Time

Service Time

Probability

Cumulative Probability

Random Number Interval

30 seconds

0.20

 

 

60 seconds

0.45

 

 

90 seconds

0.25

 

 

120 seconds

0.10

 

 

 

 

Random Numbers

(A)

(B)

(C)

6320

1094

1995

4630

7371

7971

8657

2809

3554

0030

5148

6300

5624

9115

5495

6728

1469

5165

5925

6480

9339

2829

2447

6997

7939

7031

1443

6476

8442

3574

3319

7387

0150

8134

1788

0933

1712

4891

7082

6317

1149

5025

6605

8822

4081

2734

9451

4100

0432

2990

7190

3441

8314

6822

0726

7176

5053

6969

2766

8284


 Complete the table below to show the results of the simulation.

 

Customer

Random Number

Arrival Time

Random Number

Mode of Payment

Random Number

Service Time

Service Time

Waiting Time

 

 

 

 

 

 

 

Begins

Ends

Cash

Credit

1

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

4

 

 

 

 

 

 

 

 

 

 

5

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

 

7

 

 

 

 

 

 

 

 

 

 

8

 

 

 

 

 

 

 

 

 

 

9

 

 

 

 

 

 

 

 

 

 

10

 

 

 

 

 

 

 

 

 

 

11

 

 

 

 

 

 

 

 

 

 

12

 

 

 

 

 

 

 

 

 

 

13

 

 

 

 

 

 

 

 

 

 

14

 

 

 

 

 

 

 

 

 

 

15

 

 

 

 

 

 

 

 

 

 

16

 

 

 

 

 

 

 

 

 

 

17

 

 

 

 

 

 

 

 

 

 

18

 

 

 

 

 

 

 

 

 

 

19

 

 

 

 

 

 

 

 

 

 

20

 

 

 

 

 

 

 

 

 

 

                     

Average Waiting Time (Cash)=

 

Average Waiting Time (Credit)=

 

                       

 

 

Subject Mathematics
Due By (Pacific Time) 08/25/2013 03:00 pm
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