A grocery store has only one checkout counter. Customers arrive at this checkout

Question

A grocery store has only one checkout counter. Customers arrive at this checkout at

         random from 1 to 8 minutes apart each possible value of inter-arrival time has the same       

         probability of occurrence as given below. Analyze the system by simulating the arrival         

        of 20 customers using the random numbers 913, 727, 15, 948, 309, 922, 753, 235, 302,      

         109, 93, 607, 738, 359, 888, 106, 212, 493 and 535. Also, calculate the average time    

         between arrival

Distribution of time between arrivals                 

Time Arrivals (Minutes)

1

2

3

4

5

6

7

8

Probability  

0.125

0.125

0.125

0.125

0.125

0.125

0.125

0.125

Explanation / Answer

Analyze the system by simulating the arrival of 20 customers using the random numbers is

the average time between arrival is

Time Arrivals (Minutes)    Probability    x.p
1   0.125   0.125
2   0.125   0.25
3   0.125   0.375
4   0.125   0.5
5   0.125   0.625
6   0.125   0.75
7   0.125   0.875
8   0.125   1
   Average    4.5

Time Arrivals (Minutes) Probability   Cumulative Random number 1 0.125 0.125 1-125 2 0.125 0.25 126-250 3 0.125 0.375 251-375 4 0.125 0.5 376-500 5 0.125 0.625 501-625 6 0.125 0.75 626-750 7 0.125 0.875 751-875 8 0.125 1 876-1000

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