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 Probability
(Minutes)   
1 0.125
2 0.125   
3 0.125
4 0.125
5 0.125
6 0.125   
7 0.125
8 0.125

Explanation / Answer

Simulated Average Time between Arrivals = 4 minutes

Probability distribution function Inter-Arrival Time Probability Cumulative Probability 0 1 0.125 0.125 2 0.125 0.250 3 0.125 0.375 4 0.125 0.500 5 0.125 0.625 6 0.125 0.750 7 0.125 0.875 8 0.125 1.000 Simulation Cycle Random Number Inter-Arrival Time 1 913 8 2 727 6 3 15 1 4 948 8 5 309 3 6 922 8 7 753 7 8 235 2 9 302 3 10 109 1 11 93 1 12 607 5 13 738 6 14 359 3 15 888 8 16 106 1 17 212 2 18 493 4 19 535 5 20 1 1

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