This programming assignment is an extension of the "Servicing Customers" problem solving session. To make sure you help Bob pass on to his boss the correct recommendation on how many express lanes to open, you will simulate the problem first to verify your theoretical solution. You decide to approximate the Poisson customer arrival process using short-interval Bernoulli trials process. 1) First you simulate the customer arrivals for one hour using only one express lane. You treat each one-second interval as a Bernoulli trial. Assign it to be a one, if there is a customer arrives during that interval, zero if no customer arrives. What is the probability that there is a customer arriving during a one-second interval? (Hint: what is the arrival occurrence rate per second for the customer arrival Poisson process?) 2) You count the total number of customers arrive during a one-minute interval. 3) You count the total number of minutes out of a one-hour period that have two or fewer customers arrive. Does this number give your probability close to your calculation in the problem-solving session? 4) Next you simulate the customer arrivals for one hour using the number of express lanes you recommended to open. Assign the arrivals in step 1 with equal probabilities to the number of express lanes you recommended. 5) You count the total number of customers arrive at each lane during a one-minute interval. 6) You count the total number of minutes out of a one-hour period that all lanes have two or fewer customers arrive. Does this number give you probability close to your calculation in the problemsolving session? Hint: If you use MATLAB, you can generate an array of customer arrivals in one hour using the technique in Quiz 1.7 from Programming Assignment 1..

1. This programming assignment is an extension of the "Servicing Customers" problem solving
session. To make sure you help Bob pass on to his boss the correct recommendation on how
many express lanes to open, you will simulate the problem first to verify your theoretical solution.
You decide to approximate the Poisson customer arrival process using short-interval Bernoulli
trials process. 1) First you simulate the customer arrivals for one hour using only one express
lane. You treat each one-second interval as a Bernoulli trial. Assign it to be a one, if there is a
customer arrives during that interval, zero if no customer arrives. What is the probability that there
is a customer arriving during a one-second interval? (Hint: what is the arrival occurrence rate per
second for the customer arrival Poisson process?) 2) You count the total number of customers
arrive during a one-minute interval. 3) You count the total number of minutes out of a one-hour
period that have two or fewer customers arrive. Does this number give your probability close to
your calculation in the problem-solving session? 4) Next you simulate the customer arrivals for one
hour using the number of express lanes you recommended to open. Assign the arrivals in step 1
with equal probabilities to the number of express lanes you recommended. 5) You count the total
number of customers arrive at each lane during a one-minute interval. 6) You count the total
number of minutes out of a one-hour period that all lanes have two or fewer customers arrive.
Does this number give you probability close to your calculation in the problemsolving session?
Hint: If you use MATLAB, you can generate an array of customer arrivals in one hour using the
technique in Quiz 1.7 from Programming Assignment 1.