The manager of a small post office is concerned that the growing township is ove

Question

The manager of a small post office is concerned that the growing township is overloading the one-window service being offered. For the post office studies, the data about customer interarrival times are given in the following table. Service time are uniformly distributed between 1 and 3.5 minutes. Time Between Arrivals (min.s) Prob. 1 0.10 2 0.35 3 0.30 4 0.20 5 0.05 Simulate 200 arrivals to estimate the following statistics in your spreadsheet. (Hand in only the values and formulas print-outs). a) Number of customers waited for the service b) Probability of waiting for the service c) Average customer waiting time d) Maximum service time e) Average time a customer spent in the system f) Number of customers who waited more than 2 minutes g) Probability of customers waited more than 2 minutes

Explanation / Answer

There are two things to be generated (simulated)

1. Intertime arrival between 2 customers, this will also give the time of arrival. As

Second customer time of arrival = first customer time of arrival + intertime arrival of second customer

and similarly third customer TOA = second TOA+ intertime arrival of third customer

This can be done by Random Number Generation (Data Analysis add-in ) in excel and specifiying the probabiliyt distribution as discrete and the distribution range to the table

2. Service time which is uniformly distributed between 1 and 3.5 minutes.

this can be generated by the formula rand()*(3.5-1)+1

Generate 200 inter arrival time and service time

Find the start time for every new customer, if the previous customer is not completed then the new customer's start time is previous customer's completed time, else it is the new customer's arrival time.

Find the completed time for every new customer. It is the (start time +service time)

Find if the customer waited or not, if the previous customer's completed time > new customer's start time then the new customer waited else the queue was free.

Find the waiting time. If new customer's arrival time is lesser than the previous customer's completed time, then the waiting time is (previous customer's completed time-new customer's arrival time ) else it is 0.

A snapshot of the formulae is given in the excel

Once all these columns are generated it is easy to answer the questions.

a)

Number of customers waited for the service = count of waited in customer waited column (j column) = 120

b)

probability of waiting for service = 120/200 = 0.6

c)

average customer waiting time = average of waiting time column(k column) = 0.89

d)

maximum service time = maximum of g column = 3.48

e)

average time a customer spent in the system = average of (waiting time + service time) = 3.16

f)

number of customers who waited more than 2 minutes = 34

g)

probability of customer waiting for mroe than 2 mins = 34/200 = 0.17

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