Hi, please solve the below problem in Excel for MBA 550. Please show how problem

Question

Hi, please solve the below problem in Excel for MBA 550. Please show how problem is solved and formulas used if any. Thanks The ticket booth on the Tech campus is operated by one person, who is selling tickets for the annual Tech versus State football game on Saturrday. The ticket seller can serve an average of 12 customers per hour; on average, 10 customers arrive to purchase tickets each hour (poisson distributed). Determine the average time a ticket buyer must wait and the portion of time of ticket seller is busy.

Explanation / Answer

We assume that average time taken for a ticket seller to serve a customer follows a negative exponential distribution

Let, arrival rate of customer = a = 10 / hour

Service rate of customers = s = 12/ hour

This is a single queuing system of M/M/1 type as per Kendall’s notation

Thus,

Average time a ticket buyer must wait

= a/ s x ( s – a )

= 10 / 12 x ( 12 – 10) hour

= 10/24 hour

=25 minutes

Portion of time a ticket seller is busy = a/s x 100 = 10/12 x 100 = 83.33 %

AVERAGE TIME A BUYER MUST WAIT = 25 MINUTES

PORTION OF TIME A TICKET SELLER IS BUSY = 83.33 %

AVERAGE TIME A BUYER MUST WAIT = 25 MINUTES

PORTION OF TIME A TICKET SELLER IS BUSY = 83.33 %

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