SOLVER 8 Problems: Queuing Problems Bank of Ohio in Zanesville has a single driv

Question

SOLVER 8 Problems: Queuing Problems Bank of Ohio in Zanesville has a single drive-in teller window. Customers arrive at the window about every 10 minutes on average with an exponential distribution or the hourly arrival rate is = 6. It take an average of five minutes (exponentially distributed) to complete each customer order or the hourly service rate is = 12. You are asked following tasks: Determine • Expected number of customers in the system, including those being served. • Expected number of customers in the queue, excluding those being served. • Expected waiting time in the system, including service time, for an individual customer. • Expected waiting time in the queue, excluding service time, for an individual customer. • Utilization factor • The probability that waiting time in the system exceeds 0.25 hours (15 minutes) • The probability that waiting time in the queue exceeds 0.25 hours (15 minutes) • The probability that the system has 5 customers in the system PLEASE MAKE SURE YOU DO IT ON EXCEL AND USE SOLVER... THANK YOU. IF YOU CAN MAKE AN ATACHTMENT FOR ME TO DOWNLOAD THAT WOULD BE GREAT!

Explanation / Answer

here = 6 and = 12

Utilization = / = 0.5

Expected number of customers in the system = /(-) = 1

Expected number of customers in the queue =  ^2/(*(-)) = 0.5

Expected waiting time in the system = 1/(-) = 0.1667

Expected waiting time in the queue = /(*(-)) = 0.0833

The probability that waiting time in the system exceeds 0.25 hours (15 minutes) = 0.2231

The probability that waiting time in the queue exceeds 0.25 hours (15 minutes) = 0.1116

The probability that the system has 5 customers in the system = 0.0156

Arrival Rate 6 service rate 12 average utilization 0.5 average number of customer in line 0.5 average number of customers in system 1 average waiting time in the line 0.083333333 average time in the system 0.166666667

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