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Customers arrive at a bank teller machine at the rate one every three minutes. Each customer spends an average of two minutes at the teller machine. The arrival rate and the service rate are approximated by Poisson and negative exponential distributions respectively.

Determine the following:
f – probability of three customers in the system
g – probability of two or more customers in the system.

Explanation / Answer

Arrival Rate=L=1/3 min=0.33 customers/min Sevice rate=m=1/2 customers/min=0.5 customers/min Probability of no unit in system=1-L/m=1-0.33/0.5=0.34 Probability of 3 customers in system=(0.33/0.5)^3*0.34=0.098 Probability= ((L/m)^n)*Po Probability of 2 or more customers Customers Probability 0 (0.33/0.5)^0*0.34= 0.34 1 (0.33/0.5)^1*0.34= 0.2244 hence probability of 2 or more customers=1-0.34-0.224=0.436

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