Operations Research20825 marksNumerical: Queuing theory M/M/1Average waiting time calculations
In a certain bank, customers arrive in a Poisson fashion with an average time of 20 minutes between arrivals of the customers. The service time of the bank cashier follows the exponential distribution with mean time 15 minutes. Under the assumptions of single channel queuing model, find (a) The aver
In a certain bank, customers arrive in a Poisson fashion with an average time of 20 minutes between arrivals of the customers. The service time of the bank cashier follows the exponential distribution with mean time 15 minutes. Under the assumptions of single channel queuing model, find (a) The average time spent by a customer in the queue.(a);The;average;time;spent;by;a;customer;in;the;queue.(a)Theaveragetimespentbyacustomerinthequeue.(b) The probability that there are 3 customers in the bank.(b);The;probability;that;there;are;3;customers;in;the;bank.(b)Theprobabilitythatthereare3customersinthebank.[5]
- Mean inter-arrival time = 20 minutes - Mean service time = 15 minutes - Single channel model (M/M/1) Arrival rate: $$\lambda = \frac{1}{20} = 0.05 \text{ customers/min}$$ Service rate: $$\mu = \frac{1}{15} \approx 0.06667 \text{ customers/min}$$ Traffic intensity: $$\rho = \frac{\lambda}{\mu} =...