Operations Research20805 marksNumerical: M/M/1 queuing modelAverage number of customers in system and queue
Customers arrive at a bank having single counter at the rate of 25 customers per hour. Time required to serve a customer has exponential distribution and average number of customers served per hour is 30. Find the average number of customers in queue and in system as well.
Customers arrive at a bank having single counter at the rate of 25 customers per hour. Time required to serve a customer has exponential distribution and average number of customers served per hour is 30. Find the average number of customers in queue and in system as well. [5]
- Arrival rate: $\lambda = 25$ customers/hour - Service rate: $\mu = 30$ customers/hour - Single counter with exponential service time → M/M/1 model $$\rho = \frac{\lambda}{\mu} = \frac{25}{30} = \frac{5}{6} \approx 0.833$$ Since $\rho < 1$, the system is stable. $$L = \frac{\lambda}{\mu - \lambd...