Operations Research20815 marksNumerical: Queuing theory M/M/1Average number of customers in system and queue
A bank operates a single-channel queuing system with customers arriving at a rate of 6 per hour and each customer being served at an average rate of 8 per hour. Calculate (a) the average number of customers in the system and (b) the average waiting time. λ=6 per hour\lambda = 6\;per\;hourλ=6perhourμ
A bank operates a single-channel queuing system with customers arriving at a rate of 6 per hour and each customer being served at an average rate of 8 per hour. Calculate (a) the average number of customers in the system and (b) the average waiting time. λ=6 per hour\lambda = 6;per;hourλ=6perhourμ=8 per hour\mu = 8;per;hourμ=8perhour[5]
- Arrival rate: $\lambda = 6$ customers/hour - Service rate: $\mu = 8$ customers/hour - Model: M/M/1 (single server, Poisson arrivals, exponential service) - Utilization: $\rho = \lambda/\mu = 6/8 = 0.75 < 1$ (stable) $$Ls = \frac{\lambda}{\mu - \lambda} = \frac{6}{8 - 6} = \frac{6}{2} = 3 \text{...