Operations Research05 marksNumerical: M/M/1 queuing modelSingle channel queuing model
An airlines organization has one reservation clerk on duty in its local branch at any given time. The clerk handles information regarding passenger reservations and flight timing. Assume that the number of customers arriving during any given period is Poisson distributed with an arrival rate of eigh
An airlines organization has one reservation clerk on duty in its local branch at any given time. The clerk handles information regarding passenger reservations and flight timing. Assume that the number of customers arriving during any given period is Poisson distributed with an arrival rate of eight per hour and that the reservation clerk can service a customer in six minutes on an average, with an exponentially distributed service time. (a) What is the probability that the system is busy? (b) What is the average time a customer spends in the system? [5]
- Arrival rate: $\lambda = 8$ customers/hour (Poisson arrivals) - Mean service time: $6$ minutes per customer (exponential) - Service rate: $\mu = \dfrac{60}{6} = 10$ customers/hour - Single server $\Rightarrow$ M/M/1 model --- The system is busy whenever the server is occupied, i.e. the traffic ...