$2\mathrm{.}25$ Give some examples of queuing systems in transportation systems.

In what basis are different types of queues distinguished?

Nhy do queues form?

It a given airport, aircraft arrive at an average rate of $8$ aircraft $\frac{?}{hr}$ folowing a Poisson distribution. The average landing time for an aircraft is minutes. However, this time varies from one aircraft to another. This ariation can be assumed to be exponentially distributed. Determine

a$)$ The average number of aircraft awaiting clearance to land;

b$)$ The average time an aircraft spends in the system;

z$)$ The probability that there will be more than five aircraft awaiting clearance to land.