Consider two queueing systems.

The first has one server and no limit on the length of the queue. Customers arrive according to a Poisson process with rate. The service time is exponentially distributed with ratek.kis proportional to the number of people in the system. That is, wherekis the number of people in the systemandis a constant.

k = ku

=1.5

=1.6

Part 1

0.0/10.0 points (graded)

Determine the steady-state probability

1(Please round to 3 decimal places).

Calculate the average number of people in the system (Please round to 3 decimal places).

Calculate their average time in the system.

The second is anM/M/

queue. It has an infinite number of servers and no limit on the number of customers. Customers arrive according to a Poisson process with rate

. The service time of each server is exponentially distributed with rate

Determine the steady-state probability

1(Please round to 3 decimal places).

Calculate the average number of people in the system (Please round to 3 decimal places).

Calculate their average time in the system.