Question: 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

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 rate

is proportional to the number of people in the system. That is, wherek

is the number of people in the systemand

is a constant.

=1.5

=1.6

1. Determine the steady-state probability1

(Please round to 3 decimal places).

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

3. 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.

4. Determine the steady-state probability1

(Please round to 3 decimal places).

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