Determine the steady-state probability

Reference no: EM132464648

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

μk = ku

λ=1.5

μ=1.6

a. Determine the steady-state probability π1 (Please round to 3 decimal places).

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

c. Calculate their average time in the system.

The second is an M/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 λ . The service time of each server is exponentially distributed with rate μ

Determine the steady-state probability π1 (Please round to 3 decimal places).

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

e. Calculate their average time in the system.

Reference no: EM132464648

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