A manufacturing cell has four identical machines where jobs can be run on any of the

machines. Jobs arrive according to a Poisson process with a rate of $\backslash$lambda $=4$ per hour. All jobs

have the same service rate $\backslash$mu $=3$ per hour, and the distribution of service times is assumed to

be exponential. No jobs may be awaiting work in the cell, so at most $4$ jobs may be present

in the cell at a given time.

$($a$)$ Give the Kendall notation that describes this queueing system.

$($b$)$ What is the probability that all servers will be full when a new job arrives?

$($c$)$ What percentage of time will the cell be completely idle?

$($d$)$ What is the average number of jobs in the system and its throughput?