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 = 2 per hour. All jobs have the same service rate = 1.5 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 queuing system?

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

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

(d) What is the average number of jobs in the system?

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 1 = 2 per hour. All jobs have the same service rate u = 1.5 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