Question: A workstation has enough storage space to store three jobs in addition to the one being processed. Excess jobs are routed to another workstation, which is used solely to handle this overflow of jobs from the regular workstation. Jobs arrive to the regular workstation according to a Poisson process with a mean of 8 jobs per day. The process time in the regular workstation is exponentially distributed with a mean of 30 min. A workday is comprised of 8 h.

a. Construct the rate diagram describing this queuing process.

b. Develop the balance equations and use them to determine the steady-state probability distribution for finding n customers in the system {Pn, n = 0, 1, 2, 3,...}.

c. Identify a specialized queuing model that describes this queuing process and use the corresponding formulas to determine the steady-state probability distribution for finding n customers in the system {Pn, n = 0, 1, 2, 3, ...}. Compare the results to part (b).

d. Determine the fraction of time that the storage space at the regular work center is adequate to handle the demand.

e. What is the average number of jobs stored at the regular work center (excluding the job being processed) and what is the average waiting time in line before processing?