Consider a seven-node, open single-server Jackson network, where only nodes 2 and 4 get input from the outside (at rate 5/min). Nodes 1 and 2 have service rates of 85, nodes 3 and 4 have rates of 120, node 5 has a rate of 70, and nodes 6 and 7 have rates of 20 (all in units per minute). The routing matrix is given by

Find the average system size and mean line delay at each node.
4.11. Boobtube Boychicks, a TV repair facility that services many of the region's retail electronics stores' TV repair maintenance policies, receives sets to repair according to a Poisson process at an average rate of 9/h. All incoming sets are first looked at by a triage specialist, who determines whether the sets go to the facility's general repair station, require special attention and go to the expert repair station, or cannot be fixed locally and must be returned to the manufacturer and are sent to shipping. About 17% of all sets are sent directly to shipping to be returned to manufacturers. Of the 83% that are kept, 57% go to general repair, while 43% are sent to the experts. All repaired sets are sent to shipping; however, 5% of the sets received at the general repair station are sent back, unrepaired, to triage for redetermination.
(Note: It is allowed for triage to send this set back again to general repair).
Because of the varied nature of the problems and varying sizes of the sets, the exponential distribution is found to be an adequate representation for triage, repair (both general and expert), and shipping times. There is a single person at triage, taking a mean time of 6 min per set. There are three general repairpeople, each taking, on average, 35 min per set (including the ones they can't fix and send back to triage). Barry, Barney, Billy, and Bennie Boychick (quadruplets as it turns out) are the four experts manning the expert repair station and take, on average, 65 min to repair a set (they never fail to "fix 'em"). There are two shipping clerks, each of whom take an average time of 12.5 min to package the sets. Betty Boychick, Barry's wife and CEO of the company (who has an MS degree in OR from a major state university and teaches part-time at a local university) decides to ask her class to find the average number of sets at each node, the average time spent at each node, and the average time a set spends after it enters the receiving-triage station until it is packed and ready for delivery.

18 0 0 0 0 0 0 1313 96 0 0 96 96 9696 LLLS LS 4697 1105118 0 0 0 9797 16 1313 OO-16 0