We consider again the job shop
considered earlier when all arrival and service processes were
Poisson. In this case we specify the stations as non-Markovian
and use the non-Markovian Queuing formulas. The only difference
between this case and the one considered earlier has the coefficients
of service times reduced to 0.5.
A difficulty arises when considering this kind of system.
The arrivals to each station may come from several other stations.
Although we compute the departure COV for each station, there
is no simple way to compute the COV of an arrival process consisting
of several streams coming from different stations. Notice that
the program does not compute the interarrival COV's in row
39 as it did for the serial case.
Although we don't have a general approximation for a complete
analysis, this option may be useful in several ways. By leaving
all the COV's of arrival times as 1, the analysis yields something
of an upper bound for the queues of the network. With the arrival
COV at 1, the arrivals appear to be random at a station. Although
it is conceivable that a situation might occur that results
in a COV greater than 1, we suspect that this would not be
likely. Putting the arrival COV's at 0, should provide lower
bound estimates of the queue statistics. Thus the two extremes
should provide upper and lower bound analyses of the times
and numbers for a system.
Another use for this structure is to set all variation (all
COV's) to zero. Many networks have complex flows between stations.
Simply solving for the arrival rates at each station is not
trivial. The equations provided by the add-in accomplish this
result with no additional effort.