General Network - Job Shop Revisited
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