After the OK button is pressed on the state number dialog,
the add-in constructs the worksheet that holds the rate matrix.
We have entered names for each state in the State Name array,
where S0 refers to the state when the foyer is empty, S1 is
the state when one person is being served, and so on. Transition
rates are entered in the rate matrix according the problem definition.
For example, the mean time between arrivals is 0.5 minutes,
so using minutes as the time interval, we determine an arrival
rate of 2 per minute. When there are n persons using
or waiting for the ATM (n < 5), an arrival adds one
more to that number, so we place the number 2 as the rate of
transition from state n to state n + 1 (when n
is not equal to 5). We assume that arrivals balk when the foyer
is full, so the row for state 5 does not show the arrival rate.
Service transitions are handled similarly. With a single ATM,
the rate of departures is 2.5 per minute, so we use this rate
for transitions from state n to state n -1 (when
n is not equal to zero). When the foyer is empty, no
departures can occur so this rate does not appear in row 0.
All other entries in the rate matrix are 0, because no other
single event causes a transition in the ATM example.
The figure shows the Matrix worksheet
for the ATM example. The buttons at the top control actions
within this sheet. The Change button brings forth the
state definition dialog to allow the number of states to be
changed. If the number is changed, rows and columns are added
or deleted according to whether the new number is more or less
than the original. Data already entered into the matrix is
not affected unless rows and columns are deleted.
The Calculate button initiates calculations on the
worksheet. The Analyze initiates a program to identify
the classes of states for the model. States are identified
as being in one class or another, and as being transient or
The buttons along the left margin control the analyses performed
on the rate matrix. Some are discussed on these pages. Whenever
one of these buttons is pressed, a new worksheet is created
to perform the specified analysis.