The Economics worksheet is automatically constructed
when a rate matrix is defined. It allows the specification of
values associated with residing in a state and moving to a new
state. The State Cost Rate is the cost expended per unit
time residing in the state. The Transition Cost Matrix
holds the cost expended whenever a transition is made, independent
of time. Assuming each customer experiences a cost proportional
to the time spent in the foyer, we select a cost per minute
equal to the number in the system. The time dimension of the
cost rates are the same as the dimension used for rates in the
rate matrix, minutes for the example.
The Combined Cost Rate is a computed quantity, adding
the state cost rate to the transition costs divided by the expected
time to make a transition. The Combined Cost per Step
is the expected cost for each step of the embedded Markov Chain.
We provide a cell to hold the Economic Measure. Here it is
cost, but it can also be profit or any measure implied by the
entries in the data arrays. Another holds the discount rate
for problems in which the net present value is a relevant measure.
Present value computations use continuous compounding. Again
the discount rate has the same time dimension as the transition
The buttons on the worksheet recalculate the worksheet or return
the focus to the Matrix worksheet. The latter button
is included on all worksheets created by the add-in.