Operators enter the system randomly to request the use of a vehicle.
small so as to minimize costs, but large enough to ensure that the blocking probability is tolerable.
Let Then, the probability of blocking is given by[1] By rearranging terms, one can rewrite the above formula as[2] where
Alternatively, any numerical package that supports the hypergeometric function can be used.
Python with SciPy MATLAB with the Symbolic Math Toolbox In practice, it is often the case that the source arrival rate
In this case, one can substitute the relationship between the source arrival rate and blocking probability into the Engset formula to arrive at the fixed point equation where While the above removes the unknown
from the formula, it introduces an additional point of complexity: we can no longer compute the blocking probability directly, and must use an iterative method instead.
[2] Alternatively, it is possible to use one of bisection or Newton's method, for which an open source implementation is available.