Call blocking probabilities for dynamic and fixed assignment of a single channel in a linear cellular array

We consider the problem of assigning a single channel in a linear cellular array, and compare the call blocking probabilities for dynamic and fixed channel assignment (DCA and FCA). Our principal concern is the derivation of closed-form expressions for these blocking probabilities as a function of the array size and traffic load, assuming a Markov traffic model.

The limiting behavior of the blocking probabilities for DCAFCA relative to increasing array size and extreme traffic loads is also discussed. Moreover, it is shown that there is a unique cross-over traffic load such that DCA has a lower blocking probability than FCA for traffic loads less than the cross-over load, and vice versa.