An analytical model for telephone systems with correlated channel demand

In cellular telephony, systems are designed to operate with a probability of 0.01 or 0.02 that a subscriber will be blocked from attempting a call at any randomly chosen moment. This design constraint, called the blocking probability, is satisfied by supplying a certain number of channels relative to the expected traffic load of the cell at worst case (busy hour) loading. The relationship between the cell´s expected traffic level and the number of channels needed by the system is traditionally characterized in terms of a probability density called the Erlang B distribution. There are, however, a number of telephony systems where this assumption of uncorrelated channel demand may not hold. Since these systems operate under demand conditions not assumed in the derivation of the Erlang B density, a question arises as to whether the Erlang B distribution can accurately assess the number of channels required to meet a specified blocking probability. This paper provides an exact probabilistic analysis of this situation and explores to what extent the results are different from those obtained by using the Erlang B density