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.