Algorithmic Solutions to Two-Dimensional Birth---Death Processes with Application to Capacity Planning

Abstract

Capacity planning of modern telecommunication systems using the Erlang-B or Erlang-C models is hampered by the inability of these models to capture critical system characteristics. Two-dimensional birth---death models offer the opportunity to remedy this. The steady state behavior of two-dimensional birth---death processes is found by numerically solving a linear matrix equation whose special structure is exploited to substantially speed its solution. Two detailed applications drawn from telecommunications capacity planning are presented.