Queuing models for cellular networks with generalised Erlang service distributions

Providing seamless handover is one of the major problems in mobile communication environments. Careful dimensioning of the network and the underlying teletraffic analysis plays a major role in determining the various grade of services (GoSs) that can be provided at various network loads for handover users. It has been shown that the channel holding time of a cell, one of the important parameters in any teletraffic analysis, can be accurately modelled by Erlang distributions. This paper focuses on solving queuing systems with generalised Erlang service distributions and exponential arrival distributions. We present the quasi-birth-death (QBD) process, which characterises the queuing models with generalised Erlang service and exponential interarrival distributions. We then use the properties of Erlang distributions and characteristics of channel allocation process of cellular networks to simplify the queues used to model cellular networks. The use of these simplifications provide a significant reduction in computation time required to solve these QBDs.