On the hand-off arrival process in cellular communications

Hand-offs in cellular communication systems cause interactions among cells that can be modeled using multi-dimensional birth-death process approaches and the concept of system state. However, exact numerical calculation of traffic performance characteristics is hindered by unmanageably large system state spaces even for systems of modest size. Previous analytical models get around the difficulty by isolating a cell of interest and invoking a Poisson process assumption for hand-off arrivals to the cell. The current paper seeks to explore the interactions in more detail. Two additional approximate analytical models are developed for this purpose. Each of these is more complicated than the simple Poisson process model, but is analytically tractable-at least for small system sizes. One model isolates a cluster of cells (rather than just the cell of interest) from the system and invokes a Poisson process assumption for cells on the cluster periphery. Performance is calculated for the central cell. The second model also isolates a cluster of cells surrounding the cell of interest, but uses an equivalent two-state Markov modulated Poisson process (MMPP) to characterize hand-off arrival processes to the cell of interest from each of the neighboring cells. Poisson hand-off arrivals to cells on the cluster periphery are assumed. This approach has fewer states than the cluster approach. It was found that all are in close agreement with the original “single isolated cell, Poisson hand-off arrival model”, which requires the least states