We consider large cellular networks. The traffic entering the network
is assumed to be correlated in both space and time. The space
dependency captures the possible correlation between the arrivals to
different nodes in the network, while the time dependency captures the
time correlation between arrivals to each node. We model such traffic
with a MarkovModulated Poisson Process(MMPP).
It is shown that even in the single node environment, the problem is
not mathematically tractable. A model with an infinite number of
circuits is used to approximate the finite model. A novel recursive
methodology is introduced in finding the joint moments of the number
of busy circuits in different cells in the network leading to accurate
determination of blocking probability. A simple mixedPoisson
distribution is introduced as an accurate approximation of the
distribution of the number ofbusy circuits.
We show that for certain cases, in the system with an infinite number
of circuits in each cell, there is no effect of mobility on the
performance of the system. Our numerical results indicate that the
traffic burstiness has a major impact on the system performance. The
mixedPoisson approximation is found to be a very good fit to the
exact finite model. The performance of this approximation using few
moments is affected by traffic burstiness and average load. We find
that in a reasonable range of traffic burstiness, the mixedPoisson
distribution provides a close approximation.
