  Cloud radio access network (C-RAN) is proposed recently to reduce network
cost, enable cooperative communications, and increase system flexibility
through centralized baseband processing. By pooling multiple virtual base
stations (VBSs) and consolidating their stochastic computational tasks, the
overall computational resource can be reduced, achieving the so-called
statistical multiplexing gain. In this paper, we evaluate the statistical
multiplexing gain of VBS pools using a multi-dimensional Markov model, which
captures the session-level dynamics and the constraints imposed by both radio
and computational resources. Based on this model, we derive a recursive formula
for the blocking probability and also a closed-form approximation for it in
large pools. These formulas are then used to derive the session-level
statistical multiplexing gain of both real-time and delay-tolerant traffic.
Numerical results show that VBS pools can achieve more than 75% of the maximum
pooling gain with 50 VBSs, but further convergence to the upper bound
(large-pool limit) is slow because of the quickly diminishing marginal pooling
gain, which is inversely proportional to a factor between the one-half and
three-fourth power of the pool size. We also find that the pooling gain is more
evident under light traffic load and stringent Quality of Service (QoS)
requirement.
