  We analyze in this paper a system composed of two data centers with limited
capacity in terms of servers. When one request for a single server is blocked
at the first data center, this request is forwarded to the second one. To
protect the single server requests originally assigned to the second data
center, a trunk reservation policy is introduced (i.e., a redirected request is
accepted only if there is a sufficient number of free servers at the second
data center). After rescaling the system by assuming that there are many
servers in both data centers and high request arrival rates, we are led to
analyze a random walk in the quarter plane, which has the particularity of
having non constant reflecting conditions on one boundary of the quarter plane.
Contrary to usual reflected random walks, to compute the stationary
distribution of the presented random walk, we have to determine three unknown
functions, one polynomial and two infinite generating functions. We show that
the coefficients of the polynomial are solutions to a linear system. After
solving this linear system, we are able to compute the two other unknown
functions and the blocking probabilities at both data centers. Numerical
experiments are eventually performed to estimate the gain achieved by the trunk
reservation policy.
