Performance of a trunk reservation policy in distributed data centres

In this paper, we analyse a system composed of two data centres with limited capacity in terms of computing (namely virtual cores). When one request for a single core is blocked at the first data centre, this request is forwarded to the second one. To protect the requests originally assigned to the second data centre, a trunk reservation policy is introduced (i.e., a redirected request is accepted only if the number of free cores at the second data centre is greater than a given threshold). After rescaling the system when there are many cores in both data centres and high request arrival rates, we are led to analyse a random walk in the quarter plane, which has the particularity of having nonconstant reflecting conditions on one boundary of the quarter plane. Computing the stationary distribution of the present random walk requires the determination of 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 numerically solving this linear system, we are able to compute the two other unknown functions and the blocking probabilities at both data centres. Numerical experiments are eventually performed to estimate the gain achieved by the trunk reservation policy. (C) 2018 Elsevier B.V. All rights reserved.