Analysis of a trunk reservation policy in the framework of fog computing

TL;DR

This paper models a fog computing system with two data centers, introducing a trunk reservation policy to optimize request handling and analyzing its impact on blocking probabilities through complex stochastic processes.

Contribution

It presents a novel analysis of a trunk reservation policy in fog computing using advanced random walk models with non-standard boundary conditions.

Findings

The trunk reservation policy reduces blocking probabilities.

The model provides explicit computation methods for stationary distributions.

Numerical results show performance gains from the policy.

Abstract

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.