Large Deviations Analysis of a Coupled-Processors System

Abstract

In this article, we derive closed-form expressions of the large deviations local rate function in terms of the arrival and service parameters for the zero path in exponential queueing networks corresponding to a coupled-processors system+

Series Expansions for Finite-State Markov Chains

“…The series given in (21) is obviously a power series. Moreover, it is shown in [7] that under v-geometric ergodicity of P u , the term P u ((Q 2P)D P u ) n is equal to dP u /du n . This means that (21) is a Taylor series.…”

Discrete Scattering and Simple and Nonsimple Face-Homogeneous Random Walks

“…The second is the same model with additional input whenever a queue is empty. To be clear, for all models in Hordijk and Popov [7], the conjecture can be shown to hold. However, the derivations are analogous to the one presented here and we prefer to focus on the two versions mentioned.…”

“…Indeed, the local rate function for the path identically 0 is precisely the maximum of the local rates for the path identically 0, conditioned on the almost closed sets containing the origin of space. Section 5 aims to show validity of the conjecture for two versions of the models studied in Hordijk and Popov [7]. The first is the "coupled processors system with switched-off processors whenever a queue is empty."…”

“…Hordijk and Popov [6] derive large deviation bounds for face-homogenous random walks on the quarter plane. As an application of this article, the local rate function is derived in Hordijk and Popov [7] in explicit form for the path identically 0 in exponential queuing networks corresponding to a coupled processors system. Hidden in the analysis of these articles, but essential for the derivation of their result, is the assertion of Conjecture 1.1, applied to the appropriate random walk.…”

Series Expansions for Finite-State Markov Chains

“…Moreover, it is shown in [7] that under v-geometric ergodicity of P u , the term P u ((Q 2P)D P u ) n is equal to dP u /du We apply our theoretical results to the coupled processors model. Consider a system with two finite queues, each with their own server.…”