A functional approximation for the M/G/1/N queue

Abstract

This paper presents a new approach to the functional approximation of the M/G/1/N built on a Taylor series approach. Specifically, we establish an approximative expression for the remainder term of the Taylor series that can be computed in an efficient manner. As we will illustrate with numerical examples, the resulting Taylor series approximation turns out to be of practical value.

Development of computational algorithm for multiserver queue with renewal input and synchronous vacation

“…Remark 5 Note that the approach presented in this paper is different from those presented in [1,10]. In fact, the result put forward in Theorem 1 is different from the one in [1].…”

“…In fact, the result put forward in Theorem 1 is different from the one in [1]. However, in the latter result, the higher-order derivatives of the stationary distribution π θ with respect to θ are established in terms of the deviation matrix D θ ; and those introduced in Theorem 1 are exhibited in terms of the fundamental matrix Z θ , where we have proceeded by following a different sketch of proof that is provided in Theorem 1 in [1].…”

“…However, in [1], to compute the deviation matrix the authors have used the formula (39), i.e., D θ = (I − P θ + Π θ ) −1 −Π θ , which is more expensive in terms of the algorithmic' complexity. Besides, our approach is easy to implement and it overcomes restrictions imposed by some methods like those established in [10], which requires the geometric ergodicity of the Markov chain with respect to a particular type of norm corresponding to the Lyapunov function of the system.…”

Taylor series expansion approach for epistemic uncertainty propagation in queueing‐inventory models

“…For estimating the remainder term , we will follow the same line of arguments in Abbas et al Then, the derivative D κ + 1 π ξ can be estimated by the following | m |th order Taylor approximation: …”

Statistical Taylor series expansion: An approach for epistemic uncertainty propagation in Markov reliability models

“…Specifically, by using this new approach, we establish an approximative expression for the components of the stationary distribution of the Markov chain describing the state of the considered model. These components are represented as polynomial functions of the input parameters, which are given under the form (1). More specifically, we provide a recursive form of the higher derivatives of the stationary distribution in terms of the fundamental matrix of the associated continuous-time Markov chain [20].…”