arXiv subjects

Floske M. Spieksma

Publications and source records attributed to Floske M. Spieksma.

5 recordsLinked to original sources

arXiv2026

To Control or not to Control

We introduce a model with control vacations instead of standard queueing control systems with permanent control. The researched model is an M/M/1 queue with temporary periods of service rate control with two available service rates. After a control period of exponentially distributed length, a control vacation is initiated during which a fixed service rate $μ$ is used. The start of the next control period needs to be scheduled directly at a certain cost. We will use the Markov Decision Process from Kanavetas et al. arXiv:2605.31573 to find a sufficient condition that ensures that the average expected cost can be reduced w.r.t. the model that only uses the fixed service rate. Under this condition we will use properties of this related process to construct a cost reducing policy. The process with control vacations under specific policies induces a renewal reward process. We use a Tauberian theorem to relate the average expected cost of this renewal reward process to a vanishing discount method and analytically determine a lower bound of the average expected cost reduction. Finally, we study the actual attained average cost reduction for these policies through simulation.

math.OC↗

arXiv2026

The Value of Temporary Control for the M/M/1 Queue

In this article, a one-off option for temporary service rate control for the M/M/1 queue is considered. After taking this option, during a single exponentially distributed period, two service rates are available for use. Once service rate control is lost, the system continues with a fixed service rate $μ$. The objective is to minimise the sum of holding costs and service costs. We approximate the expected total saved cost by taking the one-off option, depending on the starting state or starting distribution. Using the Value Iteration algorithm with $M$-uniform geometric recurrence, we present methods to approximate the expected total saved future cost, as well as the expected total saved discounted future cost. Furthermore, we obtain theoretical results on the structure of optimal policies and strong Blackwell optimality. The paper is concluded by numerically applying the methods to various instances of the model.

math.OC↗

arXiv2015

On the Solution to a Countable System of Equations Arising in Stochastic Processes

In this paper we develop a method to compute the solution to a countable (finite or infinite) set of equations that occurs in many different fields including Markov processes that model queueing systems, birth-and-death processes and inventory systems. The method provides a fast and exact computation of the inverse of the matrix of the coefficients of the system. In contrast, alternative inverse techniques perform much slower and work only for finite size matrices. Furthermore, we provide a procedure to construct the eigenvalues of the matrix under consideration.

math.OC↗

arXiv2015

Level product form QSF processes and an analysis of queues with Coxian inter-arrival distribution

In this paper we study a class of Quasi-Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the ${\it Cox(k)}/M^Y/1$-queue, that can be modelled as a QSF process on a two-dimensional state space. In addition we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queue, their mean sojourn time and the variance as a function of $k$ for fixed mean arrival rate.

math.PR↗

arXiv2015

A Comparative Analysis of the Successive Lumping and the Lattice Path Counting Algorithms

This article provides a comparison of the successive lumping (SL) methodology with the popular lattice path counting algorithm in obtaining rate matrices for queueing models, satisfying the quasi birth and death structure. The two methodologies are compared both in terms of applicability requirements and numerical complexity by analyzing their performance for the same classical queueing models. The main findings are: i) When both methods are applicable SL based algorithms outperform the lattice path counting algorithm (LPCA). ii) There are important classes of problems (e.g., models with (level) non-homogenous rates or with finite state spaces) for which the SL methodology is applicable and for which the LPCA cannot be used. iii) Another main advantage of successive lumping algorithms over LPCAs is that the former includes a method to compute the steady state distribution using this rate matrix.

math.PR↗