arXiv subjects

Odysseas Kanavetas

Publications and source records attributed to Odysseas Kanavetas.

8 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.

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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.

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arXiv2026

Two-Product Make-to-Stock System: Strategic Joining and Optimal Inventory Levels

This paper analyzes a two-product make-to-stock queueing system where a single production facility serves two customer classes with independent Poisson arrivals. Customers make strategic join-or-balk decisions without observing current inventory levels. The analysis establishes the existence and uniqueness of Nash equilibria in customer joining strategies for various inventory scenarios. Optimal base-stock levels are characterized from both profit-maximizing and welfare-maximizing perspectives, with closed-form expressions for key performance measures.

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arXiv2025

Optimal Data Driven Resource Allocation under Multi-Armed Bandit Observations

This paper introduces the first asymptotically optimal strategy for a multi armed bandit (MAB) model under side constraints. The side constraints model situations in which bandit activations are limited by the availability of certain resources that are replenished at a constant rate. The main result involves the derivation of an asymptotic lower bound for the regret of feasible uniformly fast policies and the construction of policies that achieve this lower bound, under pertinent conditions. Further, we provide the explicit form of such policies for the case in which the unknown distributions are Normal with unknown means and known variances, for the case of Normal distributions with unknown means and unknown variances and for the case of arbitrary discrete distributions with finite support.

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arXiv2020

Ameso Optimization: a Relaxation of Discrete Midpoint Convexity

In this paper we introduce the Ameso optimization problem, a special class of discrete optimization problems. We establish its basic properties and investigate the relation between Ameso optimization and the convex optimization. Further, we design an algorithm to solve a multi-dimensional Ameso problem by solving a sequence of one-dimensional Ameso problems. Finally, we demonstrate how the knapsack problem can be solved using the Ameso optimization framework.

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arXiv2015

Asymptotically Optimal Multi-Armed Bandit Policies under a Cost Constraint

We develop asymptotically optimal policies for the multi armed bandit (MAB), problem, under a cost constraint. This model is applicable in situations where each sample (or activation) from a population (bandit) incurs a known bandit dependent cost. Successive samples from each population are iid random variables with unknown distribution. The objective is to design a feasible policy for deciding from which population to sample from, so as to maximize the expected sum of outcomes of $n$ total samples or equivalently to minimize the regret due to lack on information on sample distributions, For this problem we consider the class of feasible uniformly fast (f-UF) convergent policies, that satisfy the cost constraint sample-path wise. We first establish a necessary asymptotic lower bound for the rate of increase of the regret function of f-UF policies. Then we construct a class of f-UF policies and provide conditions under which they are asymptotically optimal within the class of f-UF policies, achieving this asymptotic lower bound. At the end we provide the explicit form of such policies for the case in which the unknown distributions are Normal with unknown means and known variances.

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arXiv2015

Inventory Policies for Two Products under Poisson Demand: Interaction between Demand Substitution, Limited Storage Capacity and Replenishment Time Uncertainty

We consider a two-product inventory system with independent Poisson demands, limited joint storage capacity and partial demand substitution. Replenishment is performed simultaneously for both products and the replenishment time may be fixed or exponentially distributed. For both cases we develop a Continuous Time Markov Chain model for the inventory levels and derive expressions for the expected profit per unit time. We prove that the profit function is submodular in the order quantities, which allows for a more efficient algorithm to determine the optimal ordering policy. Using computational experiments we assess the effect of substitution and replenishment time uncertainty on the order quantities and the profit as a function of the storage capacity.

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arXiv2012

Adaptive Policies for Sequential Sampling under Incomplete Information and a Cost Constraint

We consider the problem of sequential sampling from a finite number of independent statistical populations to maximize the expected infinite horizon average outcome per period, under a constraint that the expected average sampling cost does not exceed an upper bound. The outcome distributions are not known. We construct a class of consistent adaptive policies, under which the average outcome converges with probability 1 to the true value under complete information for all distributions with finite means. We also compare the rate of convergence for various policies in this class using simulation.

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