Scheduling services in a queuing system with impatience and setup costs

International audienceWe consider a single server queue in discrete time, in which customers must be served before some limit sojourn time of geometrical distribution. A customer who is not served before this limit leaves the sys- tem. The fact of serving customers, holding them in queue or losing them induce costs. The purpose is to decide when to serve the customers so as to minimize these costs. We use a Markov Decision Process with infinite horizon and discounted criterion. We establish the structural properties of the stochastic dynamic programming operator, and we deduce that the optimal policy is of threshold type, and we compute the threshold explicitly

Performance analysis of a discrete-time queueing system with customer deadlines

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the "deadline" of the customer. Deadlines of consecutive customers are modelled as independent and geometrically distributed random variables. The arrival process of new customers, furthermore, is assumed to be general and independent, while service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for quantities as the mean system content, the mean customer delay, and the deadline-expiration ratio. These formulas, however, contain infinite sums and infinite products, which implies that truncations are required to actually compute numerical values. Therefore, we also derive some easy-to-evaluate approximate results for the main performance measures. These approximate results are quite accurate, as we show in some numerical examples. Possible applications of this type of queueing model are numerous: the (variable) deadlines could model, for instance, the fact that customers may become impatient and leave the queue unserved if they have to wait too long in line, but they could also reflect the fact that the service of a customer is not useful anymore if it cannot be delivered soon enough, etc

Contrôle optimal de l’admission en service dans une file d’attente avec impatience et coûts de mise en route

We consider a single server queue in continuous time, in which customers must beserved before some limit sojourn time of exponential distribution. A customer who is not servedbefore this limit leaves the system: it is impatient. The fact of serving customers and the fact oflosing them due to impatience induce costs. The fact of holding them in the queue also induces aconstant cost per customer and per unit time. The purpose is to decide when to serve the customersso as to minimize costs. We use a Markov Decision Process with infinite horizon and discountedcost. Since the standard uniformization approach is not applicable here, we introduce a familyof approximated uniformizable models, for which we establish the structural properties of thestochastic dynamic programming operator, and we deduce that the optimal policy is of thresholdtype. The threshold is computed explicitly. We then pass to the limit to show that this thresholdpolicy is also optimal in the original model. A particular care is given to the completeness of theproof. We also illustrate the difficulties involved in the proof with numerical examples.Nous considérons un modèle d’une file d’attente à un serveur en temps continu, danslaquelle les clients doivent être servis avant une durée de séjour finie aléatoire, de distribution expo-nentielle. Un client qui n’est pas servi avant cette limite quitte le système: il est impatient. Le fait deservir les clients et le fait de perdre des clients par impatience induisent des coûts. Le fait de les garderdans la file induit également un coût constant par client et par unité de temps. Il s’agit de décider defaçon optimale quand servir les clients. Nous utilisons un processus de décision Markovien à horizoninfini et à coûts actualisés. La méthode standard d’uniformisation ne s’appliquant pas à cette situation,nous introduisons une famille de modèles approchés uniformisables pour lesquels nous établissons lespropriétés structurelles de l’opérateur de programmation dynamique stochastique, et nous déduisonsque la politique optimale est à seuil. Le seuil est calculé explicitement. Nous passons ensuite à lalimite pour montrer que cette politique à seuil est également optimale dans le modèle initial. Une at-tention particulière est apportée à la complétude de la preuve. Nous illustrons également les difficultésrencontrées à l’aide d’exemples numériques

Optimal control of admission in service in a queue with impatience and setup costs

International audienceWe consider a single server queue in continuous time, in which customers must be served before some limit sojourn time of exponential distribution. Customers who are not served before this limit leave the system: they are impatient. The fact of serving customers and the fact of losing them due to impatience induce costs. The fact of holding them in the queue also induces a constant cost per customer and per unit time. The purpose is to decide whether to serve customers or to keep the server idle, so as to minimize costs. We use a Markov Decision Process with infinite horizon and discounted cost. Since the standard uniformization approach is not applicable here, we introduce a family of approximated uniformizable models, for which we establish the structural properties of the stochastic dynamic programming operator, and we deduce that the optimal policy is of threshold type. The threshold is computed explicitly. We then pass to the limit to show that this threshold policy is also optimal in the original model and we characterize the optimal policy. A particular care is given to the completeness of the proof. We also illustrate the difficulties involved in the proof with numerical examples

Port pricing : principles, structure and models

Price level and price transparency are input to shippers’ choice of supply chain and transport mode. In this paper, we analyse current port pricing structures in the light of the pricing literature and consider opportunities for improvement. We present a detailed overview of pricing criteria, who sets prices and who ultimately foots the bill for port-of-call charges, cargo-handling fees and congestion charges. Current port pricing practice is based on a rather linear structure and fails to incorporate modern pricing tools such as price differentiation or revenue management. Consequently, ports apply neither profit maximising pricing nor pricing designed to exploit available capacity more efficiently

Performance Analysis for Heterogeneous Cloud Servers Using Queueing Theory

© 2020 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] In this article, we consider the problem of selecting appropriate heterogeneous servers in cloud centers for stochastically arriving requests in order to obtain an optimal tradeoff between the expected response time and power consumption. Heterogeneous servers with uncertain setup times are far more common than homogenous ones. The heterogeneity of servers and stochastic requests pose great challenges in relation to the tradeoff between the two conflicting objectives. Using the Markov decision process, the expected response time of requests is analyzed in terms of a given number of available candidate servers. For a given system availability, a binary search method is presented to determine the number of servers selected from the candidates. An iterative improvement method is proposed to determine the best servers to select for the considered objectives. After evaluating the performance of the system parameters on the performance of algorithms using the analysis of variance, the proposed algorithm and three of its variants are compared over a large number of random and real instances. The results indicate that proposed algorithm is much more effective than the other four algorithms within acceptable CPU times.This work is supported by the National Key Research and Development Program of China Grant No. 2017YFB1400801, the National Natural Science Foundation of China Grant Nos. 61572127, 61872077, 61832004 and Collaborative Innovation Center of Wireless Communications Technology. Rub~en Ruiz is partly supported by the Spanish Ministry of Science, Innovation, and Universities, under the project "OPTEP-Port Terminal Operations Optimization" (No. RTI2018-094940-BI00) financed with FEDER funds.Wang, S.; Li, X.; Ruiz García, R. (2020). Performance Analysis for Heterogeneous Cloud Servers Using Queueing Theory. IEEE Transactions on Computers. 69(4):563-576. https://doi.org/10.1109/TC.2019.2956505S56357669

Qualitative Strategy for Inbound Call Center Outsourcing

An analysis of the various challenges of the call center industry, together with the challenges of outsourcing, revealed a need for developing a strategy that acts as a guide for organizations that are willing to outsource their call center operations. This research therefore develops a strategy for this purpose. The research first provides mitigation strategies for the challenges of outsourcing and the challenges of the call center industry, followed by a strategy for the outsourcing of call center services. Telephone call centers are an integral part of today‘s business world, serving as a primary channel for customer contact for organizations in many industries. Globalization, the advancements in the telecommunication and technology industries, and the availability of cost effective work forces around the world are compelling organizations to outsource their functions (call center services) to reap the benefits that come with outsourcing. Organizations outsource functions, especially a function that is not their core competence, for a multitude of reasons. These reasons may include cost savings, quality enhancement/improvement, reduced time to market, tax benefits, and risk management. Outsourcing also comes with its share of issues. A few examples of the challenges involved in outsourcing include cultural differences, knowledge transfer to suppliers while protecting intellectual property (IP), knowledge retention, language barriers, ethics, norms of behavior, distance and time zones, infrastructure, privacy and security, skill set/quality, objectivity, geopolitical climate, labor backlash, communication, end-user resistance, and governance. There are also many challenges associated with the call center industry, such as, but not limited to, deploying the right number of staff members with the right skills to the right schedules in order to meet an uncertain and time-varying demand of service, forecasting traffic, acquiring capacity, deploying resources, and managing service delivery. Therefore, despite the advancements in telecommunications and information technology, the challenges faced by client organizations that outsource their inbound call center services abound. While choosing outsourcing/offshoring as their strategy, an organization can avoid many of the disadvantages that arise due these risks/issues by adapting a proactive and careful approach such as the strategy developed in this research