Service capacity pooling in M/G/1 service systems

International audienceWe study the cost-sharing problem among independent service providers in a service capacity pooling system. The effective improvement of such pooling system can be achieved by reducing the resource idleness in case of congestion. In this paper, we model both the service provider and the cooperative coalition as a single server queue. We attempt to answer the following questions: (i) which coalition strategy should be used; and (ii) which allocation rule should be selected in order to maintain the stability of the coalition? In particular, we consider the service pooling with a fixed service capacity for M/G/1 service systems. The benefit of the pooling system is due to the shortened waiting queue in the overall system. We develop the corresponding cooperative game with transferable utility, and analyze the core allocations. Although it is difficult to express a core allocation explicitly for the game, we prove the non-emptiness of the core. We give a reasonable expression of Equal Profit Method to distribute the cost for our game, and investigate a number of cost allocation rules under three typical situations to evaluate the gain of the service pooling strategy for each service provider. The numerical results show that the cost allocation rule proposed gives a reasonable cost-sharing result considering the contribution of each participant

Service Systems with Finite and Heterogeneous Customer Arrivals

International audienceW e consider service systems with a finite number of customer arrivals, where customer interarrival times and service times are both stochastic and heterogeneous. Applications of such systems are numerous and include systems where arrivals are driven by events or service completions in serial processes as well as systems where servers are subject to learning or fatigue. Using an embedded Markov chain approach, we characterize the waiting time distribution for each customer, from which we obtain various performance measures of interest, including the expected waiting time of a specific customer, the expected waiting time of an arbitrary customer, and the expected completion time of all customers. We carry out extensive numerical experiments to examine the effect of heterogeneity in interarrival and service times. In particular, we examine cases where interarrival and service times increase with each subsequent arrival or service completion, decrease, increase and then decrease, or decrease and then increase. We derive several managerial insights and discuss implications for settings where such features can be induced. We validate the numerical results using a fluid approximation that yields closed-form expressions

Call centers with a postponed callback offer

We study a call center model with a postponed callback option. A customer at the head of the queue whose elapsed waiting time achieves a given threshold receives a voice message mentioning the option to be called back later. This callback option differs from the traditional ones found in the literature where the callback offer is given at customer’s arrival. We approximate this system by a two-dimensional Markov chain, with one dimension being a unit of a discretization of the waiting time. We next show that this approximation model converges to the exact one. This allows us to obtain explicitly the performance measures without abandonment and to compute them numerically otherwise. From the performance analysis, we derive a series of practical insights and recommendations for a clever use of the callback offer. In particular, we show that this time-based offer outperforms traditional ones when considering the waiting time of inbound calls

Air Traffic Flow Management Under Emission Policies: Analyzing the Impact of Sustainable Aviation Fuel and Different Carbon Prices

As part of the global efforts to make aviation activities more environmentally friendly, the worldwide goal is to achieve a 50% reduction in the 2005 emissions by 2050. In this context, aviation emissions represent a critical challenge to aviation activities, especially with the increasing travel demand up to the beginning of the COVID-19 crisis, starting in 2020. One of the potential drivers that would help the aviation industry reduce its emissions is the use of sustainable aviation fuel (SAF). In this study, we analyzed the impact of SAF from an air traffic flow management (ATFM) perspective, considering delay and re-routing costs. We developed an optimization model that considers, in addition to the traditional ATFM costs, fuel costs and carbon dioxide emissions. We investigated the impact of accounting for these two new aspects, that is, fuel costs and emissions, on ATFM performance, and we compared SAF with conventional fuel. The analysis of a real case study revealed that, in addition to delay and re-routing costs, fuel cost should be included in the ATFM model so that the resulting solution becomes economically and environmentally realistic for airlines. The increase in the fuel cost and network delays when using SAF requires setting an appropriate carbon price under an emission policy, such as the carbon offsetting and reduction scheme for international flights policy, to make SAF more attractive. Furthermore, flexible re-routing programs for flights operated using SAF make it advantageous from an ATFM perspective

Central authority controlled air traffic flow management: An optimization approach.

Despite various planning efforts, airspace capacity can sometimes be exceeded, typically due to disruptive events. Air traffic flow management (ATFM) is the process of managing flights in this situation. In this paper, we present an ATFM model that accounts for different rerouting options (path rerouting and diversion) and pre-existing en-route flights. The model proposes having a central authority to control all decisions, which is then compared with current practice. We also consider inter-flight and inter-airline fairness measures in the network. We use an exact approach to solve small-to-medium-sized instances, and we propose a modified fix-and-relax heuristic to solve large-sized instances. Allowing a central authority to control all decisions increases network efficiency compared to the case where the ATFM authority and airlines control decisions independently. Our experiments show that including different rerouting options in ATFM can help reduce delays by up to 8% and cancellations by up to 23%. Moreover, ground delay cost has much more impact on network decisions than air delay cost, and network decisions are insensitive to changes in diversion cost. Furthermore, the analysis of the trade-off between total network cost and overtaking cost shows that adding costs for overtaking can significantly improve fairness at only a small increase in total system cost. A balanced total cost per flight among airlines can be achieved at a small increase in the network cost (0.2 to 3.0%) when imposing airline fairness. In conclusion, the comprehensiveness of the model makes it useful for analyzing a wide range of alternatives for efficient ATF

Modèles Stochastiques pour l'Aide à la Décision dans les Centres d'appels

In the past few years, call centers have been introduced with great success by many service-oriented companies such as banks and insurance companies. They become the main point of contact with the customer, and an integral part of the majority of corporations. The large-scale emergence of call centers has created a fertile source of management issues. In this thesis, we focus on various operations management issues of call centers. The objective of our work is to derive, both qualitative and quantitative, results for practical management. In the first part of the thesis, we investigate the impact of team-based organizations in call centers management. We develop queueing models that show that the benefits of the team based organization in providing more efficient answers to customers very often outweigh its drawback coming from the loss of pooling. Next, we consider a two-class call center and develop real-time scheduling policies that determine the rule of assignment of new arrivals to the waiting lines. We focus on service levels criteria related to the fraction of abandoning customers and the variance of queueing delays. Finally, we propose a call center model in which we provide information about delays to customers, and we quantify its effect upon performance.In the second part of the thesis, we tackled the quantitative analysis of stochastic processes and queueing models. First, we derive several closed-form expressions of the moments of first passage times in general birth-death processes, and we point out their applications. Second, we investigate some monotonicity results for the probability of being served in markovian queueing systems with impatient customers.Depuis quelques années, les centres d'appels enregistrent une forte croissance dans le monde. Les entreprises s'orientent de plus en plus vers ce choix qui leur offre une relation privilégiée avec leurs clients. Ainsi, ils disposent d'un moyen convivial et peu coûteux pour fidéliser leurs clients tout en essayant d'en acquérir de nouveaux. Le sujet de cette thèse porte sur le développement et l'analyse de modèles stochastiques pour l'aide à la décision dans les centres d'appels. Dans la première partie, nous considérons un centre d'appels où tous les agents sont groupés dans un même pool et les clients sont traités indifféremment par un des agents. Nous étudions les bénéfices de la migration depuis cette configuration vers un centre d'appels où les clients sont divisés en classes (appelées portefeuilles de clients). Chaque portefeuille de clients est servi par un pool de conseillers qui lui est exclusivement dédié. Ensuite, nous considérons un centre d'appels avec deux classes de clients impatients. Nous développons des politiques dynamiques pour l'affectation des clients (selon leurs types) aux différentes files d'attente. L'objectif étant lié aux qualités de service différentiées exprimées en terme du pourcentage des clients perdus, ainsi qu'en terme de la variance du temps d'attente. Enfin, nous étudions un centre d'appels qui annonce le délai d'attente à chaque nouveau client. Nous montrons les avantages de l'annonce sur les performances du centre d'appels.Dans la deuxième partie, nous considérons un processus de naissance et de mort de forme générale. Nous calculons ensuite les moments de plusieurs variables aléatoires liées aux temps de premiers passages (ordinaires et conditionnels). Ensuite, nous montrons un résultat de concavité dans une file d'attente avec capacité limitée et avec une seule classe de clients impatients. Nous démontrons que la probabilité d'entrer en service est strictement croissante et concave en fonction de la taille de la file d'attente

Analysis of a last come first served queueing system with customer abandonment

International audienceMotivated by manufacturing and service applications, we consider a single class multi-server queueing system working under the LCFS discipline of service. After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time she will abandon and be lost. For the GI/GI/s+M queue, we present some structural results to describe the relation between various performance measures and the scheduling policies. We next consider the LCFS M/M/s+M queue and focus on deriving new results for the virtual waiting time and the sojourn time in the queue (either before service or before abandonment). We provide an exact analysis using Laplace-Stieltjes transforms. We also conduct some numerical analysis to illustrate the impact of customer impatience and the discipline of service on performance