43 research outputs found

    Data-Driven Aircraft Assignment and Stochastic Models for Service Systems

    Get PDF
    This dissertation consists of two parts: data-driven aircraft assignment and stochastic models for service systems. In Part I, we propose a data-driven approach to reduce the delay propagation by optimizing the assignment between incoming and outgoing flights flown by an airline. There are two projects in this part. In the first project, we consider the aircraft assignment problem at a single airport. We propose a data-driven approach to estimate the assignment cost by considering covariates including scheduled arrival time, originating airport and aircraft type of the flights. We conclude that the stochastic assignment derived from this data-driven approach significantly outperforms the actual assignment. In the second project in this part, we extend the previous project to a network of airports by optimizing the assignment between incoming and outgoing flights at each airport in the network. We propose a similar data-driven approach to estimate the assignment costs at each airport, and show that our approach performs better than the benchmark policies. In Part II, we consider the stochastic models for service systems. There are two projects in this part as well. In the first project, we consider a joint staffing and admission control problem under minimal, partial and full information cases. We compare the profit under different information cases over the parameter space in detail. In the second project, we consider the joint admission and service rate control problem for a general reward structure under an unobservable (minimal information case) single server queueing system. We show that when the per unit service cost is less than or equal to a critical value, it is optimal to admit all the customers, otherwise, it is optimal to admit none. We show that this socially optimal policy induces the customers to behave in a socially optimal way with self-regulation.Doctor of Philosoph

    Stability Problems for Stochastic Models: Theory and Applications II

    Get PDF
    Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

    Estimating customer impatience in a service system with unobserved balking

    Full text link
    This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. The main objective is to estimate the customers' patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual queue-length process only. The main complication, and distinguishing feature of our setup, lies in the fact that customers who decide not to join are not observed, but, remarkably, we manage to devise a procedure to estimate the load they would generate. We express our system in terms of a multi-server queue with a Poisson stream of customers, which allows us to evaluate the corresponding likelihood function. Estimating the unknown parameters relying on a maximum likelihood procedure, we prove strong consistency and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. The performance of our approach is further assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized-hyperexponential distributions our method provides a robust estimation framework for any continuous patience-level distribution

    Analysis of Stochastic Models through Multi-Layer Markov Modulated Fluid Flow Processes

    Get PDF
    This thesis is concerned with the multi-layer Markov modulated fluid flow (MMFF) processes and their applications to queueing systems with customer abandonment. For the multi-layer MMFF processes, we review and refine the theory on the joint distribution of the multi-layer MMFF processes and develop an easy to implement algorithm to calculate the joint distribution. Then, we apply the theory to three quite general queueing systems with customer abandonment to show the applicability of this approach and obtain a variety of queueing quantities, such as the customer abandonment probabilities, waiting times distributions and mean queue lengths. The first application is the MAP/PH/K+GI queue. The MMFF approach and the count-server-for-phase (CSFP) method are combined to analyze this multi-server queueing system with a moderately large number of servers. An efficient and easy-to-implement algorithm is developed for the performance evaluation of the MAP/PH/K +GI queueing model. Some of the queueing quantities such as waiting time distributions of the customers abandoning the queue at the head of the waiting queue are difficult to derive through other methods. Then the double-sided queues with marked Markovian arrival processes (MMAP) and abandonment are studied. Multiple types of inputs and finite discrete abandonment times make this queueing model fairly general. Three age processes related to the inputs are defined and then converted into a multi-layer MMFF process. A number of aggregate queueing quantities and quantities for individual types of inputs are obtained by the MMFF approach, which can be useful for practitioners to design stochastic systems such as ride-hailing platforms and organ transplantation systems. The last queueing model is the double-sided queues with batch Markovian arrival processes (BMAP) and abandonment, which arise in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. The abandonment time of a customer depends on the batch size and the position in the queue of the customer. Similar to the previous double-sided queueing model, a multi-layer MMFF process related to some age processes is constructed. A number of queueing quantities including matching rates, fill rates, sojourn times and queue length for both sides of the system are derived. This queueing model is used to analyze a vaccine inventory system as a case study in the thesis. Overall, this thesis studies the joint stationary distribution of the multi-layer MMFF processes and shows the power of this approach in dealing with complex queueing systems. Four algorithms are presented to help practitioners to design stochastic systems and researchers do numerical experiments

    Graduate Catalog of Studies, 2017-2018

    Get PDF

    Analysis of Fluid Queues Using Level Crossing Methods ID: 11563

    Get PDF
    This dissertation is concerned with the application of the level crossing method on fluid queues driven by a background process. The basic assumption of the fluid queue in this thesis is that during the busy period of the driving process, the fluid content fills at net rate r_1, and during the idle period of the driving process, the fluid content, if positive-valued, empties at a rate r_2. Moreover, nonempty fluid content, leaks continuously at a rate r_2. The fluid models considered are: the fluid queue driven by an M/G/1 queue in Chapter 2, the fluid queue driven by an M/G/1 queue with net input and leaking rate depending on fluid level, and type of arrivals in the driving M/G/1 queue, in chapter 3, and the fluid queue driven by an M/G/1 queue with upward fluid jumps in Chapter 4. In addition, a triangle diagram has been introduced in this thesis as a technique to visualize the proportion of time that the content of the fluid queue is increasing or decreasing during nonempty cycles. Finally, we provide several examples on how the probability density function of the fluid level is related to the probability density function of the waiting time of M/G/1 queues with different disciplines
    corecore