Strong approximations for time-varying infinite-server queues with non-renewal arrival and service processes

In real stochastic systems, the arrival and service processes may not be renewal processes. For example, in many telecommunication systems such as internet traffic where data traffic is bursty, the sequence of inter-arrival times and service times are often correlated and dependent. One way to model this non-renewal behavior is to use Markovian Arrival Processes (MAPs) and Markovian Service Processes (MSPs). MAPs and MSPs allow for inter-arrival and service times to be dependent, while providing the analytical tractability of simple Markov processes. To this end, we prove fluid and diffusion limits for MAP(t)/MSPt/ queues by constructing a new Poisson process representation for the queueing dynamics and leveraging strong approximations for Poisson processes. As a result, the fluid and diffusion limit theorems illuminate how the dependence structure of the arrival or service processes can affect the sample path behavior of the queueing process. Finally, our Poisson representation for MAPs and MSPs is useful for simulation purposes and may be of independent interest.111sciescopu

Stability Problems for Stochastic Models: Theory and Applications II

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

A Markovian approach to the mathematical control of NPD projects

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A Metamodel-Based Monte Carlo Simulation Approach for Responsive Production Planning of Manufacturing Systems

Production planning is concerned with finding a release plan of jobs into the manufacturing system so that its actual outputs over time match the customer demand with the least cost. The biggest challenge of production planning lies in the difficulty to quantify the performance of a release plan, which is the necessary basis for plan optimization. Triggered by an input plan over a time horizon, the system outputs, work in process (WIP) and job departures, are non-stationary bivariate time series that interact with customer demand (another time series), resulting in the fulfillment/non-fulfillment of demand and in the holding cost of both WIP and finished-goods inventory. The relationship between a release plan and its resulting performance metrics (typically, mean/variance of the total cost and the demand fulfill rate is far from being adequately quantified in the existing literature of production planning. In this dissertation, a metamodel-based Monte Carlo simulation (MCS) method is developed to accurately capture the dynamic and stochastic behavior of a manufacturing system, and to allow for real-time evaluation of a release plan in terms of its performance metrics. This evaluation capability is embedded in a multi-objective optimization framework to enable the quick search of good (or optimum) release plans. The developed method has been applied to a scaled-down semiconductor fabrication system to demonstrate the quality of the metamodel-based MCS evaluation and the plan optimization results

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included