Discrete-time queues with zero-regenerative arrivals: moments and examples

In this paper we investigate a single-server discrete-time queueing system with single-slot service times. The stationary ergodic arrival process this queueing system is subject to, satisfies a regeneration property when there are no arrivals during a slot. Expressions for the mean and the variance of the queue content in steady state are obtained for this broad class which includes among others autoregressive arrival processes and M/G/infinity-input or train arrival processes. To illustrate our results, we then consider a number of numerical examples

Queues with Galton-Watson-type arrivals

This paper presents the analysis of a discrete-time single server queueing system with a multi-type Galton-Watson arrival process with migration. It is shown that such a process allows to capture intricate correlation in the arrival process while the corcesponding queueing analysis yields closed-form expressions for various moments of queue content and packet delay

Scheduling analysis with martingales

This paper proposes a new characterization of queueing systems by bounding a suitable exponential transform with a martingale. The constructed martingale is quite versatile in the sense that it captures queueing systems with Markovian and autoregressive arrivals in a unified manner; the second class is particularly relevant due to Wold’s decomposition of stationary processes. Moreover, using the framework of stochastic network calculus, the martingales allow for a simple handling of typical queueing operations: (1) flows’ multiplexing translates into multiplying the corresponding martingales, and (2) scheduling translates into time-shifting the martingales. The emerging calculus is applied to estimate the per-flow delay for FIFO, SP, and EDF scheduling. Unlike state-of-the-art results, our bounds capture a fundamental exponential leading constant in the number of multiplexed flows, and additionally are numerically tight

Business process simulation and process quality assessment of Czech online bookshop

Accurate estimation of times between arrivals is a key aspect of process simulations and thus efficient decision making. Times between arrivals typically exhibit strong autocorrelation structure which is commonly ignored in the queueing theory. In order to capture the time dependence accurately, we utilize a Generalized Autoregressive Score (GAS) model based on the generalized gamma distribution. Once the process of arrivals is estimated, a process assessment can be performed using process simulations. The results from an empirical study of an online bookshop in Prague, Czech Republic pointed out insufficient resources allocated for the pre-processing and the final stage

On random coefficient INAR(1) processes

The random coefficient integer-valued autoregressive process was recently introduced by Zheng, Basawa, and Datta. In this thesis we study the asymptotic behavior of this model (in particular, weak limits of extreme values and the growth rate of partial sums) in the case where the additive term in the underlying random linear recursion belongs to the domain of attraction of a stable law

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