Analysis of finite-buffer state-dependent bulk queues

<p>In this paper, we consider a general state-dependent finite-buffer bulk queue in which the rates and batch sizes of arrivals and services are allowed to depend on the number of customers in queue and service batch sizes. Such queueing systems have rich applications in manufacturing, service operations, computer and telecommunication systems. Interesting examples include batch oven processes in the aircraft and semiconductor industry; serving of passengers by elevators, shuttle buses, and ferries; and congestion control mechanisms to regulate transmission rates in packet-switched communication networks. We develop a unifying method to study the performance of this general class of finite-buffer state-dependent bulk queueing systems. For this purpose, we use semi-regenerative analysis to develop a numerically stable method for calculating the limiting probability distribution of the queue length process. Based on the limiting probabilities, we present various performance measures for evaluating admission control and batch service policies, such as the loss probability for an arriving group of customers and for individual customers within a group. We demonstrate our method by means of numerical examples.</p>

Load dependent lead time modelling: a robust optimization approach

Due to copyright restrictions, the access to the full text of this article is only available via subscription.Although production planning models using nonlinear CFs have shown promising results for semiconductor wafer fabrication facilities, the lack of an effective methodology for estimating the CFs is a significant obstacle to their implementation. Current practice focuses on developing point estimates using least-squares regression approaches. This paper compares the performance of a production planning model using a multi-dimensional CF and its robust counterpart under several experimental settings. As expected, as the level of uncertainty is increased, the resulting production plan deviates from the optimal solution of the deterministic model. On the other hand, production plans found using the robust counterpart are less vulnerable to parameter estimation errors

Rounding heuristics for multiple product dynamic lot-sizing in the presence of queueing behavior

Due to copyright restrictions, the access to the full text of this article is only available via subscription.We present heuristics for solving a difficult nonlinear integer programming (NIP) model arising from a multi-item single machine dynamic lot-sizing problem. The heuristic obtains a local optimum for the continuous relaxation of the NIP model and rounds the resulting fractional solution to a feasible integer solution by solving a series of shortest path problems. We also implement two benchmarks: a version of the well-known Feasibility Pump heuristic and the Surrogate Method developed for stochastic discrete optimization problems. Computational experiments reveal that our shortest path based rounding procedure finds better production plans than the previously developed myopic heuristic and the benchmarks

Control of a batch-processing machine: a computational approach

Batch processing machines, where a number of jobs are processed simultaneously as a batch, occur frequently in semiconductor manufacturing environments, particularly at diffusion in wafer fabrication and at burn-in in final test. In this paper we consider a batch-processing machine subject to uncertain (Poisson) job arrivals. Two different cases are studied: (1) the processing times of batches are independent and identically distributed(IID), corresponding to a diffusion tube; and (2) the processing time of each batch is the maximum of the processing times of its constituent jobs, where the processing times of jobs are IID, modelling a burn-in oven. We develop computational procedures to minimize the expected long-run-average number of jobs in the system under a particular family of control policies. The control policies considered are threshold policies, where processing of a batch is initiated once a certain number of jobs have accumulated in the system. We present numerical examples of our methods and verify their accuracy using simulation