اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExtreme-value theory for large fork-join queues, with an application to high-tech supply chains
189
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study extreme values in certain fork-join queueing networks: consider $N$ identical queues with a common arrival process and independent service processes. All arrival and service processes are deterministic with random perturbations following Brownian motions. We prove that as $Nrightarrow infty$, the scaled maximum of $N$ steady-state queue lengths converges in distribution to a normally distributed random variable. We also explore repercussions of this result for original equipment manufacturers (OEMs) that assemble a large number of components, each produced using specialized equipment, into complex systems. Component production capacity is subject to fluctuations, causing a high risk of shortages of at least one component, which in turn results in costly system production delays. OEMs hedge this risk by investing in a combination of excess production capacity and component inventories. We formulate a stylized model of the OEM that enables us to study the resulting trade-off between shortage risk, inventory costs, and capacity costs. Our asymptotic extreme value results translate into various asymptotically exact methods for cost-optimal inventory and capacity decisions, some of which are in closed form. Numerical results indicate that our results are asymptotically exact, while for transient times they depend on model parameters.
قيم البحث
اقرأ أيضاً
In this paper, we study an $N$ server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as $Ntoinfty$. This fluid limit depends on the initial number of tasks. In
order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths.
We present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. Our result can be viewed as a new improvement to the LIL.
Unlike consumer goods industry, a high-tech manufacturer (OEM) often amortizes new product development costs over multiple generations, where demand for each generation is based on advance orders and additional uncertain demand. Also, due to economic
reasons and regulations, high-tech OEMs usually source from a single supplier. Relative to the high retail price, the wholesale price for a supplier to produce high-tech components is low. Consequently, incentives are misaligned: the OEM faces relatively high under-stock costs and the supplier faces high over-stock costs. In this paper, we examine supply contracts that are intended to align the incentives between a high-tech OEM and a supplier so that the supplier will invest adequate and yet non-verifiable capacity to meet the OEMs uncertain demand. When focusing on a single generation, the manufacturer can coordinate a decentralized supply chain and extract all surplus by augmenting a traditional wholesale price contract with a contingent penalty should the supplier fail to fulfill the OEMs demand. When the resulting penalty is too high to be enforceable, we consider a new class of contingent renewal wholesale price contracts with a stipulation: the OEM will renew the contract with the incumbent supplier for the next generation only when the supplier can fulfill the demand for the current generation. By using non-renewal as an implicit penalty, we show that the contingent renewal contract can coordinate the supply chain. While the OEM can capture the bulk of the supply chain profit, this innovative contract cannot enable the OEM to extract the entire surplus.
This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to construct
fractional integro-differential equations for the ruin probabilities in collective renewal risk models, with inter-arrival time distributions from the aforementioned family. Gamma-time risk models and fractional Poisson risk models are two specific cases among them, whose ruin probabilities have explicit solutions, when claim sizes distributions exhibit rational Laplace transforms.
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the total numb
er of customers in the system, as well as a measure-valued process that keeps track of the ages of customers in service. Under mild assumptions on the service time distribution, as the number of servers goes to infinity, a law of large numbers (or fluid) limit is established for this pair of processes. The limit is characterised as the unique solution to a coupled pair of integral equations, which admits a fairly explicit representation. As a corollary, the fluid limits of several other functionals of interest, such as the waiting time, are also obtained. Furthermore, in the time-homogeneous setting, the fluid limit is shown to converge to its equilibrium. Along the way, some results of independent interest are obtained, including a continuous mapping result and a maximality property of the fluid limit. A motivation for studying these systems is that they arise as models of computer data systems and call centers.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
