Smart Policies for Multisource Inventory Systems and General Tandem Queues with Order Tracking and Expediting

2021 ◽  
Author(s):  
Jing-Sheng Song ◽  
Li Xiao ◽  
Hanqin Zhang ◽  
Paul Zipkin
Keyword(s):  
Numerical Study ◽  
Inventory Systems ◽  
Product Form ◽  
Tandem Queue ◽  
Supply Source ◽  
State Dependent ◽  
Online Retailers ◽  
Special Cases ◽  
Simple Product ◽  
Almost All

We study an inventory system with multiple supply sources and expediting options. The replenishment lead times from each supply source are stochastic, representing congestion and disruption. We construct a family of smart ordering and expediting policies that utilize real-time supply information. Such dynamic policies are generally difficult to evaluate, because the corresponding supply system is a tandem queue with state-dependent arrivals and routing, whose queue-length steady-state distribution is usually not in product form. Our main result is to identify two appealing special cases of the general policy, Policy-M and Policy-E, which possess simple product-form solutions and lead to closed-form performance measures. Policy-M retains full sourcing flexibility, but ignores upstream congestion in making expediting decisions. Policy-E only orders from the normal, farthest source, but makes expediting decisions based on both upstream and downstream information. A numerical study shows that the best Policy-M leads to a lower average cost than the best Policy-E in almost all cases. Also, implementing the best Policy-M parameters, the general policy only performs slightly better than Policy-M. These observations reveal the value of combining sourcing flexibility with some, but limited, dynamic expediting. Our findings are equally applicable to the equivalent tandem queue. They thus may aid dynamic routing and expediting decisions for online retailers and logistics providers, among others.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (2) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network.This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

scholarly journals Boundary behavior and product-form stationary distributions of jump diffusions in the orthant with state-dependent reflections

2008 ◽  
Vol 40 (02) ◽  
pp. 529-547
Author(s):  
Francisco J. Piera ◽  
Ravi R. Mazumdar ◽  
Fabrice M. Guillemin
Keyword(s):  
Random Fields ◽  
Diffusion Coefficients ◽  
Boundary Behavior ◽  
Stationary Regime ◽  
Product Form ◽  
Local Times ◽  
Nonnegative Orthant ◽  
State Dependent ◽  
The Times ◽  
And Diffusion

In this paper we consider reflected diffusions with positive and negative jumps, constrained to lie in the nonnegative orthant of ℝ n . We allow for the drift and diffusion coefficients, as well as for the directions of reflection, to be random fields over time and space. We provide a boundary behavior characterization, generalizing known results in the nonrandom coefficients and constant directions of the reflection case. In particular, the regulator processes are related to semimartingale local times at the boundaries, and they are shown not to charge the times the process expends at the intersection of boundary faces. Using the boundary results, we extend the conditions for product-form distributions in the stationary regime to the case when the drift and diffusion coefficients, as well as the directions of reflection, are random fields over space.

scholarly journals Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

2020 ◽  
Vol 10 (2) ◽  
pp. 226-236
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Trapezium Type ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Preinvex Functions ◽  
Almost All

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

scholarly journals A Note on a Triple Integral

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2056
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Polynomial Functions ◽  
Fundamental Constants ◽  
Form Expression ◽  
Zero Distribution ◽  
Special Cases ◽  
Almost All

A closed form expression for a triple integral not previously considered is derived, in terms of the Lerch function. Almost all Lerch functions have an asymmetrical zero-distribution. The kernel of the integral involves the product of the logarithmic, exponential, quotient radical, and polynomial functions. Special cases are derived in terms of fundamental constants; results are summarized in a table. All results in this work are new.

scholarly journals On the General Consensus Protocol in Multiagent Networks with Double-Integrator Dynamics and Coupling Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao
Keyword(s):  
Time Delay ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Algorithm ◽  
Directed Network ◽  
Consensus Protocol ◽  
Special Cases ◽  
Coupling Time ◽  
Almost All ◽  
Double Integrator

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

DKP equation with smooth barrier

2021 ◽  
Author(s):  
O. Langueur ◽  
M. Merad ◽  
A. Rassoul
Keyword(s):  
Hypergeometric Function ◽  
Numerical Study ◽  
Confluent Hypergeometric Function ◽  
Reflection Coefficients ◽  
Step Potential ◽  
Dkp Equation ◽  
Transmission And Reflection Coefficients ◽  
Special Cases ◽  
Rectangular Barrier ◽  
Transmission And Reflection

In this paper, we study the Duffin–Kemmer–Petiau (DKP) equation in the presence of a smooth barrier in dimensions space–time (1+1) dimensions. The eigenfunctions are determined in terms of the confluent hypergeometric function [Formula: see text]. The transmission and reflection coefficients are calculated, special cases as a rectangular barrier and step potential are analyzed. A numerical study is presented for the transmission and reflection coefficients graphs for some values of the parameters [Formula: see text] are plotted.

Implementation of DTM as a numerical study for the Casson fluid flow past an exponentially variable stretching sheet with thermal radiation

2021 ◽  
pp. 2150111
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Numerical Method ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transformation Method ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Special Cases

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

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