Analysis of a feedback fluid model for heterogeneous TCP sources

In this paper we consider a bottleneck link and buffer used by one or two fluid sources subject to feedback. During overflow, the buffer sends negative feedback signals to the sources to reduce the sending rate. Otherwise the buffer sends positive signals to indicate that the sources can increase the rate. The analysis is targeted at the Transport Control Protocol of the Internet. In this specific context we find closed form expressions for the eigenvalues and eigenvectors of the solution for the single-source case. The case of two sources extends the single-source analysis considerably so that now source parameters, e.g. feedback rate, can be individually specified. By deriving a sufficient number of boundary conditions for the solution values and derivatives we prove that the related two-point boundary value problem is uniquely solvable in the stationary case. We establish also a numerically efficient procedure to compute the coefficients of the solution of the differential equations. The numerical results of this model are presented in an accompanying paper.\u

Performance analysis of heterogeneous interacting TCP sources

In this paper we develop a fluid model for TCP sources that share a bottleneck router. The model allows to specify for each source individually the maximum window size, the packet size, and the (stochastic) roundtrip time. First we consider the situation in which one source uses the link. In this setting we study the impact of buffer size, link rate, and source parameters on the link utilization. We observe that conservative source behavior is optimal with respect to utilization. Then we focus on two sources sharing the link. By computing the throughput for each source separately we obtain insight in fairness issues. We find analytic support for TCP's bias against sources with: (1) longer roundtrip times; (2) smaller maximum congestion windows; (3) smaller packet sizes. Another interesting point is that when buffering delay forms a substantial part of the roundtrip time, on which the feedback loop depends, a large buffer size is detrimental to link utilization.\u

Admission policies for the customized stochastic lot scheduling problem with strict due-dates

This papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times. We model the joint admission control/scheduling problem as a Markov decision process (MOP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward. (C) 2011 Elsevier B.V. All rights reserved

Order acceptance and scheduling policies for a make-to-order environment with family-dependent lead and batch setup times

<p>In many make-to-order production situations with batch setup times, customer orders are grouped into family-dependent batches to limit the loss of capacity due to setups. These batches, however, cannot be too large, since the make-to-order character requires that orders have to be produced in time. This trade-off between setup time efficiency and due-date adherence creates a challenging scheduling problem referred to in the literature as the Customised Stochastic Lot Scheduling Problem. Typically, suppliers reduce the complexity of the production problem by quoting lead times that are equal for all customer families. This choice, however, is in many cases too restrictive. In this paper, we show quantitatively by means of Markov decision processes (MDPs) that using family-dependent lead times can result in a significant gain in profit as compared with using standard lead times. We develop a simple heuristic acceptance/scheduling policy, and demonstrate that this heuristic performs very well compared with the optimal policy of the MDP for a wide range of parameters.</p>

On the Optimal Policy for the Single-product Inventory Problem with Set-up Cost and a Restricted Production Capacity

The single-product, stationary inventory problem with set-up cost is one of the classical problems in stochastic operations research. Theories have been developed to cope with finite production capacity in periodic review systems, and it has been proved that optimal policies for these cases are not of the (modified) (s, S)-type in general, but more complex. In this paper we consider a production system such that the production rate is constrained, rather than the amount as is common in periodic review models. Thus, in our case the production rate is positive and finite when the system is on and zero when off, while a cost is incurred to switching on or off. We prove that a long-run optimal stationary policy exists for this single-item continuous review inventory problem with non-zero switching cost and finite production rate, and that this optimal policy has an (s,S)-structure. We also provide an efficient numerical procedure to compute the parameters of the optimal policy.

Moving Two-Fluid Systems Using the Volume-of-Fluid Method and Single-Temperature Approximation

I.Introduction SLOSHING experiments using cryogenic liquid nitrogen, executed at the Centre of Applied Space Technology and Microgravity(ZARM) in Bremen, Germany, were simulated numerically using a computational fluid dynamics (CFD) program based on the volume-of-fluid (VOF) method and a single-temperature-per-cell approximation. In contrast to sloshing of storable liquids (a fluid that is in the liquid phase at room temperature and pressure), sloshing of a cryogenic liquid introduces important thermodynamic effects in addition to the dynamical aspect of a sloshing motion.The dynamic behavior of a sloshing liquid has been extensively studied[1], whereas the thermodynamic aspects have not been the subject of many studies and are not understood well. Therefore, the focus of the experiments and simulations is on these thermodynamic aspects. It will be shown in this Note that codes using the previously mentioned methods are not able to simulate the thermodynamic aspects of such experiments accurately, and it will be explained why that is the case