Admission Control in Stochastic Event Graphs

In this paper, we show that the expected workload and the expected waiting time in (max,+) linear system under a single input sequence is multimodular. We use this result to construct the optimal deterministic admission control in the (max,+) system under rate constraints

Direct visualization of lipid aggregates in native human bile by light- and cryo-transmission electron-microscopy

AbstractThe evolution of microstructures present in human gallbladder and hepatic bile was observed simultaneously by video-enhanced light microscopy (VELM) and transmission electron microscopy of vitrified specimens (cryo-TEM), as a function of time after withdrawal from patients. Fresh centrifuged gallbladder bile samples contained small (6 nm) spherical micelles in coexistence with vesicles (40 nm). Out of the seven bile samples investigated four contained, in addition, two types of elongated aggregates that have not been previously described. Uncentrifuged gallbladder bile also contained a mixture of ribbon- and plate-like crystals seen by VELM, but not by cryo-TEM. In aged (3–6-week-old) gallbladder bile samples VELM also revealed spiral and helical crystal structures. No such crystals were present in hepatic bile samples, although microcrystals, not observable by VELM were seen by cryo-TEM in addition to micelles and vesicles. The similarity of these observations to those observed in bile models lends strong support for the validity of the model systems. Furthermore, the presence of microcrystals in hepatic bile samples, apparently devoid of crystals by light microscopy, indicates that under certain conditions the common criterion of ‘nueleation time’ (NT), based on light microscopy, does not represent the real time of nucleation. In the human bile samples investigated in this study the dissociation between NT and the time of observation of microcrystals was seen in hepatic but not in gallbladder bile samples. Hence, crystal growth may be rate limiting only in dilute biles

Admission Control in Stochastic Event Graphs

In this paper, we show that the expected workload and the expected waiting time in (max,+) linear system under a single input sequence is multimodular. We use this result to construct the optimal deterministic admission control in the (max,+) system under rate constraints

Discrete-event control of stochastic networks multimodularity and regularity

Opening new directions in research in both discrete event dynamic systems as well as in stochastic control, this volume focuses on a wide class of control and of optimization problems over sequences of integer numbers. This is a counterpart of convex optimization in the setting of discrete optimization. The theory developed is applied to the control of stochastic discrete-event dynamic systems. Some applications are admission, routing, service allocation and vacation control in queueing networks. Pure and applied mathematicians will enjoy reading the book since it brings together many disciplines in mathematics: combinatorics, stochastic processes, stochastic control and optimization, discrete event dynamic systems, algebra

Optimal Open-Loop Control of Vacations, Polling and Service Assignment

We consider in this paper the optimal open-loop control of vacations in queueing systems. The controller has to take actions without state information. We first consider the case of a single queue, in which the question is when should vacations be taken so as to minimize, in some general sense, workloads and waiting times. We then consider the case of several queues, in which service of one queue constitutes a vacation for others. This is the optimal polling problem. We solve both problems using new techniques from [2, 4] based on multimodularity

Balanced Sequences and Optimal Routing

The objective pursued in this paper is two-fold. The first part gives an overview of the following combinatorial problem: is it possible to construct an infinite sequence over n letters where each letter is distributed as "evenly" as possible and appears with a fixed rate? The second objective of the paper is to relate this construction to the framework of optimal routing in queueing networks. We show under rather general assumptions that the optimal deterministic routing in stochastic event graphs is such a sequence

Multimodularity, Convexity and Optimization Properties

We investigate in this paper the properties of multimodular functions. In doing so we give elementary proofs for properties already established by Hajek, and we generalize some of his results. In particular, we extend the relation between convexity and multimodularity to some convex subsets of Z^m. We also obtain general optimization results for average costs related to a sequence of multimodular functions rather than to a single function. Under this general context, we show that the expected average cost problem is optimized by using balanced sequences. We nally illustrate the usefulness of this theory in admission control into a D/D/1 queue with xed batch arrivals, with no state information. We show that the balanced policy minimizes the average queue length for the case of an innite queue, but not for the case of a nite queue. When further adding a constraint on the losses, it is shown that a balanced policy is also optimal for the nite queue case. Keywords Multimodular fun..

Balanced Sequences and Optimal Routing

The objective pursued in this paper is two-fold. The first part addresses the following combinatorial problem: is it possible to construct an infinite sequence over n letters where each letter is distributed as "evenly" as possible and appears with a given rate? The second objective of the paper is to use this construction in the framework of optimal routing in queuing networks. We show under rather general assumptions that the optimal deterministic routing in stochastic event graphs is such a sequence

Multimodularity, Convexity and Optimization Properties

We investigate in this paper the properties of multimodular functions. In doing so we give alternative proofs for properties already established by Hajek, and we extend his results. In particular, we show the relation between convexity and multimodularity, which allows us to restrict the study of multimodular functions to convex subsets of Z m . We then obtain general optimization results for average costs related to a sequence of multimodular functions. In particular, we establish lower bounds, and show that the expected average problem is optimized by using balanced sequences. We ønally illustrate the usefulness of this theory in admission control into a D/D/1 queue with fixed batch arrivals, with no state information. We show that the balanced policy minimizes the average queue length for the case of an infinite queue, but not for the case of a finite queue. When further adding a constraint on the losses, it is shown that a balanced policy is also optimal for the case of finite queue