Queueing Dynamics and Maximal Throughput Scheduling in Switched Processing Systems

We study a processing system comprised of parallel queues, whose individual service rates are specified by a global service mode (configuration). The issue is how to switch the system between various possible service modes, so as to maximize its throughput and maintain stability under the most workload-intensive input traffic traces (arrival processes). Stability preserves the job inflow–outflow balance at each queue on the traffic traces. Two key families of service policies are shown to maximize throughput, under the mild condition that traffic traces have long-term average workload rates. In the first family of cone policies, the service mode is chosen based on the system backlog state belonging to a corresponding cone. Two distinct policy classes of that nature are investigated, MaxProduct and FastEmpty. In the second family of batch policies (BatchAdapt), jobs are collectively scheduled over adaptively chosen horizons, according to an asymptotically optimal, robust schedule. The issues of nonpreemptive job processing and non-negligible switching times between service modes are addressed. The analysis is extended to cover feed-forward networks of such processing systems/nodes. The approach taken unifies and generalizes prior studies, by developing a general trace-based modeling framework (sample-path approach) for addressing the queueing stability problem. It treats the queueing structure as a deterministic dynamical system and analyzes directly its evolution trajectories. It does not require any probabilistic superstructure, which is typically used in previous approaches. Probability can be superposed later to address finer performance questions (e.g., delay). The throughput maximization problem is seen to be primarily of structural nature. The developed methodology appears to have broader applicability to other queueing systems.     

Design of Stacked Self-Healing Rings Using a Genetic Algorithm

Ring structures in telecommunications are taking on increasing importance because of their self-healing properties. We consider a ring design problem in which several stacked self-healing rings (SHRs) follow the same route, and, thus, pass through the same set of nodes. Traffic can be exchanged among these stacked rings at a designated hub node. Each non-hub node may be connected to multiple rings. It is necessary to determine to which rings each node should be connected, and how traffic should be routed on the rings. The objective is to optimize the tradeoff between the costs for connecting nodes to rings and the costs for routing demand on multiple rings. We describe a genetic algorithm that finds heuristic solutions for this problem. The initial generation of solutions includes randomly-generated solutions, complemented by seed solutions obtained by applying a greedy randomized adaptive search procedure (GRASP) to two related problems. Subsequent generations are created by recombining pairs of parent solutions. Computational experiments compare the genetic algorithm with a commercial integer programming package.     

Exact analysis for multiserver queueing systems with cross selling

Annals of Operations Research - Exact analysis of a multi-server Markovian queueing system with cross selling in steady-state is presented. Cross selling attempt is initiated at the end of a...     

Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers

Motivated by modern call centers, we consider large-scale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steady-state queue length and virtual waiting time. The proposed routing scheme is FSF which assigns customers to the Fastest Servers First. The asymptotic regime considered is the Halfin-Whitt many-server heavy-traffic regime, which we refer to as the Quality and Efficiency Driven (QED) regime; it achieves high levels of both service quality and system efficiency by carefully balancing between the two. Additionally, expressions are provided for system limiting performance measures based on diffusion approximations. Our analysis shows that in the QED regime this heterogeneous server system outperforms its homogeneous server counterpart. AMS subject classification: 60K25, 68M20, 90B22     

New insights on the active species and mechanism of cytotoxicity of salan-Ti(IV) complexes: a stereochemical study

Following the discovery of cisplatin, much effort has been devoted to the exploration of transition metal complexes as cytotoxic agents. We have recently introduced the highly efficient C(2)-symmetrical salan-Ti(IV) family of complexes, demonstrating high cytotoxicity toward colon and ovarian cells and enhanced hydrolytic stability in mixed organic/water solutions. The effect of stereochemistry is hereby reported, by comparing the cytotoxic activity and hydrolysis of pure enantiomers and their racemic mixture for four complexes of this family with different aromatic substitutions: para-Me, para-Cl, ortho-Cl, and ortho-OMe. These complexes include the trans-diaminocyclohexyl bridge, which enables ligand-to-metal chiral induction to give solely the Δ isomer when starting from the R,R ligand and vice versa. Different activity is obtained for the different stereochemical forms (Δ, Λ, and rac) in two of the four complexes, where for the other two either all forms are inactive or all are highly active. Additionally, where not all are of similar activity, the racemic mixture is the least active of the three. We therefore conclude that the salan ligand is essential for the fruitful biological interaction, which probably involves a chiral cellular target. The activity of the racemate differing from that expected from a simple mixture of enantiomers operating separately may be explained by the involvement of a polynuclear active species, where different metal centers might be of different configurations. This is particularly supported by the different polynuclear products of hydrolysis obtained from an optically pure complex and from the racemic one, as analyzed crystallographically. The former is an all-R,R chiral C(1)-symmetrical homodimer, while the latter is an achiral R,R-S,SC(i)-symmetrical heterodimer obtained through chiral recognition.     

Unexpected influence of stereochemistry on the cytotoxicity of highly efficient Ti(IV) salan complexes: new mechanistic insights

The effect of stereochemistry on the cytotoxicity of highly active and hydrolytically stable N-methylated Ti(IV) salan complexes is reported. Four bis(isopropoxo) complexes incorporating N-methylated salan ligands with different aromatic substitution patterns have been prepared in racemic and optically active forms for the first time by ligand-to-metal chiral induction from trans-diaminocyclohexyl-based chiral ligands. The configuration of the metal center that derives from that of the ligand has an enormous influence on cytotoxicity, with the racemic mixture mostly being more active than the single enantiomers that are of either similar or different activity. This implies that the active species is a salan-bound heterochiral polynuclear compound, interacting with a chiral target. Four additional complexes of achiral salan and chiral labile sec-butoxo ligands, analyzed as racemic and as homochiral, revealed no influence of stereochemistry, supporting early dissociation of the labile ligands to give the polynuclear products.