A Switching Fluid Limit of a Stochastic Network Under a State-Space-Collapse Inducing Control with Chattering

Routing mechanisms for stochastic networks are often designed to produce state space collapse (SSC) in a heavy-traffic limit, i.e., to confine the limiting process to a lower-dimensional subset of its full state space. In a fluid limit, a control producing asymptotic SSC corresponds to an ideal sliding mode control that forces the fluid trajectories to a lower-dimensional sliding manifold. Within deterministic dynamical systems theory, it is well known that sliding-mode controls can cause the system to chatter back and forth along the sliding manifold due to delays in activation of the control. For the prelimit stochastic system, chattering implies fluid-scaled fluctuations that are larger than typical stochastic fluctuations. In this paper we show that chattering can occur in the fluid limit of a controlled stochastic network when inappropriate control parameters are used. The model has two large service pools operating under the fixed-queue-ratio with activation and release thresholds (FQR-ART) overload control which we proposed in a recent paper. We now show that, if the control parameters are not chosen properly, then delays in activating and releasing the control can cause chattering with large oscillations in the fluid limit. In turn, these fluid-scaled fluctuations lead to severe congestion, even when the arrival rates are smaller than the potential total service rate in the system, a phenomenon referred to as congestion collapse. We show that the fluid limit can be a bi-stable switching system possessing a unique nontrivial periodic equilibrium, in addition to a unique stationary point

A Fluid Limit for an Overloaded X Model Via a Stochastic Averaging Principle

We prove a many-server heavy-traffic fluid limit for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the fixed-queue-ratio-with-thresholds (FQR-T) control, which we proposed in a recent paper as a way for one service system to help another in face of an unexpected overload. Under FQR-T, customers are served by their own service pool until a threshold is exceeded. Then, one-way sharing is activated with customers from one class allowed to be served in both pools. After the control is activated, it aims to keep the two queues at a pre-specified fixed ratio. For large systems that fixed ratio is achieved approximately. For the fluid limit, or FWLLN, we consider a sequence of properly scaled X models in overload operating under FQR-T. Our proof of the FWLLN follows the compactness approach, i.e., we show that the sequence of scaled processes is tight, and then show that all converging subsequences have the specified limit. The characterization step is complicated because the queue-difference processes, which determine the customer-server assignments, remain stochastically bounded, and need to be considered without spatial scaling. Asymptotically, these queue-difference processes operate in a faster time scale than the fluid-scaled processes. In the limit, due to a separation of time scales, the driving processes converge to a time-dependent steady state (or local average) of a time-varying fast-time-scale process (FTSP). This averaging principle (AP) allows us to replace the driving processes with the long-run average behavior of the FTSP.Comment: There are 55 pages, 46 references and 0 figure

Stochastic Systems ACHIEVING RAPID RECOVERY IN AN OVERLOAD CONTROL FOR LARGE-SCALE SERVICE SYSTEMS

We consider an automatic overload control for two large service systems modeled as multi-server queues, such as call centers. We assume that the two systems are designed to operate independently, but want to help each other respond to unexpected overloads. The proposed overload control automatically activates sharing (sending some customers from one system to the other) once a ratio of the queue lengths in the two systems crosses an activation threshold (with ratio and activation threshold parameters for each direction). To prevent harmful sharing, sharing is allowed in only one direction at any time. In this paper, we are primarily concerned with ensuring that the system recovers rapidly after the overload is over, either (i) because the two systems return to normal loading or (ii) because the direction of the overload suddenly shifts in the opposite direction. To achieve rapid recovery, we introduce lower thresholds for the queue ratios, below which one-way sharing is released. As a basis for studyin

© 2012 INFORMS Overflow Networks: Approximations and

Motivated by call center cosourcing problems, we consider a service network operated under an overflow mechanism. Calls are first routed to an in-house (or dedicated) service station that has a finite waiting room. If the waiting room is full, the call is overflowed to an outside provider (an overflow station) that might also be serving overflows from other stations. We establish approximations for overflow networks with many servers under a resource-pooling assumption that stipulates, in our context, that the fraction of overflowed calls is nonnegligible. Our two main results are (i) an approximation for the overflow processes via limit theorems and (ii) asymptotic independence between each of the in-house stations and the overflow station. In particular, we show that, as the system becomes large, the dependency between each in-house station and the overflow station becomes negligible. Independence between stations in overflow networks is assumed in the literature on call centers, and we provide a rigorous support for those useful heuristics. Subject classifications: overflow networks; cosourcing; heavy-traffic approximations; separation of time scales

Proteasome Inhibitor-Related Cardiotoxicity: Mechanisms, Diagnosis, and Management.

Multiple myeloma is the second most common hematologic malignancy in the USA, with over 32,000 new cases and nearly 13,000 deaths expected in 2019. The past few decades in myeloma research have yielded significant advances, leading to the expansion of novel anti-myeloma agents. This review describes the incidence and mechanisms of cardiotoxicity for the FDA-approved proteasome inhibitors in myeloma and proposes strategies to assess and manage resultant cardiovascular adverse events.Proteasome inhibition precipitates protein aggregation and alters transcriptional activation of NF-κB targets which contributes to a pro-apoptotic signaling cascade in myeloma cells. Similar effects in cardiomyocytes and vascular smooth muscle endothelium, along with off-target downregulation of autophagy and signaling alterations of nitric oxide homeostasis, may be linked to observed cardiotoxic effects. There is preliminary evidence for cardioprotective potential for rutin, dexrazoxane, and apremilast that could have clinical applicability in the future. Of the proteasome inhibitors used in clinical practice, carfilzomib is the most strongly associated with cardiotoxicity. Patients with anticipated carfilzomib treatment should undergo assessment and optimization of baseline cardiovascular risk, with close monitoring during treatment. Previous clinical trials were not specifically designed to assess proteasome inhibitor-related cardiotoxicity, creating a need for future studies to identify and risk stratify vulnerable individuals and to develop potential cardioprotective strategies in attenuating cardiac injury