Convergence to Equilibrium States for Fluid Models of Many-server Queues with Abandonment

Fluid models have become an important tool for the study of many-server queues with general service and patience time distributions. The equilibrium state of a fluid model has been revealed by Whitt (2006) and shown to yield reasonable approximations to the steady state of the original stochastic systems. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under a mild condition. Our method builds on the framework of measure-valued processes developed in Zhang (2013), which keeps track of the remaining patience and service times

Phosphorus removal and membrane fouling and cleaning in iron-dosed submerged membrane bioreactor treatment of wastewaters

Iron (Fe) has been widely dosed into membrane bioreactors (MBRs) in order to reduce organics in the supernatant, however limited information on the impact of Fe-dosing at the concentrations required for effective phosphorus (P) removal on MBR performance is available. Bench scale MBR studies revealed that influent phosphorus concentrations of 10 mg/L were consistently reduced to effluent concentrations of less than 0.02 mg/L and 0.03-0.04 mg/L when an Fe(III)/P molar ratio of 4.0 and Fe/P molar ratio (for both Fe(II) and Fe(III)) of 2.0 were used, respectively. The sub-critical fouling time (tcrit) after which fouling becomes much more severe was substantially shorter with Fe(III) dosing (672 hrs) than with Fe(II) dosing (1200-1260 hrs) at Fe/P molar ratios of 2.0. Not surprisingly, membrane fouling was substantially more severe at Fe/P ratios of 4. Fe(II) doses yielding Fe/P molar ratios of 2 or less with dosing to the aerobic chamber were found to be optimal in terms of P removal and fouling mitigation performance. In long term operation, however, the use of iron for maintaining appropriately low effluent P concentrations results in more severe irreversible fouling with amorphous ferric oxyhydroxide particles (AFO) and gelatinous assemblages containing Fe(III) bound to polysaccharide materials responsible for gel layer formation and pore blockage. The prevalent chemical cleaning agents, sodium hypochlorite and citric acid, are not particularly effective in removing iron species from the membrane, while ascorbic acid-mediated reductive and citric acid-ascorbic acid-mediated ligand-promoted reductive dissolution are extremely effective. The presence of oxygen reduced cleaning effectiveness as a result of the Fe(III)-catalyzed oxidation of ascorbate with Fe(III) replenished by the relatively rapid heterogeneous oxidation of Fe(II). The presence of citrate in the ascorbic acid solution enhanced the reductive dissolution due to the accumulation of surface Fe(III)CitFe(II) which, in turn, readily detaches to solution. Use of frequent replenishment of freshly prepared ascorbic acid and/or dual agents-ascorbic acid and citric acid under oxic conditions is recommended for the cleaning of iron-fouled membranes as a reasonable balance between cleaning effectiveness and cost

Mega-Reward: Achieving Human-Level Play without Extrinsic Rewards

Intrinsic rewards were introduced to simulate how human intelligence works; they are usually evaluated by intrinsically-motivated play, i.e., playing games without extrinsic rewards but evaluated with extrinsic rewards. However, none of the existing intrinsic reward approaches can achieve human-level performance under this very challenging setting of intrinsically-motivated play. In this work, we propose a novel megalomania-driven intrinsic reward (called mega-reward), which, to our knowledge, is the first approach that achieves human-level performance in intrinsically-motivated play. Intuitively, mega-reward comes from the observation that infants' intelligence develops when they try to gain more control on entities in an environment; therefore, mega-reward aims to maximize the control capabilities of agents on given entities in a given environment. To formalize mega-reward, a relational transition model is proposed to bridge the gaps between direct and latent control. Experimental studies show that mega-reward (i) can greatly outperform all state-of-the-art intrinsic reward approaches, (ii) generally achieves the same level of performance as Ex-PPO and professional human-level scores, and (iii) has also a superior performance when it is incorporated with extrinsic rewards