Scheduling for a processor sharing system with linear slowdown

We consider the problem of scheduling arrivals to a congestion system with a finite number of users having identical deterministic demand sizes. The congestion is of the processor sharing type in the sense that all users in the system at any given time are served simultaneously. However, in contrast to classical processor sharing congestion models, the processing slowdown is proportional to the number of users in the system at any time. That is, the rate of service experienced by all users is linearly decreasing with the number of users. For each user there is an ideal departure time (due date). A centralized scheduling goal is then to select arrival times so as to minimize the total penalty due to deviations from ideal times weighted with sojourn times. Each deviation penalty is assumed quadratic, or more generally convex. But due to the dynamics of the system, the scheduling objective function is non-convex. Specifically, the system objective function is a non-smooth piecewise convex function. Nevertheless, we are able to leverage the structure of the problem to derive an algorithm that finds the global optimum in a (large but) finite number of steps, each involving the solution of a constrained convex program. Further, we put forward several heuristics. The first is the traversal of neighbouring constrained convex programming problems, that is guaranteed to reach a local minimum of the centralized problem. This is a form of a “local search”, where we use the problem structure in a novel manner. The second is a one-coordinate “global search”, used in coordinate pivot iteration. We then merge these two heuristics into a unified “local–global” heuristic, and numerically illustrate the effectiveness of this heuristic.     

Lowest priority waiting time distribution in an accumulating priority Lévy queue

We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.     

Bicriteria problems to minimize maximum tardiness and due date assignment cost in various scheduling environments

We study bicriteria problems of minimizing maximum tardiness and total due date assignment cost in various scheduling environments. We assume that each job can be assigned a different due date without any restriction, and that each due date assignment cost is a non-decreasing function of the quoted due date. We settle the complexity of most of the problems studied by either proving that they are NP-hard or finding a polynomial time solution for them. We also include approximation and non-approximability results for several parallel-machine problems.     

Complexity analysis of an assignment problem with controllable assignment costs and its applications in scheduling

We extend the classical linear assignment problem to the case where the cost of assigning agent j to task i is a multiplication of task i’s cost parameter by a cost function of agent j. The cost function of agent j is a linear function of the amount of resource allocated to the agent. A solution for our assignment problem is defined by the assignment of agents to tasks and by a resource allocation to each agent. The quality of a solution is measured by two criteria. The first criterion is the total assignment cost and the second is the total weighted resource consumption. We address these criteria via four different problem variations. We prove that our assignment problem is NP-hard for three of the four variations, even if all the resource consumption weights are equal. However, and somewhat surprisingly, we find that the fourth variation is solvable in polynomial time. In addition, we find that our assignment problem is equivalent to a large set of important scheduling problems whose complexity has been an open question until now, for three of the four variations.     

Preliminary investigations of ultrasound induced acoustic streaming using particle image velocimetry

Particle image velocimetry was used to investigate ultrasound-induced acoustic streaming in a system for the enhanced uptake of substances from the aquatic medium into fish. Four distinct regions of the induced streaming in the system were observed and measured. One of the regions was identified as an preferential site for substance uptake, where the highest velocities in proximity to the fish surface were measured. A positive linear relationship was found between the ultrasound intensity and the maximum streaming velocity, where a unitless geometric factor, specific to the system, was calculated for correcting the numerical relationship between the two parameters. The results are part of a comprehensive study aimed at improving mass transdermal administrations of substances (e.g. vaccines, hormones) into fish from the aquatic medium.     

Drying of porous oil shales

Rate processes including change of phase are modelled analytically for a half-space porous substance exposed to a jump in external temperature. The model predicts, in a closed form, the pressure build-up and the rate of evaporation of volatiles from a porous matrix. It assumes two distinct regions separated by a moving interface where the change of phase takes place. One region maintains its initial concentration of volatiles while the second is devoid of volatiles. Different thermophysical properties are considered for the two regions. The model was applied for the evaporation of moisture from oil-shale. Results are given in a parametric form     

Thermal dehydration and decomposition of copper selenate pentahydrate

Temperature programmed desorption mass spectrometry (TPD-MS) and thermal gravimetry (TG) were utilized for the study of the thermal dehydration and decomposition of copper selenate pentahydrate (CuSeO₄·5H₂O). From the two techniques we suggest that the dehydration is a 3-step process reaching completion at 300 °C. The decomposition process however, is far more complicated consisting of several successive steps occurring between 480 and 900 °C. Initiated with the emission of oxygen, the decomposition of the anhydrous salt continues with SeO₂ emission via several unstable intermediates up to the conversion of the remaining copper monoxide into dicopper monoxide accompanied by oxygen emission.     

Separation and detection of VX and its methylphosphonic acid degradation products on a microchip using indirect laser-induced fluorescence

The application of indirect LIF (IDLIF) technique for on-chip electrophoretic separation and detection of the nerve agent O-ethyl S-[2-(diisopropylamino)ethyl] methylphosphonothiolate (VX) and its major phosphonic degradation products, ethyl methylphosphonic acid (EMPA) and methylphosphonic acid (MPA) was demonstrated. Separation and detection of MPA degradation products of VX and the nerve agent isopropyl methylphosphonofluoridate (GB) are presented. The negatively charged dye eosin was found to be a good fluorescent marker for both the negatively charged phosphonic acids and the positively charged VX, and was chosen as the IDLIF visualization fluorescent dye. Separation and detection of VX, EMPA, and MPA in a simple-cross microchip were completed within less than a minute, and consumed only a 50 pL sample volume. A characteristic system peak that appeared in all IDLIF electropherograms served as an internal standard that increased the reliability of peak identification. The negative peak of both VX and the MPAs is in agreement with indirect detection theory and with previous reports in the literature. The LOD of VX and EMPA by IDLIF was 30 and 37 microM, respectively. Despite the fact that the detection sensitivity is relatively low, the rapid simultaneous on-chip analysis of both VX and its degradation products as well as the separation and detection of the MPA degradation products of both VX and GB, increases detection reliability and may present a choice when sensitivity is not critical compared with speed and simplicity of the assay.