Dynamic control of a single-server system with abandonments

In this paper, we discuss the dynamic server control in a two-class service system with abandonments. Two models are considered. In the first case, rewards are received upon service completion, and there are no abandonment costs (other than the lost opportunity to gain rewards). In the second, holding costs per customer per unit time are accrued, and each abandonment involves a fixed cost. Both cases are considered under the discounted or average reward/cost criterion. These are extensions of the classic scheduling question (without abandonments) where it is well known that simple priority rules hold.     

Deconvolution gas chromatography/mass spectrometry of urinary organic acids--potential for pattern recognition and automated identification of metabolic disorders

The National Institute of Standards and Technology (NIST) Automated Mass Spectral Deconvolution and Identification System (AMDIS) is applied to a selection of data files obtained from the gas chromatography/mass spectrometry (GC/MS) analysis of urinary organic acids. Mass spectra obtained after deconvolution are compared with a special user library containing both the mass spectra and retention indices of ethoxime-trimethylsilyl (EO-TMS) derivatives of a set of organic acids. Efficient identification of components is achieved and the potential of the procedure for automated diagnosis of inborn errors of metabolism and for related research is demonstrated.     

On the role of Rouché's theorem in queueing analysis

In analytic queueing theory, Rouché's theorem is frequently used, and when it can be applied, leads quickly to tangible results concerning ergodicity and performance analysis. For more complicated models it is sometimes difficult to verify the conditions needed to apply the theorem. The natural question that arises is: Can one dispense with this theorem, in particular when the ergodicity conditions are known? In the present study we consider an M/G/1-type queueing problem which can be modelled byN coupled random walks. It is shown that it can be fully analysed without using Rouché's theorem, once it is known that the relevant functional equation has a unique solution with prescribed regularity properties.     

Measurement of the kinetic energy and lattice constant in hcp solid helium at temperatures 0.07-0.4 K

The single atom kinetic energy kappa of high purity solid hcp 4He has been measured by neutron Compton scattering, at temperatures between 0.07 and 0.4 K and a pressure of 40 bar. Within statistical error of approximately 2% no change in kappa was observed. The values of kappa at approximately 0.07 K were the same in a single crystal and a polycrystalline sample and were also unaffected (within statistical error) by the addition of 10 ppm of 3He. The lattice constant was also found to be independent of temperature to within 1 part in 2000. These results suggest that the supersolid transition in 4He has a different microscopic origin to the superfluid transition in the liquid.     

Round robin scheduling of heterogeneous parallel servers in heavy traffic

We consider scheduling for heterogeneous server systems, where tasks arrive according to a Poisson process, with their processing requirements following a discrete distribution with finite support. For a system with a dispatcher and several heterogeneous servers, we propose an optimized multi-layered round robin routing policy followed by shortest remaining processing time scheduling at each server. Using a heavy traffic approximation, we show that the proposed policy performs as well as the optimal scheduling policy for a heterogeneous servers system with a single queue (no routing) in heavy traffic. Additional simulation results suggest that such policies will be effective in more general settings.     

Optimal assignment of servers to tasks when collaboration is inefficient

Consider a Markovian system of two stations in tandem with finite intermediate buffer and two servers. The servers are heterogeneous, flexible, and more efficient when they work on their own than when they collaborate. We determine how the servers should be assigned dynamically to the stations with the goal of maximizing the system throughput. We show that the optimal policy depends on whether or not one server is dominant (i.e., faster at both stations) and on the magnitude of the efficiency loss of collaborating servers. In particular, if one server is dominant then he must divide his time between the two stations, and we identify the threshold policy the dominant server should use; otherwise each server should focus on the station where he is the faster server. In all cases, servers only collaborate to avoid idleness when the first station is blocked or the second station is starved, and we determine when collaboration is preferable to idleness as a function of the efficiency loss of collaborating servers.     

Piecewise linear test functions for stability and instability of queueing networks

We develop the use of piecewise linear test functions for the analysis of stability of multiclass queueing networks and their associated fluid limit models. It is found that if an associated LP admits a positive solution, then a Lyapunov function exists. This implies that the fluid limit model is stable and hence that the network model is positive Harris recurrent with a finite polynomial moment. Also, it is found that if a particular LP admits a solution, then the network model is transient. This revised version was published online in June 2006 with corrections to the Cover Date.