On the Relative Waiting Times in the GI/M/s and the GI/M/1 Queueing Systems

The expected steady-state waiting time, Wq(s), in a GI/M/s system with interarrival-time distribution H(·) is compared with the mean waiting time, Wq, in an "equivalent" system comprised of s separate GI/M/1 queues each fed by an interarrival-time distribution G(·) with mean arrival rate equal to 1/s times that of H(·). For H(·) assumed to be Exponential, Gamma or Deterministic three possible relationships between H(·) and G(·) are considered: G(·) can be of the "same type" as H(·); G(·) can be derived from H(·) by assigning new arrivals to the individual channels in a cyclic order; and G(·) may be obtained from H(·) by assigning customers probabilistically to the different queues. The limiting behaviour of the ratio R = Wq/Wq(s) is studied for the extreme values (1 and 0) of the common traffic intensity, ρ. Closed form results, which depend on the forms of H(·) and G(·) and on the relationships between them, are derived. It is shown that Wq is greater than Wq(s) by a factor of at least (s + 1)/2 when ρ approaches one, and that R is at least s(s!) when ρ tends to zero. In the latter case, however, R goes to infinity (!) in most cases treated. The results may be used to evaluate the effect on the waiting times when, for certain (non-queueing) reasons, it is needed to partition a group of s servers into several small groups.     

The maximal variation of a bounded martingale

Let \(\chi _0^n = \left\{ {X_t } \right\}_0^n \) be a martingale such that 0≦X_i≦1;i=0, …,n. For 0≦p≦1 denote by ? _p ⁿ the set of all such martingales satisfying alsoE(X₀)=p. Thevariation of a martingale χ ₀ ⁿ is denoted byV ₀ ⁿ and defined by \(V(\chi _0^n ) = E\left( {\sum {_{l = 0}^{n - 1} } \left| {X_{l + 1} - X_l } \right|} \right)\) . It is proved that $$\mathop {\lim }\limits_{n \to \infty } \left\{ {\mathop {Sup}\limits_{x_0^n \in \mathcal{M}_p^n } \left[ {\frac{1}{{\sqrt n }}V(\chi _0^n )} \right]} \right\} = \phi (p)$$ , where ?(p) is the well known normal density evaluated at itsp-quantile, i.e. $$\phi (p) = \frac{1}{{\sqrt {2\pi } }}\exp ( - \frac{1}{2}\chi _p^2 ) where \int_{ - \alpha }^{x_p } {\frac{1}{{\sqrt {2\pi } }}\exp ( - \frac{1}{2}\chi ^2 )} dx = p$$ . A sequence of martingales χ ₀ ⁿ ,n=1,2, … is constructed so as to satisfy \(\lim _{n \to \infty } (1/\sqrt n )V(\chi _0^n ) = \phi (p)\) .     

Minmax and maxmin of repeated games with incomplete information

For a class of 2-Person 0-sum repeated games with incomplete information,Aumann/Masch1er [1967] andStearns [1967] have given a necessary and sufficient condition for the existence of v_∞ (the value of the infinitely repeated game).Mertens/Zamir [1971] andMertens [1971/72] have given the formula (and thus proved the existence) of \(\mathop {\lim }\limits_{n \to \infty } \) v _n , the limit of the values of the games withn repetitions, for a much larger class of games than that treated byAumann/Maschler andSteams. In this paper we extend the Aumann-Maschler-Stearns results to the larger family of games studied byMertens [1971/72].     

Finite-buffer polling systems with threshold-based switching policy

We consider a system of two separate finite-buffer M / M / 1 queues served by a single server, where the switching mechanism between the queues is threshold-based, determined by the queue which is not being served. Applications may be found in data centers, smart traffic-light control and human behavior. Specifically, whenever the server attends queue i (\(Q_i\)) and the number of customers in the other queue, \(Q_j\) (\(i,j=1,2\); \(j\ne i\)), reaches its threshold level, the server immediately switches to \(Q_j\) whenever \(Q_i\) is below its threshold. When a served \(Q_i\) becomes empty we consider two scenarios: (i) non-work-conserving; and (ii) work-conserving. We present occasions where the non-work-conserving policy is more economical than the work-conserving policy when high switching costs are involved. An intrinsic feature of the process is an oscillation phenomenon: when the occupancy of \(Q_i\) decreases the occupancy of the other queue increases. This fact is illustrated and discussed. By formulating the system as a three-dimensional continuous-time Markov chain we provide a probabilistic analysis of the system and investigate the effects of buffer sizes and arrival rates, as well as service rates, on the system’s performance. Numerical examples are presented and extreme cases are investigated.     

On binary codes for identification

A code C ⊆ 𝔽₂ⁿ is called t‐identifying if the sets B_t(x) ∩ C are all nonempty and different. Constructions of t‐identifying codes are given. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 151–156, 2000     

Tungsten L transition line shapes and energy shifts resulting from ionization in warm dense matter

Spectra of the W L transitions in the energy range 8–12 keV from warm dense plasmas generated by the Naval Research Laboratory's Gamble II pulsed power machine were recorded by a newly developed high-resolution transmission-crystal X-ray spectrometer with ±2 eV accuracy. The discharges have up to 2 MV voltage, 0.5 MA current, and produce up to 2.4 MJ/cm^?3 energy density. The plasma-filled rod pinch (PFRP) diode produces a plasma with N_e ≈ 10²² cm^?3 and T_e ≈ 50 eV during the time of maximum X-ray emission. By analyzing the line shapes, it was determined that the Lβ₂ inner-shell transition from the 4d_5/2 level was shifted to higher energy by up to 23 eV relative to nearby Lβ transitions from n = 3 levels. In addition, the Lβ₂ transition was significantly broader and asymmetric compared to the n = 3 transitions. The energy shift of the Lβ₂ transition results from the ionization of electrons outside the 4d shell that perturbs the transition energies in the ions to higher values. The increased line width and asymmetry result from unresolved transitions from a range of ionization states up to +28. The ionization distribution was determined by comparison of the measured energy shifts and widths to calculated transition energies in W ions, and the ionization was correlated with Gamble discharge parameters such as the anode type and the high voltage delay time. This work demonstrates a new hard X-ray spectroscopic diagnostic technique for the direct measurement of the ionization distribution in warm dense plasmas of the heavy elements W through U that is independent of the other plasma parameters and does not require interpretation by hydrodynamic, atomic kinetics, and radiative simulation codes.     

Synthesis,Structure, and Optical Properties of New Cadmium Chalcogenide Clusters of the Type [Cd10E4(E'Ph)12(PR3)4], (E,E' = Te,Se, S)

New cadmium chalcogenide cluster molecules [Cd₁₀E₄(E'Ph)₁₂(PⁿPr₃)₄], E = Te, E' = Te ( 1 ) and [Cd₁₀E₄(E'Ph)₁₂ (PⁿPr₂Ph)₄] E = Te, E' = Se ( 2 ); E = Te E' = S ( 3 ); E = Se, E' = S ( 4 ) have been synthesized and structurally characterized by single crystal X‐ray structure analysis. The influence of the variation of the chalcogen atom is investigated by structural means and by optical spectroscopy. All cluster‐molecules have a broad emission in the blue‐visible range at low temperature as indicated by photo luminescence (PL) measurements. A clear classification of the emission peak position can be made based on the E' species suggesting that the emission is assigned to transitions associated with the cluster surface ligands. Photoluminescence excitation and absorption measurements display a systematic shift of the band gap to the higher energies with the variation of E and E' from Te to Se to S, as also occurs in the respective series of the bulk semiconductors.     

A microfluidic device for practical label-free CD4(+) T cell counting of HIV-infected subjects

Practical HIV diagnostics are urgently needed in resource-limited settings. While HIV infection can be diagnosed using simple, rapid, lateral flow immunoassays, HIV disease staging and treatment monitoring require accurate counting of a particular white blood cell subset, the CD4(+) T lymphocyte. To address the limitations of current expensive, technically demanding and/or time-consuming approaches, we have developed a simple CD4 counting microfluidic device. This device uses cell affinity chromatography operated under differential shear flow to specifically isolate CD4(+) T lymphocytes with high efficiency directly from 10 microliters of unprocessed, unlabeled whole blood. CD4 counts are obtained under an optical microscope in a rapid, simple and label-free fashion. CD4 counts determined in our device matched measurements by conventional flow cytometry among HIV-positive subjects over a wide range of absolute CD4 counts (R(2) = 0.93). This CD4 counting microdevice can be used for simple, rapid and affordable CD4 counting in point-of-care and resource-limited settings.     

A parametric study of human fibroblasts culture in a microchannel bioreactor

The culture of cells in a microbioreactor can be highly beneficial for cell biology studies and tissue engineering applications. The present work provides new insights into the relationship between cell growth, cell morphology, perfusion rate, and design parameters in microchannel bioreactors. We demonstrate the long-term culture of mammalian (human foreskin fibroblasts, HFF) cells in a microbioreactor under constant perfusion in a straightforward simple manner. A perfusion system was used to culture human cells for more than two weeks in a plain microchannel (130 microm x 1 mm x 2 cm). At static conditions and at high flow rates (>0.3 ml h(-1)), the cells did not grow in the microchannel for more than a few days. For low flow rates (<0.2 ml h(-1)), the cells grew well and a confluent layer was obtained. We show that the culture of cells in microchannels under perfusion, even at low rates, affects cell growth kinetics as well as cell morphology. The oxygen level in the microchannel was evaluated using a mass transport model and the maximum cell density measured in the microchannel at steady state. The maximum shear stress, which corresponds to the maximum flow rate used for long term culture, was 20 mPa, which is significantly lower than the shear stress cells may endure under physiological conditions. The effect of channel size and cell type on long term cell culture were also examined and were found to be significant. The presented results demonstrate the importance of understanding the relationship between design parameters and cell behavior in microscale culture system, which vary from physiological and traditional culture conditions.     

Multiple-instrument analyses of single micron-size particles.

Physical, chemical, and isotopic analyses of individual radioactive and other particles in the micron-size range, key tools in environmental research and in nuclear forensics, require the ability to precisely relocate particles of interest (POIs) in the secondary ion mass spectrometer (SIMS) or in another instrument, after having been located, identified, and characterized in the scanning electron microscope (SEM). This article describes the implementation, testing, and evaluation of the triangulation POIs re-location method, based on microscopic reference marks imprinted on or attached to the sample holder, serving as an inherent coordinate system. In SEM-to-SEM and SEM-to-SIMS experiments re-location precision better than 10 microm and 20 microm, respectively, is readily attainable for instruments using standard specimen stages. The method is fast, easy to apply, and facilitates repeated analyses of individual particles in different instruments and laboratories.