The cμ rule revisited

The cμ rule is optimal for arbitrary arrival processes provided that the service times are geometric and the service discipline is preemptive.

Sojourn times and the overtaking condition in Jacksonian networks

Consider an open multiclass Jacksonian network in equilibrium and a path such that a customer travelling along it cannot be overtaken directly by a subsequent arrival or by the effects of subsequent arrivals. Then the sojourn times of this customer in the nodes constituting the path are all mutually independent and so the total sojourn time is easily calculated. Two examples are given to suggest that the non-overtaking condition may be necessary to ensure independence when there is a single customer class.

Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling strategies the strategy SEPT maximizes the expected total reward. This strategy is one which whenever a machine becomes available starts processing the remaining job with the shortest expected processing time. In particular, for r(t) = – t, this strategy minimizes the expected flowtime.

On the Speed-Dependent Hard Collision Lineshape Models: Application to C2H2 Perturbed by Xe

Three infrared absorption lines of the nu5 band of C2H2 diluted by Xe at pressures ranging from 40 to 300 mbar have been recorded at high resolution near 750 cm-1, using a tunable diode-laser spectrometer. Their lineshapes have been first analyzed by means of models using either the Dicke narrowing effect or the absorber speed-dependent collisional broadening and shifting. None of these models have given satisfactory results over the full pressure range of the perturber. It is shown that a correct treatment must include both line narrowing effects. We have investigated two possibilities of doing so: a convolution between two profiles corresponding to each effect and a noncorrelated and speed-dependent Rautian profile that we have developed here. The latter lineshape model appears to be the most appropriate. Copyright 1997 Academic Press. Copyright 1997Academic Press

Collision Cross Sections, Pressure-Broadening Coefficients and Second Virial Coefficients for the Acetylene-Argon Complex: Experiments and Calculations on a New Potential Energy Surface

Integral cross sections and pressure-broadening coefficients have been measured by molecular beam scattering and by high-resolution infrared spectroscopy, respectively, for the acetylene-argon system. A new potential energy surface (PES) is proposed to describe structure and dynamical properties of this prototypical weakly bound complex. The PES has been parametrized exploiting a novel atom-bond pairwise additive scheme and has been fitted to the experimental data. Calculations of the scattering cross sections (both differential and integral), pressure-broadening, and second virial coefficients have been performed using both the present and also the most recent ab initio PES available in the literature. Analysis of the new experimental data indicates that the anisotropy of the interaction in the well region should be larger than that obtained in ab initio calculations. This is also in line with previous spectroscopic results.

Individually optimal routing in parallel systems

Jobs arrive at a buffer from which there are several parallel routes to a destination. A socially optimal policy is one which minimizes the average delay of all jobs, whereas an individually optimal policy is one which, for each job, minimizes its own delay, with route preference given to jobs at the head of the buffer. If there is a socially optimal policy for a system with no arrivals, which can be implemented by each job following a policy γ in such a way that no job ever utilizes a previously declined route, then we show that such a γ is an individually optimal policy for each job. Moreover γ continues to be individually optimal even if the system has an arbitrary arrival process, subject only to the restriction that past arrivals are independent of future route-traversal times. Thus, γ is an individually optimal policy which is insensitive to the nature of the arrival process. In the particular case where the times to traverse the routes are exponentially distributed with a possibly different mean time for each of the parallel routes, then such an insensitive individually optimal policy does in fact exist and is moreover trivially determined by certain threshold numbers. A conjecture is also made about more general situations where such individually optimal policies exist.

Nitrogen Broadening of Acetylene Lines in the nu5 Band at Low Temperature

N2-broadening coefficients have been measured for 22 lines of C2H2 at 173.4 K in the P and R branches of the nu5 band, using a tunable diode-laser spectrometer. The lines with J values ranging from 1 to 29 are located in the spectral range of 661-762 cm-1. The collisional widths obtained by Rautian profiles fitting closely the measured spectral shape of the lines are slightly larger than those derived from Voigt profiles. Semiclassical calculations of these broadenings have been performed by considering, in addition to electrostatic interactions, successively the atom-atom model and the Tipping-Herman intermolecular potential. The results obtained, which for some of them are in good agreement with the experimental data, depend significantly on the isotropic potential used to describe the trajectory model. By comparing broadening coefficients at room and low temperature, their temperature dependencies have been determined both experimentally and theoretically Copyright 1998 Academic Press.

A note on Norton's theorem for queuing networks

We propose a simple proof of Norton's theorem for multiclass quasireversible networks.

Line Intensities in the nu6 Band of CH3F at 8.5 μm

Infrared absolute line intensities of the nu6 band of CH3F have been measured around 8.5 μm using a diode-laser spectrometer. These line strengths were obtained by the equivalent width method and, for 13 lines, by fitting a Rautian profile to the measured shape of the lines. From these results, we have deduced the vibrational band strength to be S0v = 9.66 +/- 0.13 cm-2 atm-1 at 296 K and the first Herman-Wallis factors.

On the equivalence of flows in networks of queues

Consider a network of queues in equilibrium. When are the flows observed on two given links of that network equivalent, i.e., when do they have the same law?

The verification of the equivalence of two such point processes is first reduced to an algebraic problem by a technique based on the filtering theory.

This method is then used to show that the arrival and departure processes at an M/M/1 node in a Jackson network are not always equivalent, thereby contradicting a conjecture made in [8]. An example where that equivalence holds is also given; it provides new results on the time reversibility of some familiar processes.

Line-Mixing Effects in He- and N(2)-Broadened Sigma <-- Pi Infrared Q Branches of C(2)H(2)

Two Q branches of C(2)H(2) near 716.3 and 719.9 cm(-1) belonging to the (nu(4) + nu(5))(0) - nu(1f)(4) and 2nu(0)(5)-nu(1f)(5) bands, of Sigma <-- Pi symmetry, have been studied for He and N(2) perturbers at pressures ranging from 0.05 to 1 atm, using a tunable diode-laser spectrometer. To interpret the line-mixing effects observed in these spectra, we have applied a model based on the energy-corrected sudden approximation whose parameters have been only derived from line-broadening data. This model provides satisfactory agreement with experimental bandshapes for both bands and perturbers, especially at pressures higher than 0.1 atm. The Q-branch profiles for C(2)H(2)-He are higher and narrower than those obtained for C(2)H(2)-N(2) at the same pressure as the result of smaller broadening coefficients and larger line-mixing effects in the former system. Copyright 2000 Academic Press.

On the existence of finite-dimensional filters for Markov-modulated traffic

A Markov-modulated Poisson process (MMPP) is a Poisson process whose rate is a finite Markov chain. The Poisson process is a simple MMPP. An MMPP/M/1 queue is a queue with MMPP arrivals, an infinite capacity, and a single exponential server. We prove that the output of an MMPP/M/1 queue is not an MMPP process unless the input is Poisson. We derive this result by analyzing the structure of the non-linear filter of the state given the departure process of the queue. The practical relevance of the result is that it rules out the existence of simple finite descriptions of queueing networks with MMPP inputs.

High-Resolution Spectra of Carbon Disulfide (12)C(32)S(2) in the Region of 2 µm

By Fourier transform, spectra were recorded for carbon disulfide (12)C(32)S(2) in the region of weak absorption near 5200 cm(-1). The data were fitted and new molecular constants were determined. We also observed a band of the isotopomer (12)C(32)S(34)S. A self-broadening coefficient gamma(0) of 0.120 cm(-1). atm(-1) was obtained by recording two lines of the nu(3)-nu(1) band with a tunable diode laser. Copyright 1999 Academic Press.

Correlated and Noncorrelated Lineshape Models under Small Lineshift Condition: Analysis of Self-Perturbed CH3D

The 14 transitions belonging to the P branch of the nu3 band of CH3D, near 1250 cm-1, have been measured with a tunable diode-laser spectrometer. These lines, recorded at a total pressure ranging from 1 to 60 mbar, have been analyzed by means of soft and hard collision lineshape models. We emphasize the equivalence between the correlated and noncorrelated profiles, when the collisional lineshift may be neglected. As a result, new measurements of linestrengths, collisional self-broadening coefficients, and other parameters related to the Dicke effect are provided at room temperature. It is also shown that the instrumental distortions must be properly taken into account to avoid systematic errors on the fitted lineshape parameters, especially at low pressure. The broadening coefficients are compared with results calculated from a semiclassical theory, performed by considering, in addition to electrostatic interactions involving the octopole and hexadecapole moments of CH3D, the dispersion contributions. Copyright 1998 Academic Press.

Line-Mixing Effects in Q Branches of CO2

A theoretical model based on the energy corrected sudden (ECS) approximation is used in order to account for line-mixing effects in Delta left and right arrow Pi infrared Q branches of 12C16O2. Its quality is demonstrated by comparisons with numerous laboratory spectra of CO2-He and CO2-N2 mixtures: three Q branches in the 4 and 17 μm regions are investigated at room temperature in a wide pressure range. The influence of mixing between Q(J) lines associated with odd and even values of the rotational quantum number J is demonstrated and analyzed in detail. It is shown that, in contrast to available fitting law approaches, the ECS model correctly predicts the influence of the parity of the rotational quantum numbers J and J' on coupling between the Q(J) and Q(J') lines. Comparisons between the effects of collisions of CO2 with N2 and He are made and analyzed. They show that these two systems involve different line couplings within the Q branch. Copyright 1997 Academic Press. Copyright 1997Academic Press

Oxygen Broadening of Acetylene Lines in the nu5 Band at Low Temperature

O2-broadening coefficients have been measured for 29 lines of C2H2 at 173.2 K in the P and R branches of the nu5 band near 14 µm, using a tunable diode-laser spectrometer. The collisional widths obtained by Rautian profiles closely fitting the measured spectral shape of the lines are slightly larger than those derived from Voigt profiles. The broadening coefficients are compared with results calculated from a semiclassical theory, performed by considering, in addition to electrostatic interactions involving the hexadecapole moments of C2H2 and O2, the atom-atom Lennard-Jones model. By comparing broadening coefficients at 297 and 173.2 K from a simple power law, the temperature dependence of these broadenings has been determined both experimentally and theoretically. Copyright 1999 Academic Press.

N(2)-Broadening for Methyl Chloride at Low Temperature by Diode-Laser Spectroscopy

Using a tunable diode-laser spectrometer, we have measured N(2)-broadening coefficients of 87 individual rovibrational lines in the P and R branches of the nu(3) band of methyl chloride (CH(3)(35)Cl) at 203.2 K. These lines with J values ranging from 2 to 22 and K from 0 to 6 are located in the range 711-751 cm(-1). Most of the collisional widths are obtained by modeling the spectral region from the superposition of overlapping Voigt or Rautian profiles. We have reviewed and completed previous measurements of N(2)-broadening coefficients at room temperature in the nu(3) band, in order to compare them to the low-temperature data. A semiclassical calculation, including electrostatic, induction, and dispersion energy contributions, has provided results that are in reasonable agreement with the experimental data at room temperature, but generally larger than the data at low temperature for small or medium J values. The temperature dependence of the collisional broadenings derived from a simple power law has been determined both experimentally and theoretically. Copyright 2001 Academic Press.

Absolute Absorption Intensities in the Fundamental nu2 and nu5 Bands of 12CH3F

The absolute strengths of 93 lines belonging to the nu2 and nu5 bands of methyl fluoride were measured in the range of 1416-1503 cm-1 using a tunable diode-laser (TDL) spectrometer. These experimental line intensities were obtained from the equivalent width method. The intensities were analyzed within a dyad system, required to account properly for the strong Coriolis coupling between nu2 and nu5. The fit to the experimental data led to the determination of the dipole moment derivatives partial differentialµ/ partial differentialq2 and partial differentialµ/ partial differentialq5, as well as the first-order Herman-Wallis correction in K to partial differentialµ/ partial differentialq5. The intensities were reproduced with an overall standard deviation of 1.44%, to be compared with a mean experimental uncertainty equal to 1.58%. The values derived for the vibrational band strengths of nu2 and nu5 are 2.124 (18) cm-2.atm-1 and 36.96 cm-2.atm-1 at 296 K, respectively. Copyright 1998 Academic Press.