Perfect Simulation of M/G/cM/G/c Queues

In this paper we describe a perfect simulation algorithm for the stable $M/G/c$ queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how to build a dominated CFTP algorithm for perfect simulation of the super-stable $M/G/c$ queue operating under First Come First Served discipline, with dominating process provided by the corresponding $M/G/1$ queue (using Wolff's sample path monotonicity, which applies when service durations are coupled in order of initiation of service), and exploiting the fact that the workload process for the $M/G/1$ queue remains the same under different queueing disciplines, in particular under the Processor Sharing discipline, for which a dynamic reversibility property holds. We generalize Sigman's construction to the stable case by comparing the $M/G/c$ queue to a copy run under Random Assignment. This allows us to produce a naive perfect simulation algorithm based on running the dominating process back to the time it first empties. We also construct a more efficient algorithm that uses sandwiching by lower and upper processes constructed as coupled $M/G/c$ queues started respectively from the empty state and the state of the $M/G/c$ queue under Random Assignment. A careful analysis shows that appropriate ordering relationships can still be maintained, so long as service durations continue to be coupled in order of initiation of service. We summarize statistical checks of simulation output, and demonstrate that the mean run-time is finite so long as the second moment of the service duration distribution is finite.Comment: 28 pages, 5 figure

Optimal co-adapted coupling for the symmetric random walk on the hypercube

Let X and Y be two simple symmetric continuous-time random walks on the vertices of the n-dimensional hypercube, Z2n. We consider the class of co-adapted couplings of these processes, and describe an intuitive coupling which is shown to be the fastest in this class

Wind-tunnel acoustic results of two rotor models with several tip designs

A three-phase research program has been undertaken to study the acoustic signals due to the aerodynamic interaction of rotorcraft main rotors and tail rotors. During the first phase, two different rotor models with several interchangeable tips were tested in the Langley 4- by 7-Meter Tunnel on the U.S. Army rotor model system. An extensive acoustic data base was acquired, with special emphasis on blade-vortex interaction (BVI) noise. The details of the experimental procedure, acoustic data acquisition, and reduction are documented. The overall sound pressure level (OASPL) of the high-twist rotor systems is relatively insensitive to flight speed but generally increases with rotor tip-path-plane angle. The OASPL of the high-twist rotors is dominated by acoustic energy in the low-frequency harmonics. The OASPL of the low-twist rotor systems shows more dependence on flight speed than the high-twist rotors, in addition to being quite sensitive to tip-path-plane angle. An integrated band-limited sound pressure level, limited by 500 to 3000 Hz, is a useful metric to quantify the occurrence of BVI noise. The OASPL of the low-twist rotors is strongly influenced by the band-limited sound levels, indicating that the blade-vortex impulsive noise is a dominant noise source for this rotor design. The midfrequency acoustic levels for both rotors show a very strong dependence on rotor tip-path-plane angle. The tip-path-plane angle at which the maximum midfrequency sound level occurs consistently decreases with increasing flight speed. The maximum midfrequency sound level measured at a given location is constant regardless of the flight speed

MARKET-STRUCTURE DETERMINANTS OF NATIONAL BRAND-PRIVATE LABEL PRICE DIFFERENCES OF MANUFACTURED FOOD PRODUCTS

This paper estimates the relationships between market structure and the Lerner index of monopoly constructed from price data on processed food products sold through grocery stores. A theoretical model of a differentiated oligopoly specifies two determinants of price-cost margins: the Herfindahl-Hirschman index of seller concentration adjusted for the elasticity of demand and the industry advertising-to-sales ratio. The results indicate that the three principal determinants of price-cost margin variation, in order of their impacts, are: advertising intensity, elasticity of demand, and concentration. Previous structure-performance studies that did not incorporate the elasticity of demand were probably misspecified.Agribusiness, Demand and Price Analysis,

NEW ESTIMATES OF WELFARE AND CONSUMER LOSSES IN U.S. FOOD MANUFACTURING

In the past 15 years, industrial-organization economists have significantly expanded the range of algorithms for calculating welfare losses due to imperfect competition. We compare eleven empirical estimates of economic losses due to market power in 47 U.S. food manufacturing industries, almost all of them previously unpublished. Each of the studies incorporate different theoretical assumptions about demand conditions, supply conditions, or industry pricing behavior; or they utilize various data sources, time periods, and assumptions about the proper competitive benchmark. The estimates of average allocative losses due imperfect competition range from 0.2 percent to an impossibly high 289 percent of industry output; consumer losses range from 6.0 percent to 816 percent. However, there is a high degree of congruence in the rankings of economic losses due to market power. Hence, from the perspective of antitrust enforcement, the choice of industry targets has not been greatly altered by advances in estimation techniques.Agribusiness,

A noise study of the A-6 airplane and techniques for reducing its aural detection distance

A study was undertaken to determine the noise reduction potential of the A-6 airplane in order to reduce its aural detection distance. Static and flyby noise measurements were taken to document the basic airplane signature. The low-frequency noise which is generally most critical for aural detection was found to be broad-band in nature from this airplane, and its source is the turbojet engine exhaust. High-frequency compressor noise, which is characteristic of turbojet powerplants, and which is prominent at close range for this airplane, has no measurable effect on aural detection distance. The use of fluted-engine exhaust nozzles to change the far-field noise spectra is suggested as a possible means for reducing the aural detection distances. Detection distances associated with eight-lobe and four-lobe nozzles are estimated for a 1,000-foot altitude and grassy terrain to decrease from 4 miles to about 3 miles, and from 3 miles to about 2 miles for a 300-foot altitude and grassy terrain

§230 and Tinfoil Hats: What Conspiracy Theories Teach Us About the Marketplace of Ideas and Online Speech

Famously imputed into First Amendment jurisprudence by Justice Oliver Wendell Holmes, the Marketplace of Ideas is a foundational paradigm in free speech theory. However, current trends in social discourse suggest the Marketplace has crashed. Conspiracy theories illustrate this crash as a story of unintended consequences and, paradoxically, a consequence of judicial and legislative efforts to prevent it. Acknowledging the popularity and widespread use of the internet and social media, I explore solutions to rejuvenate the Marketplace of Ideas and better align its prominence in First Amendment doctrine with the reality of the current speech landscape