Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the l_k-norm social cost --- the objective balances overall quality of service and fairness. We consider policies with different amount of knowledge about jobs: non-clairvoyant, strongly-local and local. The analysis relies on the smooth argument together with adequate inequalities, called smooth inequalities. With this unified framework, we are able to prove the following results. First, we study the inefficiency in l_k-norm social costs of a strongly-local policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). These results ensure that SPT is close to optimal with respect to the class of l_k-norm social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price of anarchy O(2^k). Second, we consider the makespan (l_infty-norm) social cost by making connection within the l_k-norm functions. We revisit some local policies and provide simpler, unified proofs from the framework's point of view. With the highlight of the approach, we derive a local policy Balance. This policy guarantees a price of anarchy of O(log m), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.Comment: 25 pages, 1 figur

Laser applications in medicine: studies at Centre for Advanced Technology

The article provides a brief overview of the work being carried out at Centre for Advanced Technology, Indore, on laser applications in medicine as well as on the development of medical laser systems

Synchrotron radiation sources INDUS-1 and INDUS-2

The synchrotron radiation sources, INDUS-1 and INDUS-2 are electron storage rings of 450 MeV and 2 GeV beam energies respectively. INDUS-1 is designed to produce VUV radiation whereas INDUS-2 will be mainly used to produce x-rays. INDUS-1 is presently undergoing commissioning whereas INDUS-2 is under construction. Both these rings have a common injector system comprising of a microtron and a synchrotron. Basic design features of these sources and their injector system are discussed in this paper. The radiation beamlines to be set up on these sources are also described

High speed plasma diagnostics for laser plasma interaction and fusion studies

Laser plasma interaction and fusion studies involve many high speed plasma diagnostics to determine the various parameters for explaining the physical processes taking place in plasma. Detection and analysis of short-term or transient radiations (X-ray and visible) are the bases for diagnosing the physical processes occurring during laser-plasma interaction or similar radiation-emitting processes. This paper reviews the development of various high speed plasma diagnostics which are not only applicable in determining the temporal, spatial and spectral properties of X-rays for this purpose but also have wide use in various other fields of research

Development of picosecond time resolution optical and X-ray streak cameras

We describe the development of an optical and an X-ray streak camera with picosecond time resolution. The entire peripheral electronics and testing systems have been developed indigenously. Both the streak cameras provide ~ 15 mm/1 ns streak rate with a sweep voltage of ~ 1 kV amplitude and rise time of 1 ns. The time and spatial resolution of the optical streak camera have been found to be ~ 17 ps and 100 μm respectively. The sweep pulse generator developed for this purpose provides a step pulse of rise time ≤ 1 ns and amplitude ~ 2 kV. The laser diode used for testing the optical streak camera provides multiple pulsation when the pump current is increased beyond a critical threshold

Output characteristics of a 400 MW Nd:glass laser system

The paper discusses the performance characteristics of a Nd: glass laser system designed for laser produced plasma studies. It consists of a Q-switched oscillator followed by two amplifier stages. The output behaviour of the oscillator, i.e. laser pulse duration, peak power and optimum coupling, has been studied and is in good agreement with theory. Gain characteristics of amplifiers were obtained as a function of various parameters. Energies in excess of 7 J with pulse durations as small as 18 nsec were obtained giving rise to 400 MW peak power

On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum

IR MPD CDF<SUB>3</SUB> in two-frequency IR fields

The effectiveness of various sets of laser frequencies was analyzed for two-frequency MPD of CDF3 molecule at the different pressures of buffer gas. It was shown that MPD yield increased compared to either single-frequency or two adjacent frequencies irradiation

Proposed method of spike suppression in solid-state lasers

A method is proposed to suppress the spikes in the output of solid-state lasers, using passive negative feedback. A saturable absorber, normally used for Q-switching the laser, is used in a modified laser resonator, so that the resonator losses increase with laser intensity. The rate equations of a laser with such a loss mechanism are solved numerically. Numerical results for a ruby laser are presented