A Stochastic Model of Fragmentation in Dynamic Storage Allocation

We study a model of dynamic storage allocation in which requests for single units of memory arrive in a Poisson stream at rate λ and are accommodated by the first available location found in a linear scan of memory. Immediately after this first-fit assignment, an occupied location commences an exponential delay with rate parameter μ, after which the location again becomes available. The set of occupied locations (identified by their numbers) at time t forms a random subset St of {1,2, . . .}. The extent of the fragmentation in St, i.e. the alternating holes and occupied regions of memory, is measured by (St) - |St |. In equilibrium, the number of occupied locations, |S|, is known to be Poisson distributed with mean ρ = λ/μ. We obtain an explicit formula for the stationary distribution of max (S), the last occupied location, and by independent arguments we show that (E max (S) - E|S|)/E|S| → 0 as the traffic intensity ρ → ∞. Moreover, we verify numerically that for any ρ the expected number of wasted locations in equilibrium is never more than 1/3 the expected number of occupied locations. Our model applies to studies of fragmentation in paged computer systems, and to containerization problems in industrial storage applications. Finally, our model can be regarded as a simple concrete model of interacting particles [Adv. Math., 5 (1970), pp. 246–290]

Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl

An Analogy between Bin Packing Problem and Permutation Problem: A New Encoding Scheme

Part 2: Knowledge Discovery and SharingInternational audienceThe bin packing problem aims to pack a set of items in a minimum number of bins, with respect to the size of the items and capacity of the bins. This is an NP-hard problem. Several approach methods have been developed to solve this problem. In this paper, we propose a new encoding scheme which is used in a hybrid resolution: a metaheuristic is matched with a list algorithm (Next Fit, First Fit, Best Fit) to solve the bin packing problem. Any metaheuristic can be used but in this paper, our proposition is implemented on a single solution based metaheuristic (stochastic descent, simulated annealing, kangaroo algorithm). This hybrid method is tested on literature instances to ensure its good results

Delegation and coordination with multiple threshold public goods: experimental evidence

When multiple charities, social programs and community projects simultaneously vie for funding, donors risk mis-coordinating their contributions leading to an inefficient distribution of funding across projects. Community chests and other intermediary organizations facilitate coordination among donors and reduce such risks. To study this, we extend a threshold public goods framework to allow donors to contribute through an intermediary rather than directly to the public goods. Through a series of experiments, we show that the presence of an intermediary increases public good success and subjects’ earnings only when the intermediary is formally committed to direct donations to socially beneficial goods. Without such a restriction, the presence of an intermediary has a negative impact, complicating the donation environment, decreasing contributions and public good success.When multiple charities, social programs and community projects simultaneously vie for funding, donors risk mis-coordinating their contributions leading to an inefficient distribution of funding across projects. Community chests and other intermediary organizations facilitate coordination among donors and reduce such risks. To study this, we extend a threshold public goods framework to allow donors to contribute through an intermediary rather than directly to the public goods. Through a series of experiments, we show that the presence of an intermediary increases public good success and subjects’ earnings only when the intermediary is formally committed to direct donations to socially beneficial goods. Without such a restriction, the presence of an intermediary has a negative impact, complicating the donation environment, decreasing contributions and public good success

First Observation of τ→3πηντ\tau\to 3\pi\eta\nu_{\tau} and τ→f1πντ\tau\to f_{1}\pi\nu_{\tau} Decays

We have observed new channels for $\tau$ decays with an $\eta$ in the final state. We study 3-prong tau decays, using the $\eta\to\gamma\gamma$ and \eta\to 3\piz decay modes and 1-prong decays with two \piz's using the $\eta\to\gamma\gamma$ channel. The measured branching fractions are \B(\tau^{-}\to \pi^{-}\pi^{-}\pi^{+}\eta\nu_{\tau}) =(3.4^{+0.6}_{-0.5}\pm0.6)\times10^{-4} and \B(\tau^{-}\to \pi^{-}2\piz\eta\nu_{\tau} =(1.4\pm0.6\pm0.3)\times10^{-4}. We observe clear evidence for $f_1\to\eta\pi\pi$ substructure and measure \B(\tau^{-}\to f_1\pi^{-}\nu_{\tau})=(5.8^{+1.4}_{-1.3}\pm1.8)\times10^{-4}. We have also searched for $\eta'(958)$ production and obtain 90% CL upper limits \B(\tau^{-}\to \pi^{-}\eta'\nu_\tau)<7.4\times10^{-5} and \B(\tau^{-}\to \pi^{-}\piz\eta'\nu_\tau)<8.0\times10^{-5}.Comment: 11 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN