Using estimated entropy in a queueing system with dynamic routing.

In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message's waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method's accuracy through comparison with simulations

Balanced Allocations and Double Hashing

Double hashing has recently found more common usage in schemes that use multiple hash functions. In double hashing, for an item $x$, one generates two hash values $f(x)$ and $g(x)$, and then uses combinations $(f(x) +k g(x)) \bmod n$ for $k=0,1,2,...$ to generate multiple hash values from the initial two. We first perform an empirical study showing that, surprisingly, the performance difference between double hashing and fully random hashing appears negligible in the standard balanced allocation paradigm, where each item is placed in the least loaded of $d$ choices, as well as several related variants. We then provide theoretical results that explain the behavior of double hashing in this context.Comment: Further updated, small improvements/typos fixe

Statistically-secure ORAM with O~(log⁡2n)\tilde{O}(\log^2 n) Overhead

We demonstrate a simple, statistically secure, ORAM with computational overhead $\tilde{O}(\log^2 n)$; previous ORAM protocols achieve only computational security (under computational assumptions) or require $\tilde{\Omega}(\log^3 n)$ overheard. An additional benefit of our ORAM is its conceptual simplicity, which makes it easy to implement in both software and (commercially available) hardware. Our construction is based on recent ORAM constructions due to Shi, Chan, Stefanov, and Li (Asiacrypt 2011) and Stefanov and Shi (ArXiv 2012), but with some crucial modifications in the algorithm that simplifies the ORAM and enable our analysis. A central component in our analysis is reducing the analysis of our algorithm to a "supermarket" problem; of independent interest (and of importance to our analysis,) we provide an upper bound on the rate of "upset" customers in the "supermarket" problem

Using estimated entropy in a queueing system with dynamic routing.

In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message's waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method's accuracy through comparison with simulations

Using estimated entropy in a queueing system with dynamic routing.

In this article we consider a discrete time two server queueing system with dynamic routing. We prove logarithmic asymptotics for the liklihood that a message from a source that divides its messages between the two servers in a way that minimizes the message's waiting time experiences a large waiting time. We demonstrate the merit of this asymptotic by comparing its predictions with experimental data. We illustrate how estimated entropies of the traffic streams can be used to predict the likelihood of long waiting times and demonstrate the method's accuracy through comparison with simulations

Network Protocol Performance Bounding Exploiting Properties of Infinite Dimensional Linear Equations ⋆

Abstract. This paper presents a quite versatile and widely applicable performance analysis methodology that has been applied for the study of network resource allocation protocols in the past. It is based on the identification ofrenewal cycles of theoperation of thesystem andthe setting up of recursive equations with respect to quantities-indices defined over the renewal cycles and sessions that appear within. Application of the expectation operator on these equations leads to infinite dimensional systems of linear equations which are shown to posses certain properties leading to rigorous and almost arbitrarily tight bounds on various performance metrics of interest. The special case of a random access protocol is used as an example in order to illustrate the derivation of the recursive equations capturing the protocol dynamics and system inputs. Finally, some other examples of application of the methodology are briefly discussed, illustrating the versatility and powerfulness of the approach. This analysis methodology can be quite useful for understanding the behavior of current complex and large scale networking environments, as well as assessing their scalability, stability and performance.

Large deviations provide good approximation to queueing system with dynamic routing. Technical Paper DIAS-STP-04-15

We consider a system with two infinite-buffer FCFS servers (of speed one). The arrivals processes are three independent Poisson flows Ξi, of rates λi, i = 0; 1; 2, each with IID task service times. The tasks from Ξi are directed to server i; i = 1; 2 (dedicated traffic). The tasks from Ξ0 are directed to the server that has the shorter workload in the buffer at the time of arrival (opportunistic traffic). We compare the analytical data for the large deviation (LD) probabilities for the virtual waiting time in flow Ξ0 and empercial delay freqencies from simulations