Workload distributions in ASIP queueing networks

Queueing Systems - The workload of a generalized n-site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the...     

Nonoscillation theorems in convex sets

This paper presents a new and simple technique for a certain class of variational problems which includes many of the important problems of mathematical physics, e.g., the Brachistochrone, geodesies, and minimal surface of revolution problems. The technique uses Caratheodory's equivalent problems approach but combines two equivalent problems at the same time to get the sufficiency and uniqueness results. It does not use any of the classical sufficiency conditions such as the Weierstrass condition. The equations that we are led to by this new approach turn out to be the Hamilton-Jacobi and Euler-Lagrange equations for the problem, but here we have not had to use any of the classical Hamilton-Jacobi theory nor derivations to get its results (e.g., orthogonality of the extremals to the wave fronts) for this class of problems. The cases for one and n dependent variables are presented and illustrated. Implications and generalizations of the method are discussed.     

Laser photolysis studies of the photoinduced production of ion radicals in polymers

N₂-laser flash photolysis measurements of poly (N-vinylcarbazole) (PVCz) and N-isopropylcarbazole (NIPC) with p-dicyanobenzene (DCNB)_in dimethylformide (DMF) show an excitation intensity dependent quantum yield for for ion-radical production. The transient absorbance associated with the ion radical species together with light intensity dependent fluorescence decay curves demonstrate that excitation annihilation processes can compete effectively with ion-radical formation at high excitation intensities in this polymer.     

Target-Decoy Approach and False Discovery Rate: When Things May Go Wrong

The target-decoy approach (TDA) has done the field of proteomics a great service by filling in the need to estimate the false discovery rates (FDR) of peptide identifications. While TDA is often viewed as a universal solution to the problem of FDR evaluation, we argue that the time has come to critically re-examine TDA and to acknowledge not only its merits but also its demerits. We demonstrate that some popular MS/MS search tools are not TDA-compliant and that it is easy to develop a non-TDA compliant tool that outperforms all TDA-compliant tools. Since the distinction between TDA-compliant and non-TDA compliant tools remains elusive, we are concerned about a possible proliferation of non-TDA-compliant tools in the future (developed with the best intentions). We are also concerned that estimation of the FDR by TDA awkwardly depends on a virtual coin toss and argue that it is important to take the coin toss factor out of our estimation of the FDR. Since computing FDR via TDA suffers from various restrictions, we argue that TDA is not needed when accurate p-values of individual Peptide-Spectrum Matches are available.     

Shrinkage of de Morgan formulae under restriction

It is shown that a random restriction leaving only a fraction ? of the input variables unassigned reduces the expected de Morgan formula size of the induced function by a factor of O(E^(5?√2)/2) = O(?^1.63). (A de Morgan, or unate, formula is a formula over the basis {∧, ∨, ¬}.) This improves a long-standing result of O(?^1.5) by Subbotovskaya and a recent improvement to O(?^(21?√73)/8) = O(?^1.55) by Nisan and Impagliazzo. The New exponent yields an increased lower bound of n^{(7?√3)/2?o(1)} = Ω(n^2.63) for the de Morgan formula size of a function in P defined by Andreev. This is the largest formula size lower bound known, even for functions in NP. © 1993 John Wiley & Sons, Inc.     

Integrable measure equivalence and rigidity of hyperbolic lattices

We study rigidity properties of lattices in $\operatorname {Isom}(\mathbf {H}^{n})\simeq \mathrm {SO}_{n,1}({\mathbb{R}})$ , n≥3, and of surface groups in $\operatorname {Isom}(\mathbf {H}^{2})\simeq \mathrm {SL}_{2}({\mathbb{R}})$ in the context of integrable measure equivalence. The results for lattices in $\operatorname {Isom}(\mathbf {H}^{n})$ , n≥3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the lack of Mostow rigidity for n=2 we show that cocompact lattices in $\operatorname {Isom}(\mathbf {H}^{2})$ allow a similar integrable measure equivalence classification.     

Analysis of customers’ impatience in queues with server vacations

Many models for customers impatience in queueing systems have been studied in the past; the source of impatience has always been taken to be either a long wait already experienced at a queue, or a long wait anticipated by a customer upon arrival. In this paper we consider systems with servers vacations where customers’ impatience is due to an absentee of servers upon arrival. Such a model, representing frequent behavior by waiting customers in service systems, has never been treated before in the literature. We present a comprehensive analysis of the single-server, M/M/1 and M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form results. In particular, we show that the proportion of customer abandonments under the single-vacation regime is smaller than that under the multiple-vacation discipline. This work was supported by the Euro-Ngi network of excellence.     

Discrete time queues with delayed information

We study the behavior of a single-server discrete-time queue with batch arrivals, where the information on the queue length and possibly on service completions is delayed. Such a model describes situations arising in high speed telecommunication systems, where information arrives in messages, each comprising a variable number of fixed-length packets, and it takes one unit of time (a slot) to transmit a packet. Since it is not desirable to attempt service when the system may be empty, we study a model where we assume that service is attempted only if, given the information available to the server, it is certain that there are messages in the queue. We characterize the probability distribution of the number of messages in the queue under some general stationarity assumptions on the arrival process, when information on the queue size is delayedK slots, and derive explicit expressions of the PGF of the queue length for the case of i.i.d. batch arrivals and general independent service times. We further derive the PGF of the queue size when information onboth the queue length and service completion is delayedK=1 units of time. Finally, we extend the results to priority queues and show that when all messages are of unit length, thec rule remains optimal even in the case of delayed information.     

On the numerical range of a Volterra operator in Lp

LetA be the linear operator inL _p (0, 1), 1<p<∞,p≠2, defined by ,x∈L _p (0, 1),s∈[0,1]. We show that the real values of numbers in the numerical range ofA have maximum , whereq=p/(p−1). This amounts to an inequality between integrals, for which we determine the case of equality.     

A K-step look-ahead analysis of value iteration algorithms for Markov decision processes

We introduce and analyze a general look-ahead approach for Value Iteration Algorithms used in solving both discounted and undiscounted Markov decision processes. This approach, based on the value-oriented concept interwoven with multiple adaptive relaxation factors, leads to accelerating procedures which perform better than the separate use of either the concept of value oriented or of relaxation. Evaluation and computational considerations of this method are discussed, practical guidelines for implementation are suggested and the suitability of enhancing the method by incorporating Phase 0, Action Elimination procedures and Parallel Processing is indicated. The method was successfully applied to several real problems. We present some numerical results which support the superiority of the developed approach, particularly for undiscounted cases, over other Value Iteration variants.