On busy period and sojourn time distributions in the M/G/1-EPS queue with catastrophes

We derive the Laplace-Stiltjes transforms of busy period and sojourn time distributions in the M/G/1 queue with egalitarian processor sharing (EPS) and the possibility of (external) catastrophes. Each arrival of the catastrophes immediately removes all the positive jobs (and hence unfinished work) in this non work-conserving queueing system. One of the main results is obtained by means of the so-called method of decomposition into delay elements introduced by the first author.     

Entropy maximised queueing networks with blocking and multiple job classes

The method of entropy maximisation (MEM) is applied in a state space partitioning mode for the approximation of the joint stationary queue length distribution of an M/M/1/N queue with finite capacity, N( > 1), multiple and distinct classes of jobs, R( > 1), under a complete buffer sharing scheme and mixed service disciplines drawn from the first-come-first-served (FCFS), last-come-first-served with (LCFS-PR) or without (LCFS-NPR) preemption and processor sharing (PS) rules. The marginal and aggregate maximum entropy (ME) queue length distributions and the associated blocking probabilities per class are also determined. These ME results in conjunction with the first moments of the effective flows are used, as building blocks, in order to establish a new product-form approximation for arbitrary exponential open queueing networks with multiple classes of jobs under repetitive-service (RS) blocking with random destination (RD). It is verified that the ME approximation reduces to the exact truncated solution of open multi-class reversible queueing networks. Numerical experiments demonstrate a good accuracy level of ME statistics in relation to simulation. Moreover, recent extentions of MEM for arbitrary GE-type queueing networks with RS-RD blocking and multiple classes of jobs are presented.     

Threshold quantum secret sharing based on single qubit

Based on unitary phase shift operation on single qubit in association with Shamir’s (t, n) secret sharing, a (t, n) threshold quantum secret sharing scheme (or (t, n)-QSS) is proposed to share both classical information and quantum states. The scheme uses decoy photons to prevent eavesdropping and employs the secret in Shamir’s scheme as the private value to guarantee the correctness of secret reconstruction. Analyses show it is resistant to typical intercept-and-resend attack, entangle-and-measure attack and participant attacks such as entanglement swapping attack. Moreover, it is easier to realize in physic and more practical in applications when compared with related ones. By the method in our scheme, new (t, n)-QSS schemes can be easily constructed using other classical (t, n) secret sharing.     

Verifiable threshold quantum secret sharing with sequential communication

A (t, n) threshold quantum secret sharing (QSS) is proposed based on a single d-level quantum system. It enables the (t, n) threshold structure based on Shamir’s secret sharing and simply requires sequential communication in d-level quantum system to recover secret. Besides, the scheme provides a verification mechanism which employs an additional qudit to detect cheats and eavesdropping during secret reconstruction and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. Moreover, the scheme is scalable in participant number and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (t, n) threshold QSS schemes based on d-level quantum system from other classical threshold secret sharing.     

A novel secret image sharing scheme using large primes

A secret image sharing scheme is any method of distributing shares of a secret image amongst a set of peers, such that the secret may be revealed only with participation of all members of a qualified set of peers. Following Shamir’s (t, n)–threshold scheme, we propose a novel lossy/lossless secret image sharing scheme, that improves existing schemes in terms of security and performance. As opposed to the usual convention of representing a digital image by a collection of 8–bit integer values, we consider 8b–bit values where b is a positive integer. This approach accommodates a larger finite field, which in turn produces a less intrusive secret image sharing scheme. Extensive empirical results are presented to demonstrate the efficiency and robustness of the proposed scheme.     

On a strategy for the maintenance of an unreliable channel of a one-server loss queue

A semi-Markov model of a single-server queue GI/G/1/0 is constructed with regard to server maintenance that is carried out at the end of customer service if the total operation time (counted from the moment of the most recent maintenance or restoration) reaches a certain amount of time during customer service. The stationary reliability and economic characteristics of the queue are obtained. A three-criterion optimization of the execution rate of maintenance is performed.     

Transit cosmological models with domain walls in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R,T</Emphasis>) gravity

We study the physical behavior of the transition of a 5D perfect fluid universe from an early decelerating phase to the current accelerating phase in the framework of f(R, T) theory of gravity in the presence of domain walls. The fifth dimension is not observed because it is compact. To determine the solution of the field equations, we use the concept of a time-dependent deceleration parameter which yields the scale factor a(t) = sinh^1/n(αt), where n and α are positive constants. For 0 < n ≤ 1, this generates a class of accelerating models, while for n > 1 the universe attains a phase transition from an early decelerating phase to the present accelerating phase, consistent with the recent observations. Some physical and geometric properties of the models are also discussed.     

Extensions and generalizations of smoothed perturbation analysis ina generalized semi-Markov process framework

Under a very general framework, both in terms of finite-time performance measures and system structure, the authors derive smoothed perturbation analysis (SPA) estimators and prove their unbiasedness. The commuting condition, which has been key in previous work, is not required a priori, and thus the framework includes such systems as the GI/G/1/K queue and multiclass queueing networks, which do not satisfy the commuting condition. The generality achieved is traded off against the fact that the estimator is not always easily implementable on a single sample path. The use of the commuting condition in a local sense is proposed to help simplify the estimators derived: queueing and multiclass queueing networks are used as illustrative examples. For a simple multiclass closed queueing network, some simulation results are provided. When the commuting condition is satisfied globally, the framework allows the recovery of previous results on IPA and SPA estimators as corollaries of the main theorems     

A real-time secret image sharing with fairness

When traditional secret image sharing techniques reconstructed the secret, they input the shares over t. While less than t shares can know nothing about the secret, the problem arises when there are more than t shares. The cheater can use this to put their share in the last. Therefore, fairness is a important objective of the secret image sharing. Tian et al. proposed the fairness secret sharing scheme in 2012. However, they generated v polynomials for one secret data and performed v-times to reconstruct the polynomial using Lagrange interpolation. Therefore, their scheme is unsuitableness in the real-time processing. The proposed scheme generates one polynomial for the one secret data based on the fairness concept of Tian et al.’s scheme. For the providing fairness, the proposed scheme hides the verification value at the random coefficient of the polynomial. During the secret image reconstruction procedure, each shadow image brought by a participant is verified for its fairness using XOR operation. Our scheme not only satisfies the fairness, but also is suitable for the real-time process. This helps to detect the participant from intentional provision of a false or cheating. In addition, our scheme uses the steganography technique for increasing the security protection purpose. The proposed scheme as a whole offers a high secure and effective mechanism for the secret image sharing that is not found in existing secret image sharing methods. In the experimental result, PSNR of the proposed scheme is average 44.67 dB. It is higher 4 dB than the previous schemes. The embedding capacity is also similar to the other schemes.     

Optimal Path Embedding in the Exchanged Crossed Cube

The (s + t + 1)-dimensional exchanged crossed cube, denoted as ECQ(s, t), combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ(s, t) has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ(s, t). We prove the result in ECQ(s, t): if s ≥ 3, t ≥ 3, for any two different vertices, all paths whose lengths are between \( \max \left\{9,\left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +4\right\} \) and 2 ^s+t+1 ? 1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ(s, t) is \( \left\lceil \frac{s+1}{2}\right\rceil +\left\lceil \frac{t+1}{2}\right\rceil +2 \). The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ(s, t) preserves the path embedding capability to a large extent, while it only has about one half edges of CQ _n .     

The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables

A new representation is proved of the solutions of initial boundary value problems for the equation of the form u _xx (x, t) + r(x)u _x (x, t) ? q(x)u(x, t) = u _tt (x, t) + μ(x)u _t (x, t) in the section (under boundary conditions of the 1st, 2nd, or 3rd type in any combination). This representation has the form of the Riemann integral dependent on the x and t over the given section.     

Partial and complete local diagnosis in computer systems with circulant structure

System diagnosis at multiple faults of multiplicity not greater than t is considered. The conditions when the state of each system module is only determined by the testing rusults of the physically connected modules (self-determination conditions) are analysed. The diagnosability conditions are established for the case when the self-determination conditions are not satisfied for any module. A new class of locally (t _r /t)-diagnosable systems is introduced, where t is the fault multiplicity and t _r is the multiplicity of faults at which the states of all system modules can be determined correctly and completely. The values of t _r are estimated. It is shown that the local t-diagnosability can be achieved by the system test redundancy.     

Queueing system with finite memory and jump intensity of the arrival process

We consider a single-server queueing system (QS) with finite memory and exponential service with parameter µ. The QS is fed by a doubly stochastic Poisson flow whose intensity λ(t) is a jump process. We propose a matrix and a functional-analytical method to study stationary and nonstationary characteristics of the QS; we also prove existence and uniqueness of a stationary regime and stabilization of a nonstationary regime of the QS. Results of numerical analysis are discussed.     

Meaningful (2, infinity) secret image sharing scheme based on flipping operations

In this paper, a new method to construct a secret image sharing (SIS) scheme is proposed, where a secret image is shared into several shares by a perfect secure way without any knowledge of cryptography. A basic algorithm implemented by flipping operations with probability for constructing a meaningful (2, 2) SIS scheme is first proposed. Neither codebook tailor-made requirement nor pixel expansion is required in the proposed scheme. Additionally, the meaningful shares by the proposed scheme can be directly generated without any extra data hiding process. During the decrypting procedure, the secret image is visually revealed by performing XOR operations on two meaningful shares. In the following stage, a meaningful (2, infinity) SIS scheme is extended underlying the basic algorithm, where the number of shares can be extended anytime. Further, no matter how large the number of the extended shares is, the visual qualities of both the meaningful share and revealed secret image remain unchanged. Finally, sufficient number of formal proofs are provided to validate the correctness of the proposed schemes, whose superiority is also demonstrated by the experimental results.     

Nonparametric estimation of signal amplitude in white Gaussian noise

We assume that a transmitted signal is of the form S(t)f(t), where f(t) is a known function vanishing at some points of the observation interval and S(t) is a function of a known smoothness class. The signal is transmitted over a communication channel with additive white Gaussian noise of small intensity ?. For this model, we construct an estimator for S(t) which is optimal with respect to the rate of convergence of the risk to zero as ? → 0.     

An approximate transient analysis of the M(t)/M/1 queue

An approach, based on recent work by Stern [56], is described for obtaining the approximate transient behavior of both the M/M/1 and M(t)/M/1 queues, where the notation M(t) indicates an exponential arrival process with time-varying parameter λ(t). The basic technique employs an M/M/1K approximation to the M/M/1 queue to obtain a spectral representation of the time-dependent behavior for which the eigen values and eigenvectors are real.Following a general survey of transient analysis which has already been accomplished, Stern's M/M/1/K approximation technique is examined to determine how best to select a value for K which will yield both accurate and computationally efficient results. It is then shown how the approximation technique can be extended to analyze the M(t)/M/1 queue where we assume that the M(t) arrival process can be approximated by a discretely time-varying Poisson process.An approximate expression for the departure process of the M/M/1 queue is also proposed which implies that, for an M(t)/M/1 queue whose arrival process is discretely time-varying, the departure process can be approximated as discretely time-varying too (albeit with a different time-varying parameter).In all cases, the techniques and approximations are examined by comparison with exact analytic results, simulation or alternative discrete-time approaches.     

On the Number of Edges of a Uniform Hypergraph with a Range of Allowed Intersections

We study the quantity p(n, k, t₁, t₂) equal to the maximum number of edges in a k-uniform hypergraph having the property that all cardinalities of pairwise intersections of edges lie in the interval [t₁, t₂]. We present previously known upper and lower bounds on this quantity and analyze their interrelations. We obtain new bounds on p(n, k, t₁, t₂) and consider their possible applications in combinatorial geometry problems. For some values of the parameters we explicitly evaluate the quantity in question. We also give a new bound on the size of a constant-weight error-correcting code.     

Comparison results for <Emphasis Type="Italic">K</Emphasis>-nonnegative double splittings of <Emphasis Type="Italic">K</Emphasis>-monotone matrices

This paper introduces the K-nonnegative double splitting of a K-monotone matrix using knowledge of the matrices that leave a cone \(K\subseteq \mathbb {R}^n\) invariant. The convergence of this splitting is studied. Comparison theorems for two K-nonnegative double splittings of a K-monotone matrix are obtained. The results generalize the corresponding results introduced by Song and Song (Calcolo 48:245–260, 2011) for nonnegative double splitting. Some examples are provided to illustrate the main results.     

Multidimensional analogs of the kendall equation for priority queueing systems: computational aspects

An analogy between celebrated Kendall equation for busy periods in the system M|GI|1 and analytical results for busy periods in the priority systemsM _r |GI _r |1 is drawn. These results can be viewed as generalizations of the functional Kendall equation. The methodology and algorithms of numerical solution of recurrent functional equations which appear in the analysis of such queueing systems are developed. The efficiency of the algorithms is achieved by acceleration of the numerical procedure of solving the classical Kendall equation. An algorithm of calculation of the system workload coefficient calculation is given.