System Steady-state Probabilities Research Articles

Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage properties.

We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and thermodynamic efficiency. The ratchet's broken spatial symmetry rectifies the particles' self-propelled motion, resulting in a positive current that peaks at finite values of the diffusion strength, ratchet height, and particle self-propulsion speed. Similar nonmonotonic behavior is also observed for the extractable power and efficiency. We find the optimal apex position for generating maximum current varies with diffusion and that entropy production can have nonmonotonic dependence on diffusion. In particular, for vanishing diffusion, entropy production remains finite when particle self-propulsion is weaker than the ratchet force. Furthermore, power extraction with near-perfect efficiency is achievable in certain parameter regimes due to the simplifications afforded by modeling "dry" active particles. In the final part, we derive mean first-passage times and splitting probabilities for different boundary and initial conditions. This work connects the study of work extraction from active matter with exactly solvable active particle models and will therefore facilitate the design of active engines through these analytic results.

Hybrid NOMA Protocol with Relay Adaptive AF/DF Collaboration and Its Modeling Analysis in NB-IoT

In order to meet the demand for large-scale device access in Narrowband Internet of Things (NB-IoT) and to overcome the problem that some resources are wasted due to the use of single decode-and-forward (DF) or amplify-and-forward (AF) collaboration in traditional collaborative communication, this paper introduces a non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) hybrid access method into the NB-IoT and proposes a new Hybrid NOMA transmission protocol with relay adaptively selectable collaboration, which is represented as an algorithm. Based on this protocol, we classify the whole transmission process into five states after deriving the outage probability of each link. We then consider the system as a discrete-time Markov model, the closed expressions of the system outage probability and throughput are derived based on the system steady-state probability. In order to improve the system’s reliability, we further optimize the above protocol by allowing the source node to retransmit the unsuccessful received superimposed signals a limited number of times. Numerical results and simulations show that the outage probability is lower when multiple retransmissions are possible. The proposed relay adaptive collaborative hybrid NOMA transmission protocol has advantages over the pure OMA transmission mode.

Availability and cost-benefit evaluation for a repairable retrial system with warm standbys and priority

This paper investigates a warm standby repairable retrial system with two types of components and a single repairman, where type 1 components have priority over type 2 in use. Failure and repair times for each type of component are assumed to be exponential distributions. The retrial feature is considered and the retrial time of each failed component is exponentially distributed. By using Markov process theory and matrix-analytic method, the system steady-state probabilities are derived, and the system steady-state availability and some steady-state performance indices are obtained. Using the Bayesian approach, the system parameters can be estimated. The cost-benefit ratio function of the system is constructed based on the failed components and repairman's states. Numerical experiments are given to evaluate the effect of each parameter on the system steady-state availability and optimize the system cost-benefit ratio with repair rate as a decision variable.

Performance and cost comparative analysis for M/G/1 repairable machining system with N-policy vacation

The present article presents the performance analysis of a non-Markovian machining system comprised of operating and standby machines together and functioning under N-policy for vacation. The prime motive of this investigation is to schedule the repairman’s vacation policy to return to the repair job as soon as the workload reaches a pre-defined threshold. The supplementary variable approach (SVT) is employed to establish the system steady-state probabilities, which are used to predict the other performance indices. The numerical illustrations have been provided to verify the outcomes of the proposed analytical model. For the design of optimal parameters at the minimum cost, numerical results are also provided using metaheuristic particle swarm optimization and genetic algorithm techniques

Improving efficiency of service systems by performing a part of the service without the customer's presence

We propose a novel approach for service systems, according to which the service can be split into two phases: an opening service (OS), which can be provided only when the customer is present, and a complementary service (CS), which can be conducted without the customer. To improve the system's overall performance, after providing the OS, the server can postpone executing the CS to time intervals in which they are empty of customers. The prepared OSs are stored in a designated storage facility. Once the system becomes empty, the server executes the CS for the stored OSs, one at a time. We consider two unbounded dimensions system involving a multivariate probability generating function and derive closed-form expressions for the system's steady-state probabilities and various performance measures. An economic analysis compares the described model with a corresponding limited OS capacity model.

Enhanced Markov-based model for the availability analysis of distributed software and hardware systems

Markov model for a simple two-host system used in determining the system availability of homogeneously distributed software and hardware systems is based on the concept of containing only hardware and software in each host. This system is found to be quite slow and tedious resulting to delays in computing system availability at a given time. Present research aim at stochastically analysing the availability of heterogeneously distributed software and hardware systems with software redundancy in standby, using an enhanced model to address the problem of low availability. The low availability is achieved through identifying the components responsible for mitigating the availability and define actions that can improve the availability of the systems. Markov method is used to develop expressions for system steady-state probabilities and system availability respectively. The model is implemented using Java programming language. To make the computation and analysis of systems availability more efficient, numerical examples are presented in order to illustrate the performance of the model.

Improving efficiency in service systems by performing and storing “preliminary services”

We propose a novel approach to improve efficiency in service systems. The idea is to utilize the server's idle time to perform and store “preliminary services” for customers who will arrive in the future. Such a model is relevant to settings in which service consists of multiple consecutive tasks, some of which are generic and needed by all customers (and thus can be performed even in their absence), while other require the customer's presence. To show the model's benefits, we formulate a two-dimensional single-server queueing-inventory system for which we derive closed-form expressions for the system's steady-state probabilities, as well as for its performance measures. Assuming linear costs for customers waiting in line and for stored preliminary services, a cost analysis determines the optimal maximal number of stored preliminary services in the system. Numerical examples illustrated with graphs demonstrate the advantages of our approach, in terms of cost savings, as compared with the classical M/M/1 model.

A single server finite source loss model with general bulk service rule

A single server general bulk service finite source loss model has been studied. For this model the system steady state probabilities and waiting time distributions are obtained. Some performance measures are also calculated. Particular model is deduced and some numerical examples are also given.

Runway Utilization Analysis Based on the Stochastic Petri Net Model

Runway utilization is one of the key indicators of airport operational efficiency. Firstly, stochastic Petri net was introduced to built runway system operational model, and then we analyzed the reachability graph of this model, which not only prove the reachability and boundedness of this model, but also can be used to transform to homogeneous Markov chain. Secondly, The system steady-state probability expressions in various states were established based on the homogeneous Markov chain. Thirdly, runway utilization was calculated based on the steady-state probability expressions. During simulation, runway utilizations in various conditions were analyzed by changing some transitions fire rate. Both Markov chain method and petri net simulation method are useful for runway utilization improvement.

Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.

Queues where customers of one queue act as servers of the other queue

We consider a system comprised of two connected M/M/?/? type queues, where customers of one queue act as servers for the other queue. One queue, Q 1, operates as a limited-buffer M/M/1/N?1 system. The other queue, Q 2, has an unlimited-buffer and receives service from the customers of Q 1. Such analytic models may represent applications like [email protected], where idle computers of users are used to process data collected by space radio telescopes. Let L 1 denote the number of customers in Q 1. Then, two models are studied, distinguished by their service discipline in Q 2: In Model 1, Q 2 operates as an unlimited-buffer, single-server M/M/1/? queue with Poisson arrival rate ? 2 and dynamically changing service rate μ 2 L 1. In Model 2, Q 2 operates as a multi-server M/M/L 1/? queue with varying number of servers, L 1, each serving at a Poisson rate of μ 2. We analyze both models and derive the Probability Generating Functions of the system's steady-state probabilities. We then calculate the mean total number of customers present in each queue. Extreme cases are indicated.

Preventive Maintenance of Multi-State System with Phase-Type Failure Time Distribution and Non-Zero Inspection Time

Preventive maintenance is applied to improve the system availability or decrease the operational cost. This paper addresses the optimal preventive maintenance problem for multi-state deteriorating systems, where the system experiences multiple stages of performance degradation before it fails. We consider a general case where the inspection and repair time are generally distributed. The threshold type maintenance policy is employed for preventive minor maintenance and preventive major maintenance, where minor or major maintenance is carried out when the system deterioration stage is found to be larger than certain thresholds. The mathematical model of the system is set up by means of a Markov regenerative process (MRGP). With this formulation, the system steady-state probabilities under consideration are computed.

An inventory model with returns and lateral transshipments

In this paper, we propose a single-item inventory model with returns. The model allows lateral transshipment of returns from one inventory system to another. Each inventory system is under continuous review and an (r, Q) policy is employed as the inventory control. An approximated closed-form solution of the system steady-state probability distribution is derived when Q is large. The approximated inventory cost and replenishment cost can be written in terms of this distribution. We show that the rejection rate of returns is reduced significantly when transshipment of returns is allowed between the inventory systems.

A simplified graphical method for deriving system steady-state probability

This paper presents an interesting relation between the Maximum Agreement Subtree (MAST) problem and the Tree Edit Distance (TED) problem, both of which have been intensively studied in the literature. To be specific, we show that, for an arbitrary tree edit distance metric that is a derivative of the Taï tree edit distance metric, there exists a MAST-like pattern extraction problem, named Mostly Adjusted Sub-Forest (MASF) problem, such that computing a distance between trees x and y is equivalent to finding an optimal pattern shared between x and y. The MASF problem is different from the MAST problem in: (1) A pattern of the MASF problem may be a forest instead of a tree; (2) Instead of requiring exact match of labels, a pattern of a MASF problem is multi-labeled, and our flexible matching rule only requires that the label set of a vertex of a pattern includes the label of the corresponding vertex in a target tree; (3) To control ambiguity of matching caused by the flexible rule, the objective function includes a penalty function. As an application of this generic framework, we equate the Lu* tree edit distance metric with a pattern extraction problem, named the Mostly Adjusted Agreement Sub-Tree (MAAST) problem. The MAAST problem aims to find optimal agreement subtrees under the flexible matching rule and is solved in O(n2dlog⁡d)-time, where n and d are the size and the minimum degree of the input trees. The MAST problem requires O(n2.5)-time computation.

A simplified graphical method for deriving system steady-state probability

A simplified graphical method for deriving the formula for steady-state probability distributions of a large system based on graph theory is introduced. The steady-state probability distributions for some D-out-of-N:F repairable systems are derived using this graphical method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Ca/M/s/m Retrial Queue: A Computational Approach

This paper considers a service station consisting of s identical, independent exponential servers and m buffers. Customers arrive according to a Coxian process with a stages. Blocked customers may either leave the system forever or return, after an exponentially distributed amount of time, to the service station to retry for services. An efficient algorithm is developed to evaluate system steady-state probabilities, and formulas for certain system performance measures are derived in terms of the steady-state probabilities. The computational complexity of the algorithm is shown to be O(4N), where N is the total number of state probabilities evaluated. The influence of the form of interarrival time distributions on system performance measures is examined through numerical results. Issues concerning numerical stability of the algorithm are also discussed. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Reliability analysis of a k-out-of-n:G vehicle fleet

This paper presents a reliability analysis of a k-out-of-n:G on-surface vehicle fleet. The transit system is in a failed state when (n − k + 1) vehicles failed. Laplace transforms of state probabilities and reliability of the transit system are derived. The transit system steady-state probabilities and availability formulas are also developed.

Availability modelling of a vehicle fleet

This paper presents a Markov model representing an on-surface transportation system consisting of a fleet of n-vehicles operating simultaneously. The transit system steady-state probabilities and availability formulas are developed. A number of special case models are presented. The plots of transit system steady-state availability and probabilities are shown.