A new analytical algorithm for computing probability distribution of project completion time

An analytical algorithm was presented for the exact computation of the probability distribution of the project completion time in stochastic networks,where the activity durations are mutually independent and continuously distributed random variables. Firstly,stochastic activity networks were modeled as continuous-time Markov process with a single absorbing state by the well-know method of supplementary variables and the time changed from the initial state to absorbing state is equal to the project completion time.Then,the Markov process was regarded as a special case of Markov skeleton process.By taking advantage of the backward equations of Markov skeleton processes,a backward algorithm was proposed to compute the probability distribution of the project completion time.Finally,a numerical example was solved to demonstrate the performance of the proposed methodology.The results show that the proposed algorithm is capable of computing the exact distribution function of the project completion time,and the expectation and variance are obtained.

Performance Assessment and Configuration Analysis in the Study of SCADA System (Supervisory Control and Data Acquisition)

Queuing models are used to assess the functionality and aesthetics of SCADA systems for supervisory control and data collection.Here,the main emphasis is on how the queuing theory can be used in the system’s design and analysis.The analysis’s findings indicate that by using queuing models,cost-performance ratios close to the ideal might be attained.This article discusses a novel methodology for evaluating the service-oriented survivability of SCADA systems.In order to evaluate the state of service performance and the system’s overall resilience,the framework applies queuing theory to an analytical model.As a result,the SCADA process is translated using the M^(X)/G/1 queuing model,and the queueing theory is used to evaluate this design’s strategy.The supplemental variable technique solves the queuing problem that comes with the subsequent results.The queue size,server idle time,utilization,and probabilistic generating factors of the distinct operating strategies are estimated.Notable examples were examined via numerical analysis using mathematical software.Because it is used frequently and uses a statistical demarcation method,this tactic is completely acceptable.The graphical representation of this perspective offers a thorough analysis of the alleged limits.

Geom/G_1,G_2/1/1 REPAIRABLE ERLANG LOSS SYSTEM WITH CATASTROPHE AND SECOND OPTIONAL SERVICE

This paper studies a single server discrete-time Erlang loss system with Bernoulli arrival process and no waiting space. The server in the system is assumed to provide two different types of services, namely essential and optional services, to the customer. During the operation of the system, the arrival of the catastrophe will break the system down and simultaneously induce customer to leave the system immediately. Using a new type discrete supplementary variable technique, the authors obtain some performance characteristics of the queueing system, including the steady-state availability and failure frequency of the system, the steady-state probabilities for the server being idle, busy, breakdown and the loss probability of the system etc. Finally, by the numerical examples, the authors study the influence of the system parameters on several performance measures.

RANDOMIZED POLICY OF A POISSON INPUT QUEUE WITH J VACATIONS

This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation. If the number of arrivals does not reach N by the end of the jth vacation, the server remains idle in the system until the number of arrivals in the queue reaches N. If the number of customers in the queue is exactly accumulated N since the server remains idle or returns from vacation, the server is activated for services with probability p and deactivated with probability （l-p）. For such variant vacation model, other important system characteristics are derived, such as the expected number of customers, the expected length of the busy and idle period, and etc. Following the construction of the expected cost function per unit time, an efficient and fast procedure is developed for searching the joint optimum thresholds （N＊,J＊） that minimize the cost function. Some numerical examples are also presented.

ANALYSIS OF A DISCRETE-TIME GI/GEO/1/N QUEUE WITH MULTIPLE WORKING VACATIONS

This paper analyzes a finite-buffer renewal input single server discrete-time queueing system with multiple working vacations. The server works at a different rate rather than completely stopping working during the multiple working vacations. The service times during a service period, service time during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer＇s observation epochs. The analysis of actual waiting-time distribution and some performance measures are carried out. We present some numerical results and discuss special cases of the model.

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS Ⅱ： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS I:G/M(n)/1/K

In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M（n）/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate. In a subsequent companion paper, we study its dual system M（n）/G/1/K queue with statedependent vacations.

A Physics-Informed Structure-Preserving Numerical Scheme for the Phase-Field Hydrodynamic Model of Ternary Fluid Flows

Phase-field models are widely used in studying multiphase flow dynamics.Given the complexity and strong nonlinearity,designing accurate,efficient,and stable numerical algorithms to solve these models has been an active research field for decades.This paper proposes a novel numerical scheme to solve a highly cited and used phase field hydrodynamic model for simulating ternary phase fluid flows.The main novelty is the introduction of a supplementary variable to reformulate the original problem into a constrained optimization problem.This reformulation leads to several advantages for our proposed numerical algorithms compared with many existing numerical techniques for solving this model.First,the developed schemes allow more straightforward calculations for the hydrodynamic phase-field models by solving a few decoupled Helmholtz or Poisson-type systems with a constant precomputable coefficient matrix,remarkably reducing the computational cost.Secondly,the numerical schemes can maintain mass conservation and energy dissipation at the discrete level.Additionally,the developed scheme based on the secondorder backward difference formula respects the original energy dissipation law that differs from many existing schemes,such as the IEQ,SAV,and Lagrange multiplier approaches for which a modified energy dissipation law is respected.Furthermore,rigorous proof of energy stability and practical implementation strategies are provided.We conduct adequate 2D and 3D numerical tests to demonstrate the proposed schemes’accuracy and effectiveness.

Analysis of a Discrete-Time Geo/G/1 Queue in a Multi-Phase Service Environment with Disasters

This paper considers a discrete-time Geo/G/1 queue in a multi-phase service environment,where the system is subject to disastrous breakdowns, causing all present customers to leave the system simultaneously. At a failure epoch, the server abandons the service and the system undergoes a repair period. After the system is repaired, it jumps to operative phase i with probability qi, i = 1, 2 ···, n.Using the supplementary variable technique, we obtain the distribution for the stationary queue length at the arbitrary epoch, which are then used for the computation of other performance measures. In addition, we derive the expected length of a cycle time, the generating function of the sojourn time of an arbitrary customer, and the generating function of the server’s working time in a cycle. We also give the relationship between the discrete-time queueing system to its continuous-time counterpart. Finally,some examples and numerical results are presented.

ANALYSIS OF A PARALLEL SYSTEM WITH TWO DIFFERENT UNITS

In this Paper, a parallel repairable model consisting of two units and one repairman isstudied. The working time and the repair time of the two units are all exponeotially distributed.Assume that one unit after repair will be 'as good as new', but the other one not. By introducingthe geometric process and using the method of supplementary variable, some importaDt reliabilityindlces are determined.