Stochastic Modeling of Three Non Identical Complex System With Single Service Facility Available In The System

Stochastic behaviour of a two-unit standby system with better utilization of units

An approach to simulating models of highly dependable systems with general failure and repair time distributions is described. The approach combines importance sampling with event rescheduling in order to obtain variance reduction in such rare event simulations. The approach is general in nature and allows effective simulation of a variety of features commonly arising in dependability modeling. For example, it is shown how the technique can be applied to systems with periodic maintenance. The effects on the steady-state availability of the maintenance period and of different failure time distributions are explored. Some of the trade-offs involved in the design of specific rescheduling rules are described, and their potential effectiveness in simulations of systems with nonexponential failure and repair time distributions are demonstrated. It is found that an effective method for selecting the rescheduling distribution is to keep the probability of a failure transition in the range between 0.1 and 0.5.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Purpose The purpose of this paper is to present issues and challenges faced during a firm’s facility relocation decision aimed at improving both cost and service performance in an innovative service context. Design/methodology/approach The reader is given background of the decision-making process behind single service facility relocation decision using a detailed case study. Key financial, operational and business data of the firm are collected, compiled and analysed. The solution methodology uses a combination of qualitative and quantitative analyses to choose the best among the three possible discrete location choices. For propriety reasons, some information has been disguised, and some data have been sanitized. Findings The factors that significantly influence relocation decision are proximity to high transaction customers, infrastructure and other input costs, customer service level requirements and extant regulations. Transportation has a direct impact on cost as well as service level. Most of the findings are in line with literature, but some of them differ too. Research limitations/implications The approach is focused on a single case study of a pooling container firm in the Indian context and thereby limits the ability to generalize the findings. Nevertheless, this study may serve as a significant starting point for future research. Practical implications Firms can create a rational, efficient and even-handed approach for relocation of facilities applying a mix of qualitative and quantitative models judiciously. It provides managers better understanding and insights and actions needed for single service facility relocation. Originality/value This work is perhaps the first on facility relocation in emerging economies covering actual interventions and experiences. It gives new insights to a limited literature of relocating single service facility reflecting both theoretical imperatives and practitioner requirements.

This paper deals with the availability and the reliability analysis of a system consisting of two dissimilar units having a single service facility and subject to preventive maintenance. The times to failure, the repair times, and the preventive maintenance times of the units are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. By identifying suitable regenerative stochastic processes, we derive integral equations for these probabilities corresponding to different initial conditions, and we use Laplace transform technique to solve the equations. Explicit expressions for the mean down-time of the system during the period (0, t) and for the mean-time-to-system-failure are obtained. The case when the system is not subject to preventive maintenance is considered as a particular case.

Cost-benefit analysis of one-server two-unit system subject to slow switch and random service

Probabilistic analysis of a two-unit system with a warm standby subject to preventive maintenance and a single service facility

Efficient simulation techniques for estimating steady-state quantities in models of highly dependable computing systems with general component failure and repair time distributions are considered. Earlier approaches in this application setting for steady-state estimation rely on the regenerative method of simulation, which an be used when the failure time distributions are exponentially distributed. However, when the failure times are generally distributed the regenerative structure is lost and a new approach must be taken. The approach the authors take is to exploit a ratio representation for steady-state quantities in terms of cycles that are no longer independent and identically distributed. A splitting technique is used in which importance sampling is used to speed up the simulation of rare system failure events during a cycle, and standard simulation is used to estimate the expected cycle length. Experimental results show that the method is effective in practice.

For a service facility serving more than one class of customers a problem arises as to the order in which customers should be served (i.e., the priority rule). A typical example is a manufacturing facility that produces two products to meet a random stream of incoming orders. In this paper the alternating priority rule (also known as the “zero switch rule”) is introduced and investigated. Two classes of customers are served by a single service facility. Customers of class i(i = 1, 2) have priority over customers of class j(j = 1, 2; j ≠ 1) whenever a class i customer is in service. When the service facility is idle, the first arriving customer enters service and acquires the priority right for customers of his class. Within classes the “first-come, first-served” rule is observed. Customers' arrivals are assumed to be Poisson and service times are assumed to be arbitrarily distributed independent random variables. The steady-state densities of queuing times are formulated by the use of a special mathematical procedure. The expectations of queuing times and sizes of queues as well as the first two moments of the busy periods are obtained in terms of the basic parameters of the arrival process and service time distributions. All the results are related to the case where switching from one type of customers to another is not penalized by setup time. The alternating priority rule is compared to the “head-of-the-line” and the “first-come, first-served” rules with respect to expected queuing times and queue sizes. The last part of the paper discusses the possibilities of extending the suggested rule to cases involving more than two classes of customers and nonzero setup times and setup costs.

In this paper, we consider a production-inventory system with a service facility and production interruptions. Customers arrive in the system according to a Poisson process and require a random time of the service from a single service facility. The service time is assumed to be exponentially distributed. The items are produced according to an (s, S) policy. Each customer leaves the system with one item from the inventory at his service completion epoch if the inventory is available. The production is interrupted for a vacation of random time once the inventory level becomes S. The vacations are exponentially distributed. On return from a vacation, if the inventory level depletes to s, then the production is immediately switched on. It then starts production and is kept in the on mode until the inventory level becomes S. The items in stock are perishable and have exponential life times. It is assumed that no customers is allowed to join the queue when the inventory level is zero. We first derive the stability condition of the system. Then, We obtain the product form solution for the stationary joint distribution of the number of customers and the on-hand inventory level. Based on this stationary distribution, we compute explicitly some performance measures and develop a cost function. Finally, some numerical results are presented.

An approximation analysis for the availability of a parallel redundant system with general distributions

Stochastic analysis of a two unit adaptive system subject to slow switch with random service

MTTF and availability evaluation of a two-unit, two-state, parallel redundant complex system with constant human failure

An approach for simulating models of highly dependable systems with general failure and repair time distribution is described. The approach combines importance sampling with event rescheduling in order to obtain variance reductions in such rare event simulations. The approach is general in nature and allows a variety of features commonly arising in dependability modeling to be simulated effectively. It is shown how the technique can be applied to systems with redundant components and/or periodic maintenance. For different failure time distributions, the effect of the maintenance period on the steady-state availability is explored. The amount of component redundancy needed to achieve a certain reliability level is determined. >

An input source of the model is generated in accordance with a probability density function P r (n,t), where n and t are a spatial variable and a time variable, respectively. Thus the input arrives as a time-variable train. A queue consists of m blocks, and each block consists of a finite number of small waiting spaces. A single service facility is used in the model, and its service processing speed is a constant that is selected from several operational rates. The next higher operational speed and the next lower operational speed are twice as fast as and half as slow as the present constant speed, respectively. The service discipline is first-come-first-served. When the needed queuing space exceeds the queuing space available, a congestion or input loss occurs. Minimizing such input loss with the least admissible queuing space and the slowest possible service speed is desirable. When the service facility is a machine, it may be easier and more economical to increase the service speed operations rather than to furnish a larger amount of queuing space. The model is simulated on a digital computer. Two service Speed controls are examined in the simulation. The first is a deterministic control, and the second is a probabilistic control. In the former, when the amount of the queuing space available is almost consumed, the service speed is upgraded to the next higher rate. The speed remains at this rate until the amount of unused queuing space increases. Later, the speed is downgraded to the original rate. In the latter, control is switched probabilistically no matter what the queuing space may be but it can specify a service processing distribution among different speeds during a long time period. The simulated results or the probability of congestion P e with various queuing space lengths and service speeds is presented. This information may be useful for understanding input loss phenomena as well as for designing an efficient low-cost queuing system.

A closed multiple access system composed of M sources and a single service facility is analyzed. The closed network is modeled as a finite source ${M / G / 1}$ queueing system. We consider systems with a large number of sources (i.e. $M \gg 1$) and we assume that the mean time required to process an individual request is short $(O({1 / M}))$. We then construct asymptotic approximations to the stationary distribution of the number of requests in the service facility by using the method of matched asymptotic expansions. We give formulas for the first and second moments of the number of requests, for all traffic intensities.