Unreliable Server Research Articles

Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy

In this investigation, an unreliable server Markovian queueing model is developed for a service system by considering two stage service process and hybrid vacation policy. By including the features of combination of working vacation (WV) and complete vacation (CV), the steady state probability distribution of the queue size of two stage service model via matrix geometric approach has been established. The cost function has been formulated to evaluate the optimal values of the decision variables of the service system. Particle swarm optimization (PSO) and Artificial bee colony (ABC) optimization algorithms are employed to compute the optimal service rates at optimum cost. To validate the model, numerical illustrations along with sensitivity analysis have been provided.

Unreliable Server M[X]/G/1 Queue with Working Vacation and Multi-phase Repair with Delay in Verification

Unreliable Server M[X]/G/1 Queue with Working Vacation and Multi-phase Repair with Delay in Verification

Unreliable Server M[X]/G/1 Retrial Feedback Queue with Balking, Working Vacation and Vacation Interruption

Unreliable Server M[X]/G/1 Retrial Feedback Queue with Balking, Working Vacation and Vacation Interruption

Cost-Benefit Analysis of a Standby Retrial System with an Unreliable Server and Switching Failure

In many industries and plants, a stable power supply system with acceptable cost/benefit is essential. This paper investigates the cost-effectiveness of an unreliable retrial system that includes standby generators and experiences the switchover failures of standby generators. Four different standby retrial configurations are included, and each configuration includes various numbers of primary and standby generators. Upon arrival, a failed generator is repaired immediately if the server is available; otherwise, the failed generator will enter into orbit. The server is subject to breakdown even when the server is idle. The explicit expressions of the mean time-to-failure and steady-state availability for each configuration are derived and compared. We also compare the cost/benefit ratio among four configurations. The developed results can provide managers with decision reference for stable power supply system and cost reduction.

Stability analysis of a standby system with an unreliable server and switching failure

Abstract This paper is devoted to analysing stability of a standby system with an unreliable server and switching failure, where both the time-to-repair of units and the time-to-repair of server follow general distributions. By employing $C_0$ semigroup theory, we show that time-dependent solution of the system converges to steady-state solution under a rather mild condition. Further, if component’ repair rate and server’s repair rate satisfy a reasonable assumption, then the system is exponentially stable. Based on the above theoretical foundation, some steady-state reliability indices are obtained and total expected profit function per unit time is developed. Finally, a sensitivity analysis with numerical illustrations is also provided.

Analysis of a bulk arrival N-policy queue with two-service genre, breakdown, delayed repair under Bernoulli vacation and repeated service policy

This article deals with an unreliable bulk arrival single server queue rendering two-heterogeneous optional repeated service (THORS) with delayed repair, under Bernoulli Vacation Schedule (BVS) and N-policy. For this model, the joint distribution of the server’s state and queue length are derived under both elapsed and remaining times. Further, probability generating function (PGF) of the queue size distribution along with the mean system size of the model are determined for any arbitrary time point and service completion epoch, besides various pivotal system characteristics. A suitable linear cost structure of the underlying model is developed, and with the help of a difference operator, a locally optimal N-policy at a lower cost is obtained. Finally, numerical experiments have been carried out in support of the theory.

"Computational approach to Transient solution for single unreliable server Retrial Queue under non-preemptive priority"

"Single server Retrial Queueing model with system repair and breakdown under non-preemptive priority is considered in this paper. The study of the model so far is mostly explored only for steady state solutions with few exceptions to Transient solutions. Though some researchers have attempted transient solution to the model analytically, the solution thus obtained is more complicated that it cannot be solved. In this context, we have found the transient numerical solution to the model using eigenvalues and eigenvectors. Time dependent system performance measures and probability distributions are evaluated and validated with steady state solutions. Single server Retrial Queueing model with system repair and breakdown under non-preemptive priority is considered in this paper. The study of the model so far is mostly explored only for steady state solutions with few exceptions to Transient solutions. Though some researchers have attempted transient solution to the model analytically, the solution thus obtained is more complicated that it cannot be solved. In this context, we have found the transient numerical solution to the model using eigenvalues and eigenvectors. Time dependent system performance measures and probability distributions are evaluated and validated with steady state solutions."

Optimization of retrial queue with unreliable servers subject to imperfect coverage and reboot delay

ABSTRACT A retrial queue with constant retrial policy, unreliable servers and the failed servers may not be detected is investigated in this paper. Upon arrival, a customer either is attended to one of the available servers or enters a retrial orbit and retries in a random time as all servers are not available. The unreliable server can be breakdown when he is working. The breakdown server may not be detected due to some fault matters. Under such a situation, the repair facility will issue a reboot operation to locate the non-detected breakdown server. Once the breakdown server is detected and located, he will be sent for repair. After utilizing the general theory of matrix-geometric approach to determine the stationary distribution, some performance measures are proposed. A single-objective model aiming at minimizing the average cost is constructed. We apply particle swarm optimization algorithm and genetic algorithm to find the optimum combination of parameters. We also formulate a bi-objective model aiming at minimizing the expect cost and the mean waiting time of customers in orbit. Two multi-objective algorithms are developed to solve it.

The service pricing strategies and the strategic behavior of customers in an unobservable Markovian queue with unreliable server

A Stackelberg game is used to study the service pricing and the strategic behavior of customers in an unreliable and totally unobservable M/M/1 queue under a reward-cost structure. At the first stage, the server manager, acting as a leader, chooses a service price and, at the second stage, a customer, arriving at the system and acting as a follower, chooses to join the system or an outside opportunity, knowing only the service price imposed by the server manager and the system parameters. We show that the constructed game admits an equilibrium and we give explicit forms of server manager and customers equilibrium behavioral strategies. The results of the proposed model show that the assumption that customers are risk-neutral is fundamental for the standard approach usually used. Moreover, we determine the socially optimal price that maximizes the social welfare and we compare it to the Stackelberg equilibrium. We illustrate, by numerical examples, the effect of some system parameters on the equilibrium service price and the revenue of the server manager.

An M^[X]/G^(1,K)/1 Queue with Unreliable Server and Bernoulli Vacation

An M^[X]/G^(1,K)/1 Queue with Unreliable Server and Bernoulli Vacation

Service pricing and customer behaviour strategies of Stackelberg's equilibrium in an unobservable Markovian queue with unreliable server and delayed repairs

In this paper, we model as a Stackelberg game with the service pricing of server and the strategic behaviour of customers in a totally unobservable M/M/1 queueing system subject to random breakdowns and delayed repairs, under a reward-cost structure. For this, we first use the partial generating functions to determine the steady-state condition and the sojourn time of a customer in the considered queueing system. The analytical forms of the service price and the customer entrance strategies of the Stackelberg equilibrium of the game are given. Through numerical examples, we illustrate the effect of the price and the reliability parameters on the entrance probability of customers and the server profit. Finally, we define and solve the corresponding social welfare problem. This study has not only a theoretical aspect, but also a practical one, and it can be adapted to several real-life situations.

M/M/2 heterogeneous queueing system having unreliable server with catastrophes and restoration

M/M/2 heterogeneous queueing system having two kinds of server breakdowns with catastrophes and restoration, is considered. Server1 is always available and server2 is intermittently available and may subject to breakdown. However if server2 is breakdown, then it is sent to repaired immediately. During the busy period, the system may suffer by occurrence of catastrophes which will destroy all the customers and the system being empty. Meanwhile the system need some time to restart normally. In addition we describe the model and derive the probability vectors are using the Matrix-Geometric Technique (MGT). In the end give some numerical models. And the performance measures are found using the probability vectors at different values of parameters contingent the queueing model.

Retrial Queues with Unreliable Servers and Delayed Feedback

In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service of customers and when they are idle. If a server breaks down during the service of a customer, then the interrupted customer, in accordance with the Bernoulli scheme, decides either to leave the system or join a common orbit of retrial and feedback customers. An approximate method, based on the space merging approach of three-dimensional Markov chains, is proposed for the calculation of the steady-state probabilities, as well as performance measures of the system. The results of the numerical experiments are demonstrated.

Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

Analysis of M/m/c Retrial Queue with Thresholds, Ph Distribution of Retrial Times and Unreliable Servers

Analysis of M/m/c Retrial Queue with Thresholds, Ph Distribution of Retrial Times and Unreliable Servers

Variant working vacation Markovian queue with second optional service, unreliable server and retention of reneged customers

In this paper, a variant working vacation queueing system with second optional service, unreliable server, and retention of reneged customers is studied. This model has potential applications in tele-services, banks, manufacturing processes, etc. The expressions of the steady-state probabilities and the system sizes when the server is in different states are obtained using probability generating functions. This paper also discusses an optimisation problem under a given cost structure. Direct search method and quadratic fit search method (QFSM) are applied to obtain the optimum number of working vacations and optimum service rates during regular busy period and working vacation period, respectively.

An M^[X]/G(a,b)/1 queueing system with unreliable server, stand-by server, restricted arrivals, variant threshold policy for vacations

We studied the behaviour of an M[X]/G(a, b)/1 queueing system with unreliable server, stand-by server, restricted admissibility and variant threshold policy for vacations in this paper. The stand-by server is utilised only during main server's repair period. At the moment of main server's busy completion or repair completion, if the number of customers in the queue is less than 'a', the main server avails type-I vacation repeatedly until the queue length reaches at least 'a'. While getting back from vacation of type-I, if the queue has its length of value as at least 'a' then the server performs the type-II vacation continuously, until it reaches at least N(a < b ≤ N). When both types of vacation gets completed, and the length queue is at least 'N', then the server starts service to the batch of 'b' customers. The PGF of queue size and some important performance measures are derived. An extensive numerical result is illustrated.

Analysis of customer's impatience on bulk service queueing system with unreliable server, setup time and two types of multiple vacations

In this investigation, we analyse the customer's impatience on unreliable bulk queueing system with two types of vacation. Depending upon the length of queue, the server is permitted to take two types of vacation called type I vacation and type II vacation. The server is possibly affected by breakdowns and takes considerable time for setup before the repair begins to start. After repair completion, the server will start its remaining service to the batch of customers whose service was interrupted. It could be assumed that the arriving units may be balked from the system when the server is on vacation (type I or type II). By incorporating the supplementary variables technique, the probability generating function of the queue size at an arbitrary and departure time epoch for the designed queueing system are derived. Finally, the stability condition, some performance measures, particular cases are obtained with appropriate numerical illustrations and graphical presentation.

Service pricing and customer behaviour strategies of Stackelberg's equilibrium in an unobservable Markovian queue with unreliable server and delayed repairs

Service pricing and customer behaviour strategies of Stackelberg's equilibrium in an unobservable Markovian queue with unreliable server and delayed repairs

An &lt;i&gt;M&lt;/i&gt;&lt;SUP align="right"&gt;[&lt;i&gt;X&lt;/i&gt;]&lt;/SUP&gt;/&lt;i&gt;G&lt;/i&gt;(&lt;i&gt;a&lt;/i&gt;, &lt;i&gt;b&lt;/i&gt;)/1 queueing system with unreliable server, stand-by server, restricted arrivals and variant threshold policy for vacations

We studied the behaviour of an M[X]/G(a, b)/1 queueing system with unreliable server, stand-by server, restricted admissibility and variant threshold policy for vacations in this paper. The stand-by server is utilised only during main server's repair period. At the moment of main server's busy completion or repair completion, if the number of customers in the queue is less than 'a', the main server avails type-I vacation repeatedly until the queue length reaches at least 'a'. While getting back from vacation of type-I, if the queue has its length of value as at least 'a' then the server performs the type-II vacation continuously, until it reaches at least N(a < b ≤ N). When both types of vacation gets completed, and the length queue is at least 'N', then the server starts service to the batch of 'b' customers. The PGF of queue size and some important performance measures are derived. An extensive numerical result is illustrated.