Retrial G-queue Research Articles

Analysis of Unreliable Repetition G-Sequence with Holiday Disturbance under ARAS Methodology

A Due to high customer traffic, the server frequently crashes, and a vacation interruption is being contemplated. If the orbit empties at the conclusion of a positive customer service experience, the server was successful. We're going on holiday. A working vacation (WV) server with a poor service rate is functional. If there are clients on the computer at the end of each holiday, the server has a p (single WV) chance that a new visitor is inactive and on vacation. We discovered the generating function using a substantial variable method and a constant state probability for the system and its orbit. The random decay law, system performance measures, and reliability measures are all addressed. Finally, some numerical examples as well as cost optimization analysis are given. Alternatives include the Single-Server Review G-Series, the Incredible Review G-Series, and the Volume Visit Review G-Series. Preference for Evaluation: Working holiday, Bernoulli feedback, random vacations, and single vacation are all examples of vacations. Untrustworthy retrial G-queue, Batch entry As a G-sequence alternative, retrial G-queue, single server iteration is used, and working vacations, random vacations, single vacation, and Bernoulli holiday are used as evaluation parameters. A thorough supply analysis using the ARAS technique assists the team in making decisions. The ARAS method's best solution finds the solution with the shortest and longest distances from the negative-best solution in this analysis, but the comparison of these distances is not deemed important. This research is a benchmark for green supplier performance. Aims will be used to assess significance using ARAS. Criteria and options examined in this research because they are associated with uncertainty, ARAS theory for modelling uncertainties one of the primary instruments. o evaluates green suppliers in this research A collection of criteria has been established. Then, choose the finest green suppliers. ARAS is used to choose This study's contribution to green supplier assessment Hierarchical Process Techniques are used in ARAS research. On the basis of unity During the decision-making procedure When uncertainty is a major factor, ARAS shows a solution as an optimal response. A non-reliable review is rated first by G- queue, a server review is ranked third, and a bath visit review is ranked second. As a consequence, non-reliability revisit G- queue is ranked first, while volume attendance revisit G- queue is ranked last.

Non-Markovian Feedback Retrial Queue with Two Types of Customers and Delayed Repair Under Bernoulli Working Vacation

This paper deals with an M/G/1 feedback retrial G-queue and delayed repair incorporating Bernoulli working vacation. Arrivals of both favorable and unfavorable consumers are two independent Poisson processes. The server is subjected to breakdown during the regular busy period due to the arrival of unfavorable customers and then the server will be down for a short period of time. Further, the concept of delay time is also discussed. After the fulfillment of regular service, the dissatisfied consumer may re-join the orbit to receive another service as a feedback consumer. During the working vacation period, the server provides the service to consumers at a reduced rate. By applying the supplementary variable technique (SVT), we have analyzed the steady-state probability generating function (PGF) for the system size and orbit size. In addition, we have presented the system performance, reliability indicators, and stochastic decomposition property. Finally, we provided numerical examples to illustrate our model’s mathematical results.

Maximum Entropy Solution for M^X/G/1 Priority Reiterate G-queue Under Working Breakdown and Working Vacation

The maximum entropy principle has grown progressively more pertinent to queueing systems. The principle of maximum entropy (PME) presents an impartial framework as a promising method to examine complex queuing processes. This principle can be employed to assess the most appropriate probability distributions for queueing scenarios in a variety of widespread industrial issues. The aspects of general service bulk arrival retrial G-queue including working vacation, state-dependent arrival, priority users, and working breakdown are all explored in this article. Real-world applications for this kind of waiting line include computer systems, industrial companies, packet-switching networks, and communication facilities, etc. The adverse users (or negative arrivals) can make an appearance when the server (operator) is preoccupied with a positive user. Consumer’s arrival patterns follow the Poisson distribution. Priority consumers and regular (ordinary) consumers are the two groups of consumers that are considered in this investigation. Priority consumers do not have to wait in line and are granted a special right of prevention that allows them to receive services before ordinary consumers. Initially, we have estimated performance metrics including orbit size and long-run probabilities in this research work. The maximum entropy approach is then used to give a comparative perusal between the system’s exact and estimated waiting times. Apart from that a bi-objective optimization model is developed to diminish both consumers waiting times and estimated costs simultaneously. It is manageable to establish an effective balance between the standard of service and operating expenses using the analytical strategy that has been provided.

Retrial G-queue with precipitous breakdown and non-tenacious customers

We perform an analysis on an M/G/1 system that has bulk arrival Poisson process as well as instantaneous service, Precipitous breakdown and random repair, Gqueue, and operation under an MBV (Modified Bernoulli vacation) policy. The positive outcome of a customer retrial is lost when an Anti-positive customer arrives during a positive (good) customer?s assistance period. If a new customer enters and notices that the server is currently undergoing repairs or on vacation, they may renege or balk from the system. To obtain a wide variety of additional outcomes, we use the details provided by the supplementary variable method regarding the rates at which different events occur and it is possible to determine the probability-generating functions of queue length distributions as well as the explicit formulations of important performance metrics. The numerical data confirm the analytical findings about the major performance metrics.

Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors

This paper considers a retrial G-queue with collisions, transmission errors, and a finite number of sources, where service and repair time are both general distributions. The number of sources (terminals) is finite and a source cannot generate new requests until the channel (server) finishes its work, i.e., the rate at which new primary requests are generated varies inversely with the number of data frame (customer) in the system. A collision occurs when service requests arrive at a busy channel, and transmission errors prevent data frames from leaving the system after completing service. Two types of arrivals are considered. Negative customers will break down the system in the busy state and remove the customer under service. The application of our model is indicated, with a particular emphasis on communication networks such as the local-area networks (LAN) with CSMA/CD protocol. Recursive formulas have been derived to calculate the stationary joint distributions and the Laplace transform of reliability function by applying the discrete transformations method along with the supplementary variables technique (SVT). Furthermore, the comparative performance and reliability analysis have been conducted numerically. Numerical examples are provided to investigate the sensitivity of different parameters on performance measures and reliability indicators.

An M/G/1 Retrial G-queue with Multiple Working Vacation and a Waiting Server

An M/G/1 retrial G-queue with multiple working vacation and a waiting server is taken into consideration in this study. Both the retrial times and service times are assumed to follow general distribution and the waiting server follows an exponential distribution. During the working vacation period customers are served at a lesser rate of service. Before switching over to a vacation the server waits for some arbitrary amount of time and so is called a waiting server. We obtain the PGF for the number of customers and the mean number of customers in the invisible waiting area which is acquired by utilizing the supplementary variable technique. We compute the waiting time distribution. Out of interest a few special cases are conferred. Numerical outcomes are exhibited.

Evaluation of Unreliable Retrial G-queue Using Fuzzy ARAS Method

A Regular busy server crashes due to negative customer traffic, and holiday interruption is being considered. If the orbit empties at the end of a positive customer service, the server worked Going on vacation. A working vacation (WV) server at a low service rate works. If there are clients on the computer at the end of each holiday, the server the probability that a new visitor is inactive and on vacation is p (single WV) or with probability q (multiple WVs). Substantial variable technique, constant state probability for the system and its orbit we found the generating function. System performance measures, reliability measures and random decay law are discussed. Finally, Some numerical examples and cost optimization analysis provided. Alternative: Single-Server Review G- Sequence, Incredible Review G-Series, Volume Visit Review G-Series. Evaluation Preference: Working vacation, Bernoulli feedback, Random vacations, single vacation. Unreliable retrial G-queue, Batch arrival Retrial G-queue, single server iteration is taken as a G-sequence alternative and working vacations, random vacations, single vacation, and Bernoulli vacation is taken evaluation parameters. In this from analysis Fuzzy ARAS method the best solution determines the solution with the shortest distance and the longest distance from the negative-best solution, but comparison of these distances is not considered significant. As a result it seems unreliable retrial G-queue got the first rank where as is the Batch arrival Retrial G-queue is having the lowest rank.

Particle Swarm Optimization and Maximum Entropy Results for MX/G/1 Retrial G-Queue with Delayed Repair

This paper examines an MX/G/1 retrial model with negative customers including the concepts of working vacation, Bernoulli feedback, delayed repair, state-dependent and multi-optional services. Such a queue is quite relevant in real world, for instance in computer systems, manufacturing organisations, packet-switching networks, telecommunication systems, etc. The arrival pattern of customers is according to Poisson distribution. The service is such that first essential service (FES) is provided to every customer and second optional service (SOS) is provided in k phases to those who wants to opt for the same. The negative customers may arrive during the time when the server is busy in serving a positive customer. This leads to breakdown of the server and thus the server has to be restored (repair) by the repair man. Some moments may be taken by the repair man to initiate the repair process, leading to delay in repair. In our work, firstly we have calculated performance measures like long run probabilities and orbit size along with some reliability indices. Then a relative study between the exact expected waiting time and approximate expected waiting time of the system is presented via maximum entropy approach. Also we perform cost optimization using particle swarm optimization (PSO method). Few numerical results are also provided.

Performance analysis of an M/G/1 retrial G-queue with feedback under working breakdown services

Performance analysis of an M/G/1 retrial G-queue with feedback under working breakdown services

An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns

This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov chain, we obtain the necessary and sufficient condition for the stability of the system. Using the supplementary variable method, we deal with the generating functions of the number of customers in the orbit. Various system performance measures are also developed. Finally, some numerical examples and a cost optimization analysis are presented.

An M/G/1 retrial G-queue with optional re-service, impatient customers, multiple working vacations and vacation interruption

In this work, we consider a single server retrial queueing system with multiple working vacations and vacation interruption, where the regular busy server is subjected to breakdown due to the arrival of negative customers. After the completion of regular service the positive customers may demand re-service of the previous service without joining the orbit or may leave the system. When the orbit becomes empty at service completion instant for a positive customer; the server goes for multiple working vacations. The steady state probability generating function for the system size and orbit size are obtained by using the method of supplementary variable technique. Some important system performance measures and the mean busy period are obtained. The conditional stochastic decomposition law is shown for good for this model. Finally, the effects of various parameters on the system performance are analysed numerically.

An M/G/1 retrial G-queue with optional re-service, impatient customers, multiple working vacations and vacation interruption

In this work, we consider a single server retrial queueing system with multiple working vacations and vacation interruption, where the regular busy server is subjected to breakdown due to the arrival of negative customers. After the completion of regular service the positive customers may demand re-service of the previous service without joining the orbit or may leave the system. When the orbit becomes empty at service completion instant for a positive customer; the server goes for multiple working vacations. The steady state probability generating function for the system size and orbit size are obtained by using the method of supplementary variable technique. Some important system performance measures and the mean busy period are obtained. The conditional stochastic decomposition law is shown for good for this model. Finally, the effects of various parameters on the system performance are analysed numerically.

N-policy for $${M}^{{x}}/\hbox {G}/1$$ M x / G / 1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

Bulk arrival retrial G-queue with impatient customers and multi-services subject to server breakdowns has been analyzed. The system allows the arrival of two types of customers: positive customers and negative customers in the system. The negative customers make the server fail if they find the server in busy state, whereas positive customers are served if the server is idle otherwise they join the virtual pool of customers called orbit. The customers from the retrial orbit try their chance again for the service. The customers have the option of obtaining more than one service. Moreover, the customers are impatient and may renege from the system with probability \((1-r)\). The server is sent for repair as soon as it breakdowns; after repair, the service process starts again. Also, the server has the provision to initiate the service when there are N customers accumulated in the system. Using supplementary variables technique and generating functions, various performance measures like reliability indices and long run probabilities have been obtained.

Analysis of an unreliable retrial G-queue with working vacations and vacation interruption under Bernoulli schedule

Abstract In this paper, we consider a single server retrial queueing system with working vacations. Further vacation interruption is considering with the regular busy server is subjected to breakdown due to the arrival of negative customers. When the orbit becomes empty at the time of service completion for a positive customer, the server goes for a working vacation. The server works at a lower service rate during working vacation (WV) period. If there are customers in the system at the end of each vacation, the server becomes idle and ready for serving new arrivals with probability p (single WV) or it remains on vacation with probability q (multiple WVs). By using the supplementary variable technique, we found out the steady state probability generating function for the system and its orbit. System performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.

Batch arrival retrial G-queue with orbital search and non-persistent customers

An MX/G/1 retrial G-queue with orbital search and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and one of the positive customers receives service immediately if the server is free upon their arrivals and others may enter a retrial orbit and try their luck after a random time interval. Arrival of negative customer removes the positive customer being in service from the system and causes the server breakdown. After a completion of a service or a repair, the server searches for the customers in the orbit or remains idle. By using the supplementary variables method, we obtain the steady-state solutions for the system measures. The effects of various parameters on the system performance are analyzed numerically.

Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule

In this paper, we consider a batch arrival retrial queue with feedback under Bernoulli vacation schedule, where the busy server is subjected to breakdown due to the arrival of negative customers. Any arriving batch of positive customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. Arriving positive customers may balk (or renege) the system at particular times. After completion of service the unsatisfied positive customer may rejoin into the orbit to get another regular service as feedback customer. The server takes Bernoulli vacation after service completion of positive customers. After completion of service (if the server is not taking vacation), repair or vacation the server searches for the customers in the orbit or remains idle. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Some system performance measures, reliability measures and stochastic decomposition law are discussed. Finally, some numerical examples and cost optimization analysis are presented.

An M[X]/G/1 retrial g-queue with single vacation subject to the server breakdown and repair

An M[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.

An M/G/1 retrial G-queue with preemptive resume priority and collisions subject to the server breakdowns and delayed repairs

We consider an M/G/1 retrial G-queue with preemptive resume priority and collisions under linear retrial policy subject to the server breakdowns and delayed repairs. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The stability condition of the system is derived. Using generating function technique, the steady-state distributions of the server state and the number of customers in the orbit are obtained along with some interesting and important performance measures. The stochastic decomposition property is investigated. Further, some special cases of interest are discussed. Finally, numerical illustrations are provided.

A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule

We consider an M/G/1 retrial queue with negative customers and priority under Bernoulli vacation schedule subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. Positive customers receive service immediately if the server is idle upon their arrivals. Otherwise, they may either with probability p join the priority queue or with complementary probability p¯ enter a retrial orbit. A breakdown at the busy server is represented by the arrival of a negative customer which causes the the customer being in service to be lost. The server takes Bernoulli vacation after a service or a repair completion. It is assumed that the server has arbitrary repair time and vacation time distributions. With the help of Lyapunov functions we have obtained the necessary and sufficient condition for ergodicity of embedded Markov chain. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law. Besides, some special cases of interest are discussed. Finally, the effects of various parameters on the system performance are analyzed numerically.

An M/G/1 retrial G-queue with non-exhaustive random vacations and an unreliable server

This paper deals with an M/G/1 retrial queue with negative customers and non-exhaustive random vacations subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The server takes a vacation of random length after an exponential time when the server is up. We develop a new method to discuss the stable condition by finding absorb distribution and using the stable condition of a classical M/G/1 queue. By applying the supplementary variable method, we obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law. We also analyse the busy period of the system. Some special cases of interest are discussed and some known results have been derived. Finally, an application to cellular mobile networks is provided and the effects of various parameters on the system performance are analysed numerically.