Server Breakdowns Research Articles

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.

Randomized controlling arrival for a queueing system with subject to server breakdowns

This paper considers the optimal management problem of a finite-capacity M/M/1/K queueing system with -policy in which the server may break down while working. When the number of customers reaches its capacity K, no further arriving customers are allowed to enter the system. Customers are allowed to system with probability p or the customers are still unable to enter the system with probability 1 − p as the queue length decreases to a certain threshold value F. By applying the birth-and-death process, some important performance measures are derived. A cost model, developed to determine the optimal continuous and discrete control parameters for the -policy at a minimum cost, and sensitivity analysis are also studied.

Unreliable multiserver queueing system with modified vacation policy

This paper presents modeling and analysis of Markovian multiserver queue under (e, d) single vacation policy with server breakdowns and repairs. In such a system with c servers, when some (say d < c) servers become idle at a service completion time, then e(≤ d) servers take single vacation only. During idle as well as busy state, the servers are subject to accidental breakdowns. We formulate the model as a quasi-birth-and-death (QBD) process. By employing matrix geometric method, some stationary performance measures after service completion are established. Furthermore, the direct search algorithm is used to simultaneously determine the optimal number of idle, vacationing and total number of servers at minimum cost. Numerical illustration is facilitated to explore the effect of the number of servers, vacation rate, failure and repair rates on the performance measures of interest. Furthermore, the numerical results obtained are compared by using soft computing approach based on adaptive neuro fuzzy inference system (ANFIS).

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.

Performance analysis of voice over internet protocol via non Markovian loss system with preemptive priority and server break down

Voice over Internet Protocol (VoIP) or Internet telephony has become an evolutionary and promising technology in the area of telecommunications. Lower costs and simpler maintenance are the major reasons of its increasing popularity. However, the network is inherently unreliable and highly challenged when it comes to quality of service (QoS). The VoIP system is primarily a multi-server system which may also face failures. Hence, in order to study the performance of VoIP, it is proposed to develop a multi-server, loss system with general service times, server breakdown and repair together with preemptive priority queuing discipline, for two types of customers: high priority and low priority. The customers are served immediately if the server is available. However, if all servers are busy, then on the arrival of a high priority customer, the service of a low priority customer is preempted. The steady state distribution of such underlying system is obtained together with the performance measures. A numerical illustration of the obtained results is also presented graphically. The results are validated using simulation.

Transient solution of an $M^{[X]} / G / 1$ queuing model with feedback, random breakdowns and Bernoulli schedule server vacation having general vacation time distribution

This paper analyze an $M^{[X]} / G / 1$ queue with feedback, random server breakdowns and Bernoulli schedule server vacation with general(arbitrary) distribution. Customers arrive in batches with compound Poisson process and are served one by one with first come first served basis. Both the service time and vacation time follow general (arbitrary) distribution. After completion of a service the may go for a vacation with probability $\theta$ or continue staying in the system to serve a next customer, if any with probability $1-\theta$. With probability $\mathrm{p}$, the customer feedback to the tail of original queue for repeating the service until the service be successful. With probability $1-p=q$, the customer departs the system if service be successful. The system may breakdown at random following Poisson process, whereas the repair time follows exponential distribution. We obtain the time dependent probability generating function in terms of their Laplace transforms and the corresponding steady state results explicitly. Also we derive the system performance measures like average number of customers in the queue and the average waiting time in closed form.

A matrix geometric approach to the M/M/1 two-phase multi optional retrial queue with Bernoulli feedback, impatient customers and a server subject to breakdown and repair

In this paper, we use the matrix geometric approach to analyze the behaviour of an Interactive Voice Response System (IVRS). We model the system as an M/M/1 retrial queue with two phases of service (the second service is multi optional), Bernoulli feedback, impatient customers and the possibility of server breakdown and repair. We study the stability of the system by employing the Neuts and Rao (Queueing Syst. 7, 169–190 (1990)) truncation method and then we study the level dependent QBD (Quasi-Birth Death) model obtained by the above truncation method to obtain expressions for the performance measures of the system. Numerical illustrations are provided to study the sensitivity of the performance measures of the system to the changes in various parameters of the system.

Analysis of queue with two phases of service and m phases of repair for server breakdown under N-policy

The present paper deals with a single server queueing system wherein the customers join the system in bulk with varying arrival rates. The first stage regular service and second stage optional service are provided to the customers. The server may breakdown at any instant during any stage of service. There is a provision of essential and optional repair in m phases. To discuss the steady state behaviour of the system, the assumptions of probability reasoning and supplementary variable technique is employed. Various performance indices are obtained using the generating function approach. To verify the validity of these indices, the numerical illustrations are provided. The technique of principle of maximum entropy is also considered to find the approximate values of the system probabilities for the queue length distribution.

An M&lt;SUP align="right"&gt;x&lt;/SUP&gt;/G/1 retrial queue with two phase service under active server breakdowns, two types of repair and multiple vacations with N-policy

This paper analyses a single server batch arrival retrial queue with active breakdowns, two types of repair, a second optional service and multiple vacations with N-policy. The server may breakdown while providing first essential service. When the server fails, it is repaired immediately. On successful completion of first essential service, the customer may opt for second optional service with probability α. At a service completion epoch, without any request for re-service and the orbit size being zero, the server does a secondary job (vacation) repeatedly until the number of customers in the orbit reaches the threshold value N. At a secondary job completion epoch, if the orbit size in at least N, then the server remains in the system to render service for customers from main pool or from retrial group. The steady state queue size distribution of number of customers in the orbit and expected number of customers in the retrial group are obtained. Some particular cases and reliability measures are discussed. Also, some performance measures are obtained. Numerical illustrations are also provided.

Analysis of G–queue with unreliable server

This paper presents a model for a discrete time single server G-queue with two types of independent arrivals, namely positive and negative. The arrival of negative customer to queueing system removes one customer from the head of the queue (RCH), which causes server breakdown. The repair of the server is non- instantaneous and after repair server is assumed as good as new. The interarrival times of both positive and negative customers and the repair times of the server are geometrically distributed. We analyse the queueing system by using Matrix Geomet- ric method. The expressions for various performance measures such as mean queue length, throughput, delay, etc. are derived and calculated numerically.

Social Optimization Strategy in Unobserved Queueing Systems in Cognitive Radio Networks

We study a noncooperative game problem for queueing control in the Cognitive Radio (CR) system where selfish Secondary User's (SU) data packets (a.k.a. customers in this work) are served by a CR base station (a.k.a. server). The scenario is modeled as an M/M/1 queueing game with server breakdowns where each customer wants to optimize their benefit in a selfish distributed manner. We first show that the game has an inefficient unique Nash Equilibrium (NE). In order to improve the outcome efficiency, we propose an appropriate admission fee that can be easily implemented at the server. We then show that the social welfare at the equilibrium point can be coincided the social welfare of the socially optimal strategy.

Analysis and optimization of a repairable M (x) /G/1 queue with an additional optional vacation

This paper investigates an M[x]/G/1 queueing system with an unreliable server, where the server may take an additional vacation after the essential vacation. If the system becomes empty, the server leaves the system and takes the essential vacation. At the end of the essential vacation, the server may return to the system with probability p or take another vacation with probability 1-p. When the additional vacation is completed, the server returns from the vacation. If there are no customers waiting for service in the system, the server waits idly for the first arrival and starts working. It is assumed that the server is subject to break down according to a Poisson process and the repair time obeys a general distribution. For such a system, we derive the system size distribution at a random epoch, as well as various system characteristics. Finally, we develop an iterative procedure to find the optimal threshold values under a linear cost structure. Some numerical experiments are also presented. Key words: Cost, optimization, server breakdowns, vacation queue.

On a Customer-Induced Interruption in a Service System

Server induced interruptions such as server break downs, server attending a high priority customer, and server taking a vacation in queues have been extensively studied in the literature. However, customer-induced interruptions such as customers leaving in the middle of a service due to not having enough information for completing a service and customer breakdowns have not been studied so far. The purpose of this work is to introduce customer interruptions in queueing systems. We consider an infinite capacity queueing system with a single server to which customers arrive according to a Poisson process and the service time follows an exponential distribution. The customer interruption while in service occurs according to a Poisson process and the interruption duration follows an exponential distribution. The self-interrupted customers will enter into a finite buffer of size K. Any interrupted customer, finding the buffer full, is considered lost. Those interrupted customers who complete their interruptions will be placed into another buffer of same size. The interrupted customers waiting for service are given non-preemptive priority over new customers. We investigate the behavior of this queuing system. Several performance measures are evaluated. Numerical illustrations of the system behavior are also provided. An optimization problem of interest will be discussed through an illustrative example.

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.

정보보안 예산 수립에서 퍼지 AHP의 적용을 통한 위험 비용 분석

Recently, the breakdown of online banking servers and the leakage of customer information give rise to much concern about the security of information systems in financial and banking companies in Korea. The enforcement of security for information system becomes much more important issue than earlier. However, the security reinforcement of information system is restricted by a budget. In addition, the activities` cost to secure information system from threatening are under uncertain circumstances and should be established by a human decision maker who is basically uncertain and vague. Thus, making the budget for information system is exposed to any extent of the risk for these reasons. First, we introduce brief fuzzy set theory and fuzzy AHP (Analytic Hierarchy Process) methodology. Then, the cost elements that comprise yearly budget are presented and the priorities among the cost elements are calculated by fuzzy AHP. The cost elements that are exposed to risk are evaluated from the both perspectives of the risk impact and risk occurrence possibility which are expressed as linguistic terms. To get information on the risk profiles-pessimistic, most likely, and optimistic-for each cost element, the evaluation is accomplished and the result is presented. At last, the budget ranges-minimum, mode, maximum-for each cost element are estimated with the consideration of the risk profiles.

A study on the behaviour of the server breakdown without interruption in a Mx/G(a, b)/1 queueing system with multiple vacations and closedown time

The objective of this paper is to study the behavior of the server breakdown without interruption in a Mx/G(a, b)/1 queueing system with multiple vacations and closedown time. After completing a batch of service, if the server is breakdown with probability (π) then the renovation of service station will be considered. After completing the renovation of service station or if there is no breakdown of the server with probability (1−π), if the queue length is ξ, where ξ<a, then the server performs closedown work at its closedown time C. After that, the server leaves for multiple vacation of random length. After a vacation, when the server returns, if the queue length is less than ‘a’, he leaves for another vacation and so on, until he finds ‘a’ customers in the queue. After a vacation, if the server finds at least ‘a’ customers waiting for service, say ξ, then he prefers to serve a batch of size min(ξ,b) customers, where b⩾a. The probability generating function of queue size at an arbitrary time and some important characteristics of the queueing system and a cost model are derived. An extensive numerical result for a particular case of the model is illustrated.

Cost analysis of a finite capacity queue with server breakdowns and threshold-based recovery policy

This paper analyzes a repairable M/M/1/N queueing system under a threshold-based recovery policy. The threshold-based recovery policy means that the server breaks down only if there is at least one customer in the system, and the recovery can be performed when q (1≤q≤N) or more customers are present. For this queueing system, a recursive method is applied to obtain steady-state solutions in neat closed-form expressions. We then develop some important system characteristics, such as the number of customers in the system, the probability that the server is busy, the effective arrival rate and the expected waiting time in the system, etc. A cost model is constructed to determine the optimal threshold value, the optimal system capacity and the optimal service rate at a minimum cost. In order to solve this optimization problem, the direct search method and Newton's method are employed. Sensitivity analysis is also conducted with various system parameters. Finally, we present some managerial insights through an application example.

Analysis of the [formula omitted] [formula omitted]-queueing system with retrial customers

We consider a single server retrial queue with waiting places in service area and three classes of customers subject to the server breakdowns and repairs. When the server is unavailable, the arriving class-1 customer is queued in the priority queue with infinite capacity whereas class-2 customer enters the retrial group. The class-3 customers which are also called negative customers do not receive service. If the server is found serving a customer, the arriving class-3 customer breaks the server down and simultaneously deletes the customer under service. The failed server is sent to repair immediately and after repair it is assumed as good as new. We study the ergodicity of the embedded Markov chains and their stationary distributions. We obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law, the busy period of the system and the virtual waiting times. Finally, an application to cellular mobile networks is provided and the effects of various parameters on the system performance are analyzed numerically.

Survey on Security Issues in Cloud Computing and Associated Mitigation Techniques

Cloud Computing holds the potential to eliminate the requirements for setting up of high-cost computing infrastructure for IT-based solutions and services that the industry uses. It promises to provide a flexible IT architecture, accessible through internet for lightweight portable devices. This would allow multi-fold increase in the capacity or capabilities of the existing and new software. In a cloud computing environment, the entire data reside over a set of networked resources, enabling the data to be accessed through virtual machines. Since these data-centers may lie in any corner of the world beyond the reach and control of users, there are multifarious security and privacy challenges that need to be understood and taken care of. Also, one can never deny the possibility of a server breakdown that has been witnessed, rather quite often in the recent times. There are various issues that need to be dealt with respect to security and privacy in a cloud computing scenario. This extensive survey paper aims to elaborate and analyze the numerous unresolved issues threatening the cloud computing adoption and diffusion affecting the various stake-holders linked to it.

Queues with interruptions: a survey

In this paper we survey work related to queues with interruptions that occur due to many reasons such as server breakdowns, servers taking emergency breaks, and customers having incomplete information or getting distracted. We look at both continuous and discrete time queueing models with interruptions in this survey.