Vacation

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1 - Fault tolerant system with imperfect coverage, reboot and server vacation
Madhu Jain Rakesh Kumar Meena

This study is concerned with the performance modeling of a fault tolerant system consisting of operating units supported by a combination of warm and cold spares. The on-line as well as warm standby units are subject to failures and are send for the repair to a repair f أکثر

This study is concerned with the performance modeling of a fault tolerant system consisting of operating units supported by a combination of warm and cold spares. The on-line as well as warm standby units are subject to failures and are send for the repair to a repair facility having single repairman which is prone to failure. If the failed unit is not detected, the system enters into an unsafe state from which it is cleared by the reboot and recovery action. The server is allowed to go for vacation if there is no failed unit present in the system. Markov model is developed to obtain the transient probabilities associated with the system states. Runge–Kutta method is used to evaluate the system state probabilities and queueing measures. To explore the sensitivity and cost associated with the system, numerical simulation is conducted. تفاصيل المقالة

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2 - Unreliable bulk retrial queues with delayed repairs and modified vacation policy
Madhu Jain Amita Bhagat

The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy. The incoming customers join the virtual pool of customers called orbit if they find the server being busy, on vacation or in broken down stat أکثر

The present investigation deals with the bulk arrival M/G/1 retrial queue with impatient customers and modified vacation policy. The incoming customers join the virtual pool of customers called orbit if they find the server being busy, on vacation or in broken down state otherwise the service of the customer at the head of the batch is started by the server. The service is provided inkessential phases to all the customers by the single server which may breakdown while rendering service to the customers. The broken down server is sent to a repair facility wherein the repair is performed indcompulsory phases. As soon as the orbit becomes empty, the server goes for vacation and takes at mostJvacations until at least one customer is noticed. The incoming customers are impatient and may renege on seeing a long queue of the customers for the service. The probability generating functions and queue length for the number of customers in the orbit and queue have been obtained using supplementary variable technique. Various system characteristics viz. average number of customers in the queue and the orbit, long run probabilities of the system states, etc. are obtained. Furthermore, numerical simulation has been carried out to study the sensitivity of various parameters on the system performance measures by taking an illustration. تفاصيل المقالة

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3 - Analysis of M/G/ 1 queueing model with state dependent arrival and vacation
Charan Jeet Singh Madhu Jain Binay Kumar

This investigation deals with single server queueing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a vacation of a f أکثر

This investigation deals with single server queueing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a vacation of a fixed duration or may continue to be available in the system for next service. Using the probability argument, we construct the set of steady state equations by introducing the supplementary variable corresponding to elapsed service time. Then, we obtain the probability generating function of the units present in the system. Various performance indices, such as expected number of units in the queue and in the system, average waiting time, etc., are obtained explicitly. Some special cases are also deduced by setting the appropriate parameter values. The numerical illustrations are provided to carry out the sensitivity analysis in order to explore the effect of different parameters on the system performance measures. تفاصيل المقالة

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4 - Vacation model for Markov machine repair problem with two heterogeneous unreliable servers and threshold recovery
Madhu Jain Rakesh Kumar Meena

Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the server أکثر

Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the servers. The server returns back to render repair job when the pre-specified workload of failed machines is build up. The first (second) repairman turns on only when the work load of N1(N2) failed machines is accumulated in the system. The both servers may go for vacation in case when all the machines are in good condition and there are no pending repair jobs for the repairmen. Runge–Kutta method is implemented to solve the set of governing equations used to formulate the Markov model. Various system metrics including the mean queue length, machine availability, throughput, etc., are derived to determine the performance of the machining system. To provide the computational tractability of the present investigation, a numerical illustration is provided. A cost function is also constructed to determine the optimal repair rate of the server by minimizing the expected cost incurredon the system. The hybrid soft computing method is considered to develop the adaptive neuro-fuzzy inference system (ANFIS). The validation of the numerical results obtained by Runge–Kutta approach is also facilitated by computational results generated by ANFIS. تفاصيل المقالة

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5 - Analysis of a Single Server Queue with Working Vacation and Vacation Interruption
Shakir Majid P Manoharan

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant أکثر

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obtain the stationary distribution for mean queue length. Moreover, we have derived the distributions for the mean queue length and the mean waiting time and obtained their stochastic decomposition structures if N=2. Finally, numerical examples are presented. تفاصيل المقالة

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6 - Perishable Inventory Model with Retrial Demands, Negative Customers and Multiple Working Vacations
Vijaya Laxmi Pikkala Soujanya M.L.

This paper presents the analysis of a continuous review perishable inventory system wherein the life time of each item follows an exponential distribution. The operating policy is (s,S) policy where the ordered items are received after a random time which follows expone أکثر

This paper presents the analysis of a continuous review perishable inventory system wherein the life time of each item follows an exponential distribution. The operating policy is (s,S) policy where the ordered items are received after a random time which follows exponential distribution. Primary arrival follows Poisson distribution and they may turnout to be positive or negative and then enter into the orbit. The orbiting demands compete their service according to exponential distribution. The server takes multiple working vacations at zero inventory. We assume that the vacation time, service times both during regular busy period and vacation period are exponentially distributed. Matrix analytic method is used for the steady state distribution of the model. Various performance measures and cost analysis are shown with numerical results. تفاصيل المقالة

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7 - Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking
Vijaya Laxmi Pikkala Rajesh Pilla

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $\bar{b} = 1-b$. As soon as the system becomes empty, the server t أکثر

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $\bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed to be exponentially distributed and are mutually independent. We have obtained the transient-state probabilities in terms of modified Bessel function of the first kind by employing probability generating function, continued fractions and Laplace transform. In addition, we have also obtained some other performance measures. تفاصيل المقالة

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8 - Discrete Time Analysis of Multi-Server Queueing System with Multiple Working Vacations and Reneging of Customers‎
Vijaya Laxmi Pikkala Wondewosen Kassahun

This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service tim أکثر

This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customers waiting for service are subject to reneging and the reneging times are also assumed to be geometrically distributed. The explicit expressions for the steady-state probabilities are obtained recursively from the difference equations that represent the model. Closed form expressions of the system size are also derived both during regular busy period and during $WV$. In addition, we obtain some other performance measures and a cost model is formulated to determine the optimal service rate during working vacation. تفاصيل المقالة

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9 - Bat Algorithm for Optimal Service Parameters in an Impatient Customer <i>N</i>-Policy Vacation Queue
Vijaya Laxmi Pikkala

In this paper, a meta-heuristic method, the Bat Algorithm, based on the echolocation behavior of bats is used to determine the optimum service rate of a queue problem. A finite buffer M/M/1 queue withN policy, multiple working vacations and Bernoulli schedule vacation i أکثر

In this paper, a meta-heuristic method, the Bat Algorithm, based on the echolocation behavior of bats is used to determine the optimum service rate of a queue problem. A finite buffer M/M/1 queue withN policy, multiple working vacations and Bernoulli schedule vacation interruption is considered. Under the two customers' impatient situations, balking and reneging, the queue is studied using the matrix geometric method. Simulations show that the proposed algorithm seems much superior to other algorithms. تفاصيل المقالة

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10 - ANALYSIS OF A DISCRETE-TIME IMPATIENT CUSTOMER QUEUE WITH BERNOULLI-SCHEDULE VACATION INTERRUPTION
P. Vijaya Laxmi K. Jyothsna

This paper investigates a discrete-time impatient customer queue with Bernoulli-schedule vacation interruption. The vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain أکثر

This paper investigates a discrete-time impatient customer queue with Bernoulli-schedule vacation interruption. The vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. Cost analysis is carried out using particle swarm optimization. Computational experiences with a variety of numerical results are discussed. تفاصيل المقالة

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11 - FINITE POPULATION SINGLE SERVER BATCH SERVICE QUEUE WITH COMPULSORY SERVER VACATION
Rathinasabapathy Kalyanaraman R. Mahalakshmi

A single server finite population queueing model with compulsory server vacation and with fixed batch service has been considered. For this model the system steady state probabilities are obtained. Some performance measures are calculated and numerical examples are also أکثر

A single server finite population queueing model with compulsory server vacation and with fixed batch service has been considered. For this model the system steady state probabilities are obtained. Some performance measures are calculated and numerical examples are also given. تفاصيل المقالة

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12 - ON (A,C,B) POLICY QUEUE WITH CHANGE OVER TIMES UNDER BERNOULLI SCHEDULE VACATION INTERRUPTION
Vijaya Laxmi Pikkala Seleshi Demie

This paper analyzes a renewal input working vacations queue with change over times and Bernoulli schedulevacation interruption under (a,c,b) policy.The service and vacation times are exponentially distributed.The server begins service if there are at least c units in th أکثر

This paper analyzes a renewal input working vacations queue with change over times and Bernoulli schedulevacation interruption under (a,c,b) policy.The service and vacation times are exponentially distributed.The server begins service if there are at least c units in the queue and the service takes place in batches with a minimum of sizea and a maximum of size b (a<=c<= b). The change over periods follow if there are (c-1) customers (at vacation completion instant) or (a-1) customersat service completion instants. The steady state queue length distributions at arbitrary and pre-arrival epochs are obtained. Performance measures and optimal cost policy arepresented with numerical experiences.The genetic algorithm and quadratic fit search method are employed to search the optimal values of some important parameters of the system. تفاصيل المقالة

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13 - AN M/G/1 QUEUE WITH REGULAR AND OPTIONAL PHASE VACATION AND WITH STATE DEPENDENT ARRIVAL RATE
Rathinasabapathy Kalyanaraman Shanthi R

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there areno customers in the system, the server takes vacation consisting of K -phases, each phaseis generally أکثر

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there areno customers in the system, the server takes vacation consisting of K -phases, each phaseis generally distributed. Here the first phase is compulsory where as the other phases areoptional. For this model the supplementary variable technique has been applied to obtainthe probability generating functions of number of customers in the queue at the different server states. Some particular models are obtained and a numerical study is also carriedout. تفاصيل المقالة

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14 - A SINGLE SERVER BERNOULLI VACATION QUEUE WITH TWO TYPE OF SERVICES AND WITH RESTRICTED ADMISSIBILITY
R. Kalyanaraman V. Suvitha

A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue a أکثر

A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. Some performance measures are calculated. Some particular cases are obtained and numerical examples are also presented. تفاصيل المقالة

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15 - ANALYSIS OF RENEWAL INPUT STATE DEPENDENT VACATION QUEUE WITH $N$-POLICY
Vijaya Laxmi Pikkala Suchitra Vepada

This paper analyzes renewal input state dependent queuewith $N$- policy wherein the server takes exactly one vacation.Using the supplementary variable technique and recursive method,we derive the steady state system length distributions at various epochs.Various perform أکثر

This paper analyzes renewal input state dependent queuewith $N$- policy wherein the server takes exactly one vacation.Using the supplementary variable technique and recursive method,we derive the steady state system length distributions at various epochs.Various performance measures has been presented. Finally, some numericalcomputations in the form of graphs are presented to show the parametereffect on various performance measures. تفاصيل المقالة

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