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Page 1. 260 Int. J. Information and Communication Technology, Vol. 2, No. 3, 2010 Copyright © 2010 Inderscience Enterprises Ltd. Performance analysis of distributed video-on-demand (VoD) systems Madhu Jain Department ...
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This investigation deals with multi server queues with balking. The customers arrive in poisson fashion and independent of time, under the assumption that the system is initially empty. The number of customers in the system stochastically... more
This investigation deals with multi server queues with balking. The customers arrive in poisson fashion and independent of time, under the assumption that the system is initially empty. The number of customers in the system stochastically increases and distributed in a steady state (stationary state) as required. The expressions for the measure of the speed of convergence from transient state to steady state within in the probability of the system are obtained.
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The objective of this paper is to study the M/M/R machine repair queueing system with mixed standbys. The life-time and repair time of units are assumed to be exponentially distributed. Failed units are repaired on FCFS basis. The... more
The objective of this paper is to study the M/M/R machine repair queueing system with mixed standbys. The life-time and repair time of units are assumed to be exponentially distributed. Failed units are repaired on FCFS basis. The standbys have switching failure probability q (0 ≤ q ≤ 1). The repair facility of the system consists of R permanent as well as r additional removable repairmen. Due to impatience, the failed units may balk or renege, with a certain probability, on finding all repairmen busy. Transient probabilities of various states are obtained by solving the set of governing equations via Runge-Kutta method. Expressions for various performance measures are established in terms of transient probabilities of system states. By varying different parameters, the system behavior is examined with the help of numerical illustrations.
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In this paper, we study N-policy for a finite population Bernoulli feedback queuing model for machine repair problem with degraded failure. The running times of the machines between breakdowns have an exponential distribution. The repair... more
In this paper, we study N-policy for a finite population Bernoulli feedback queuing model for machine repair problem with degraded failure. The running times of the machines between breakdowns have an exponential distribution. The repair times of the machines are independent and identically distributed random variables. If at any time a machine fails, it is sent to the repairman for repairing, the repairman restores the machine to the state as before failure. When the failed machine finds the repairman busy upon its failure, it has to wait until its turn as repairman stores only one machine at a time. When all the standby components are used, the failure of components occurs in a degraded fashion. To obtain the steady-state probabilities, the supplementary variable is introduced and a recursive method is employed. Some performance measures viz. expected number of down machines, expected number of machines waiting for repair in the queue, expected number of operating machines, expect...
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Mathematical modeling based on a probabilistic approach for making decisions for organ transplantation can be successfully employed in cases when the choice of decisions can affect the results produced. In this study, the minimum... more
Mathematical modeling based on a probabilistic approach for making decisions for organ transplantation can be successfully employed in cases when the choice of decisions can affect the results produced. In this study, the minimum probability of success required for organ transplantion in case of multi-donors is determined. The governing equations are constructed in terms of probabilities and some other factors like quality adjusted life-years (QALYs) of recipients, donors, expected knowledge gain, medical benefit and expected fame of surgeon. The analytical results are obtained by solving equations and illustrated numerically.
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This paper deals with the G/G/R machining system consisting of M operating machines as well as S cold standbys. The concepts of balking and reneging are incorporated which make our model more versatile to deal with real time systems. The... more
This paper deals with the G/G/R machining system consisting of M operating machines as well as S cold standbys. The concepts of balking and reneging are incorporated which make our model more versatile to deal with real time systems. The broken-down machines are sent to repair facilities consisting of R permanent repairmen. The failure times and repair times are generally identical and independent distributed random variables. The failed machines are repaired according to FIFO rules. By using a diffusion process, the steady-state probability density function for the queue size is obtained in terms of the first two moments of inter-arrival times and repair times of machines. Some expressions in explicit form that characterize the system performance are also mentioned.
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In this paper we examine the effect of mild stenosis on blood flow, in an irregular axisymmetric artery with oscillating pressure gradient. The Herschel-Bulkley fluid model has been utilized for this study. The combined influence of an... more
In this paper we examine the effect of mild stenosis on blood flow, in an irregular axisymmetric artery with oscillating pressure gradient. The Herschel-Bulkley fluid model has been utilized for this study. The combined influence of an asymmetric shape and surface irregularities of constriction has been explored in this computational study. An extensive quantitative analysis has been performed for narrowing of vessels through numerical computations on the flow velocity, plug flow rate and the apparent fluidity. The graphical representations have been made to validate the analytical findings with a view of its applicability to stenotic diseases. Velocity profiles, plug flow rate, and apparent fluidity along the radius of the obstructed tube are determined to give the flow characteristics, for diagnostic point of view. The effects of viscosity on the flow field are examined numerically and are shown graphically.
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In this paper, we consider a multi-server queuing system in which additional servers are allowed for a longer queue to reduce the customer's balking and reneging behavior. The customers are assumed to arrive in Poisson fashion and... more
In this paper, we consider a multi-server queuing system in which additional servers are allowed for a longer queue to reduce the customer's balking and reneging behavior. The customers are assumed to arrive in Poisson fashion and their service- times follow exponential distribution. The number of servers in long run depends on the queue-length. We obtain equilibrium queue size distribution. The expression for expected number of customers in the system in the long run has been obtained. Some other performance measures have also been provided. In order to match our results with earlier work, special cases are discussed. The numerical results are presented to verify the validity of the proposed analytical method
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In the present study, we analyze the multi-channel service system with ordered entry from finite-source and finite-storage at each channel. The arrival and service rates are assumed to be state dependent. The steady state probabilities of... more
In the present study, we analyze the multi-channel service system with ordered entry from finite-source and finite-storage at each channel. The arrival and service rates are assumed to be state dependent. The steady state probabilities of the system are obtained by using Chapmann-Kolmogorov equations. Some other performance indices viz. utilization of servers, expected number of units in the system and expected number of units at each channel have been derived. A computational algorithm is developed to determine the optimal allocation of storage space facilitated in front of three heterogeneous servers. Sensitivity analysis has been carried out to study the effect of variation of different parameters on the system performance.
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In the present investigation transient, G x/G/m queuing model with balking and reneging has been studied. The diffusion process with elementary return boundary has been used for modeling purpose. The probability density function (p. d.... more
In the present investigation transient, G x/G/m queuing model with balking and reneging has been studied. The diffusion process with elementary return boundary has been used for modeling purpose. The probability density function (p. d. f.) for the number of customers in the system has been obtained. In special case, the steady state results that tally with those of Kimura and Ohsone have been established as a limiting case.
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In this paper we examine the effect of mild stenosis on blood flow, in an irregular axisymmetric artery with oscillating pressure gradient. The Herschel-Bulkley fluid model has been utilized for this study. The combined influence of an... more
In this paper we examine the effect of mild stenosis on blood flow, in an irregular axisymmetric artery with oscillating pressure gradient. The Herschel-Bulkley fluid model has been utilized for this study. The combined influence of an asymmetric shape and surface irregularities of constriction has been explored in this computational study. An extensive quantitative analysis has been performed for narrowing of vessels through numerical computations on the flow velocity, plug flow rate and the apparent fluidity. The graphical representations have been made to validate the analytical findings with a view of its applicability to stenotic diseases. Velocity profiles, plug flow rate, and apparent fluidity along the radius of the obstructed tube are determined to give the flow characteristics, for diagnostic point of view. The effects of viscosity on the flow field are examined numerically and are shown graphically.
This paper deals with the transient analysis of K-out-of-N: G system consisting of Noperatingmachines. To improve system reliability, Y cold standby and S warm standbys spares areprovided to replace the failed machines. The machines are... more
This paper deals with the transient analysis of K-out-of-N: G system consisting of Noperatingmachines. To improve system reliability, Y cold standby and S warm standbys spares areprovided to replace the failed machines. The machines are assumed to fail in multiple modes. At leastK-out-of-N machines for smooth functioning of the system. Reliability and mean time to failure areestablished in terms of transient probabilities.
Retrial queues have been widely used to model the problems in telephone switching systems, telecommunications networks, etc., wherein a job receiving incomplete service may seek service repeatedly, until served successfully. This paper... more
Retrial queues have been widely used to model the problems in telephone switching systems, telecommunications networks, etc., wherein a job receiving incomplete service may seek service repeatedly, until served successfully. This paper deals with M X /G/1 bulk retrial queue with Bernoulli service schedule. The server is being subjected to active breakdowns. The investigation is made by taking the concept of the impatient customers under both classical and constant retrial policy. Chapman-Kolmogrov equations are constructed by using supplementary variable technique and the queue size distribution by using the probability generating method has been obtained. We also analyze the stochastic decomposition property for retrial queue under consideration. Some performance characteristics and special cases are established.
In this investigation a non-equilibrium thermodynamic model of the temperature dependent biological growth of a living systems has been analyzed. The results are derived on the basis of Gompertzian growth equation. In this model, we have... more
In this investigation a non-equilibrium thermodynamic model of the temperature dependent biological growth of a living systems has been analyzed. The results are derived on the basis of Gompertzian growth equation. In this model, we have considered the temperature dependent growth rate and development parameter. The non-equilibrium thermodynamic model is also considered for exploring the variation of growth rate with temperature. The biological growth process of a living system near the threshold temperature has been studied. The growth rate has been taken as general function of temperature. The analytical solution has been obtained by solving differential equation governing the model. The solution of non linear equation provides an expression for biomass of the living systems at a time t, which is valid for a temperature near the threshold temperature. The numerical experiment has been conducted to exhibit the effects of various parameters on growth. The physical conditions of a li...
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Mathematical modeling based on a probabilistic approach for making decisions for organ transplantation can be successfully employed in cases when the choice of decisions can affect the results produced. In this study, the minimum... more
Mathematical modeling based on a probabilistic approach for making decisions for organ transplantation can be successfully employed in cases when the choice of decisions can affect the results produced. In this study, the minimum probability of success required for organ transplantion in case of multi-donors is determined. The governing equations are constructed in terms of probabilities and some other factors like quality adjusted life-years (QALYs) of recipients, donors, expected knowledge gain, medical benefit and expected fame of surgeon. The analytical results are obtained by solving equations and illustrated numerically.
With the evolution of technology, the maintenance of sophisticated systems is of concern for system engineers and system designers. The maintenance cost of the system depends in general on the replacement and repair policies. The system... more
With the evolution of technology, the maintenance of sophisticated systems is of concern for system engineers and system designers. The maintenance cost of the system depends in general on the replacement and repair policies. The system replacement may be in a strictly periodic fashion or on a random basis depending upon the maintenance policy. At failure, the repair of the system may be performed perfectly or minimally associated with some probability. When perfect repair is done, it makes the system as good as the new one. In case of minimal repair, it returns to the working condition of the system at the time of failure. In the present paper, we study the replacement policies for the system wherein minimal or perfect repair is done at the time of failure. The expressions for s- expected cost for the system with replacement and minimal or perfect repair are evaluated. The maintenance costs are discussed for various policies. Numerical simulation is performed to validate the analyt...
In this paper, a multi-repairmen machine repair problem comprising of M operating units together with k type of warm spares has been investigated. The failed units are immediately attended by repairmen if available. When there are no... more
In this paper, a multi-repairmen machine repair problem comprising of M operating units together with k type of warm spares has been investigated. The failed units are immediately attended by repairmen if available. When there are no failed units in the queue for repair, the repairmen leave for a vacation of random length. When the vacation period is terminated, the repairmen return and check for any failed unit in the queue. If the queue is non-empty, the repairmen start repairing of failed units until the queue becomes empty, and again they leave for another vacation. The repair rate of the repairmen depends upon the workload. The caretaker of the failed machines may renege on finding all repairmen busy. The steady state queue size distribution and other important performance measures have been derived using matrix recursive approach. Furthermore, a numerical example provides a profound understanding of the sensitivity of parameters with
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This investigation presents an economic production quantity (EPQ) model for deteriorating items with stock-dependent demand and shortages. It is assumed that a constant fraction of the on-hand inventory deteriorates and demand rate... more
This investigation presents an economic production quantity (EPQ) model for deteriorating items with stock-dependent demand and shortages. It is assumed that a constant fraction of the on-hand inventory deteriorates and demand rate depends upon the amount of the stock level. Expression for various optimal indices as well as cost analysis are provided. By taking numerical illustration, sensitivity analysis has been carried out. For cost optimization, Newton's method is employed.
⎯This paper is concerned with the analysis of unreliable server bulk arrival retrial queue with two class non-preemptive priority subscribers. The two types of subscribers arrive according to Poisson flow in which priority is assigned to... more
⎯This paper is concerned with the analysis of unreliable server bulk arrival retrial queue with two class non-preemptive priority subscribers. The two types of subscribers arrive according to Poisson flow in which priority is assigned to class one, and class two subscribers are of non-priority type. The subscribers in each class arrive to the system in batches; the batch sizes follow the geometric process. If the server is free at the time of any batch arrivals, the subscriber of this batch begins to be served immediately and leave the system forever. The priority subscribers that find the server busy are queued and then are served in accordance with FCFS discipline. The arriving non-priority subscribers on finding the server busy cannot be queued and leave the service area and try their chance after some random time. If a subscriber is being served at the instant of the server failure, the service is interrupted and restarted after repair. The life time of the server is assumed to ...
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Waiting in long queue is undesirable due to which in some practical situations customers become impatient and leave the system. In such cases providing additional servers can reduce long queue. This investigation deals with multi-server... more
Waiting in long queue is undesirable due to which in some practical situations customers become impatient and leave the system. In such cases providing additional servers can reduce long queue. This investigation deals with multi-server queueing system with additional servers and discouragement. The customers arrive in poisson fashion and are served exponentially by a pool of permanent and additional servers on the basis of FCFS queue discipline. The explicit formula to determine the number of customers in the queue has been obtained. Numerical illustration has been provided to validate the analytical results established. Graphs are drawn for expected number of customers in the system and probability of all additional servers being busy in order to visualize the effect of various parameters.
The present investigation presents a stochastic model for a flexible manufacturing system consisting of flexible machine, loading/unloading robot and an automated pallet- handling device. We consider unreliable flexible manufacturing cell... more
The present investigation presents a stochastic model for a flexible manufacturing system consisting of flexible machine, loading/unloading robot and an automated pallet- handling device. We consider unreliable flexible manufacturing cell (FMC) wherein machine and robot operate under individual as well as common cause random failures. The pallet- handling system is completely reliable. The pallet operation times, loading/unloading times and material handling times are considered to be random and exponentially distributed. By constructing governing equations for various system states at equilibrium, the steady-state probabilities are obtained. Some system characteristics namely utilization rate of the handling system, utilization rate of the production machine and utilization rate of the robot etc. are obtained. Some special cases are also discussed for reliable and unreliable cells. Sensitivity analysis is facilitated to examine the effect of parameters on system performance by taki...
In this paper, we investigate the M/M/1/N single server finite capacity Markovian queueing model with operational vacation and impatient behavior of the customers. To recover the server broken down during a busy period, M-threshold... more
In this paper, we investigate the M/M/1/N single server finite capacity Markovian queueing model with operational vacation and impatient behavior of the customers. To recover the server broken down during a busy period, M-threshold recovery policy along with set-up is used. Using the inflow and outflow transition rates, the state probabilities equations for different system states are constructed. For computing the stationary queue length, matrix-geometric analytic is performed. The sensitivity analysis is carried for the validation of the system performance measures. To examine the scope of the adaptive neuro-fuzzy inference system (ANFIS), computational results are presented using matric-geometric and ANFIS approaches. KeywordsM/M/1/N, Operational vacation, Impatient customers, Matrix-geometric method, ANFIS.
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This study is concerned with threshold F-policy and N-policy for controlling the arrivals and service in the queueing scenario of a machining system, having active and redundant components. For both F-policy and N-policy models, the queue... more
This study is concerned with threshold F-policy and N-policy for controlling the arrivals and service in the queueing scenario of a machining system, having active and redundant components. For both F-policy and N-policy models, the queue size distributions are determined by the recursive method. Various performance measures, namely the average number of failed units in the system, probability that the server is busy or idle in the system, etc., are established using the queue size distribution.
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In this study, we consider a single server vacation queueing model with optional bulk service and an un-reliable server. A single server provides first essential service (FES) to all arriving customers one by one; apart from essential... more
In this study, we consider a single server vacation queueing model with optional bulk service and an un-reliable server. A single server provides first essential service (FES) to all arriving customers one by one; apart from essential service, he can also facilitate the additional phase of optional service (OS) in batches of fixed size b( ≥ 1), in case when the customers request for it. The server may take a single vacation whenever he finds no customers waiting in the queue to be served. Moreover, the server is subjected to unpredictable breakdown while providing the first essential service. The vacation time, service time and repair time of the server are exponentially distributed. The steady state results are obtained in terms of probability generating function for queue size distributions. By using the maximum entropy analysis (MEA), we derive various system performance measures. A comparative study is performed between the exact and approximate waiting time of the system. By ta...
The present investigation studies a discrete time single server queue with both positive and negative arrival streams in accordance with removal of the customer from the end (RCE)-in immune and immune service killing policy. This study is... more
The present investigation studies a discrete time single server queue with both positive and negative arrival streams in accordance with removal of the customer from the end (RCE)-in immune and immune service killing policy. This study is a generalization of the queue with negative customers, wherein only positive customers need a service and negative customers arriving to the system can kill the already present positive customers from any where in the queue, otherwise get lost. The concept of both in-immune and immune service killing are taken into consideration. According to the in-immune killing policy, the negative customer is allowed to kill the most recent positive customer inspite of whether it is in service or not, while the immune service killing discipline suggests that the customer currently being served is immune from killing by the negative arrival. We analyze a queue with geometric arrivals of both positive and negative customers for a finite capacity system. The stati...
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... Priyanka Agarwal Department of Mathematics, Indian Institute of Technology, Roorkee, India NH-58, Modipuram madhufma@iitr.ernet.in Priyanka Agarwal School of Basic and Applied Sciences, Shobhit University priyanka1354@gmail.com. ...
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ABSTRACT
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ABSTRACT The present investigation deals with analysis of Markovian queueing model with finite capacity and finite population wherein the server works in fast and slow random environments depending on the status of service system with... more
ABSTRACT The present investigation deals with analysis of Markovian queueing model with finite capacity and finite population wherein the server works in fast and slow random environments depending on the status of service system with exponential distributed time parameters. On arrival of the customer in slow mode, the exponential distributed time may be fixed. Due to the impatient behavior (reneging), the customer may leave the queue after some time of joining the system if the server does not change its state before expiry of the timer. To discuss the behavior of the queue length distribution and to obtain the transient solution, Runge- Kutta method of fourth order is used. Various performance measures are determined in terms of transient probabilities of the system states. The numerical illustrations are facilitated to validate the tractability of performance measures as far as computational aspect is concerned.
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In this investigation, the loss and delay Markovian queueing system with nopassing is proposed. The customers may balk or renege with certain probability, on finding all servers busy on their arrival. To cope up with the balking and... more
In this investigation, the loss and delay Markovian queueing system with nopassing is proposed. The customers may balk or renege with certain probability, on finding all servers busy on their arrival. To cope up with the balking and reneging behaviour of the customers, ...