This is to certify that the thesis entitled “Software and Hardware Reliability of Fault Tolerant ... more This is to certify that the thesis entitled “Software and Hardware Reliability of Fault Tolerant Systems ” which is being submitted by Ms Sulekha Rani for the degree of Doctor of Philosophy in Mathematics to School of Basic and Applied Sciences, Shobhit University, Meerut, a deemed-to-be-University, established by GOI u/s 3 of UGC Act 1956, is a record of bonafide investigations and extensions of the problems carried out by her under my supervision and guidance. To the best of my knowledge, the thesis embodies the work of the candidate herself and has not been submitted to any other University or Institution for the award of any degree or diploma. It is further certified that she worked with me for the required period in the School of Basic and Applied Sciences, Shobhit University, Meerut.
Journal of Engineering and Applied Sciences , University of Engineering and Technology, Peshawar, 1994
This investigation deals with the finite queueing model where sharing of several resources takes ... more This investigation deals with the finite queueing model where sharing of several resources takes place between customers present in the service facility. The entering customers are allowed to catch a free resource (namely a server) if available otherwise form a queue. Two models (i) service facility having finite capacity (ii) finite population model, have been studied. A new method to obtain average number of customers present in the shared resource facility has been proposed by decomposing the model into two sub-models ( fork and join models).
In this paper we examine the effect of mild stenosis on blood flow, in an irregular axisymmetric ... 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.
Waiting in long queue is undesirable due to which in some practical situations customers become i... 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.
journal of King Abdulaziz University Engineering Sciences, 2012
In this study, we consider a single server vacation queueing model with optional bulk service and... 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...
journal of King Abdulaziz University Engineering Sciences, 2012
The present investigation studies a discrete time single server queue with both positive and nega... 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...
American Journal of Mathematical and Management Sciences, 2015
ABSTRACT This work studies the steady state behavior of an Mx/G/1 retrial queue with k-phases of ... more ABSTRACT This work studies the steady state behavior of an Mx/G/1 retrial queue with k-phases of heterogeneous service under different vacation policies. If the server is busy or on vacation, an arriving batch of calls either becomes impatient and balks (leaves) the system with some probability or enters in the virtual pool of blocked calls called “orbit.” The server provides service in k-phases to all the calls. After completing the kth phase of essential service of a call, the server has an option to go for lth (l = 1,2,…,M) type of vacation with probability ηl (l = 1,2,…,M) or to continue to serve the next call (if any) with probability η0where . The explicit expressions for the expected number of calls and expected waiting time of the calls in the retrial group are obtained using supplementary variable and generating function techniques. The maximum entropy principle is also employed to derive various system performance characteristics. A comparative analysis between the approximate results and the established exact results for waiting time distribution have been presented. The sensitivity analysis is carried out to demonstrate the tractability of the analytical results.
This is to certify that the thesis entitled “Software and Hardware Reliability of Fault Tolerant ... more This is to certify that the thesis entitled “Software and Hardware Reliability of Fault Tolerant Systems ” which is being submitted by Ms Sulekha Rani for the degree of Doctor of Philosophy in Mathematics to School of Basic and Applied Sciences, Shobhit University, Meerut, a deemed-to-be-University, established by GOI u/s 3 of UGC Act 1956, is a record of bonafide investigations and extensions of the problems carried out by her under my supervision and guidance. To the best of my knowledge, the thesis embodies the work of the candidate herself and has not been submitted to any other University or Institution for the award of any degree or diploma. It is further certified that she worked with me for the required period in the School of Basic and Applied Sciences, Shobhit University, Meerut.
Journal of Engineering and Applied Sciences , University of Engineering and Technology, Peshawar, 1994
This investigation deals with the finite queueing model where sharing of several resources takes ... more This investigation deals with the finite queueing model where sharing of several resources takes place between customers present in the service facility. The entering customers are allowed to catch a free resource (namely a server) if available otherwise form a queue. Two models (i) service facility having finite capacity (ii) finite population model, have been studied. A new method to obtain average number of customers present in the shared resource facility has been proposed by decomposing the model into two sub-models ( fork and join models).
In this paper we examine the effect of mild stenosis on blood flow, in an irregular axisymmetric ... 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.
Waiting in long queue is undesirable due to which in some practical situations customers become i... 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.
journal of King Abdulaziz University Engineering Sciences, 2012
In this study, we consider a single server vacation queueing model with optional bulk service and... 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...
journal of King Abdulaziz University Engineering Sciences, 2012
The present investigation studies a discrete time single server queue with both positive and nega... 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...
American Journal of Mathematical and Management Sciences, 2015
ABSTRACT This work studies the steady state behavior of an Mx/G/1 retrial queue with k-phases of ... more ABSTRACT This work studies the steady state behavior of an Mx/G/1 retrial queue with k-phases of heterogeneous service under different vacation policies. If the server is busy or on vacation, an arriving batch of calls either becomes impatient and balks (leaves) the system with some probability or enters in the virtual pool of blocked calls called “orbit.” The server provides service in k-phases to all the calls. After completing the kth phase of essential service of a call, the server has an option to go for lth (l = 1,2,…,M) type of vacation with probability ηl (l = 1,2,…,M) or to continue to serve the next call (if any) with probability η0where . The explicit expressions for the expected number of calls and expected waiting time of the calls in the retrial group are obtained using supplementary variable and generating function techniques. The maximum entropy principle is also employed to derive various system performance characteristics. A comparative analysis between the approximate results and the established exact results for waiting time distribution have been presented. The sensitivity analysis is carried out to demonstrate the tractability of the analytical results.
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Papers by Madhu Jain