Chandra Shekhar

Processor-shared service systems with queue-dependent processors

In this investigation, we analyze the finite queue-dependent heterogeneous multiprocessor service system in which processors are shared by more than one job. Whenever, the queue length of jobs in the system reaches a threshold value Nj(j=1,2,....,r-1), the (j+1)th processor starts the processing of the jobs and continues till queue length is again decreased to the same level. Steady-state queue size distribution is obtained using recursive method considering Markovian arrival and service times. We derive the system characteristics viz. expected number of jobs in the system, throughput of the system, probability that jth (j=2,3,...,r) processor rendering the service etc. A cost relationship is constructed to determine the optimal threshold levels for processors being active in order to gain maximum net profit. For illustration purpose, tables and graphs are also provided.

N-policy for a multi-component machining system with imperfect coverage, reboot and unreliable server

This investigation aims at predicting the transient performance measures of a machining system comprising of M operating units and multi types of warm standbys under the care of a single unreliable server. To deal with more realistic situations, the concepts of imperfect recovery and reboot delay are also incorporated. The queue size distribution is obtained by using the matrix method. The explicit expressions for various performance measures such as reliability, throughput, expected number of failed units in the system, failure frequency of the server, etc. are obtained. A numerical illustration is presented to demonstrate the practical application of the proposed model in the flexible manufacturing systems.

Double orbit finite retrial queues with priority customers and service interruptions

The present study deals with the double orbit finite capacity retrial queues with unreliable server. The system facilitates the arrival of two types of customers known as priority and non priority customers and can hold a maximum of L priority customers and K non-priority customers as per its capacity. The priority customers are served prior to the non-priority customers. Moreover, the server is unreliable which may breakdown while servicing either priority or non-priority customer. The failed server is sent for repair following threshold recovery policy to become as good as earlier. Both transient as well as steady state analysis of the model has been done using by matrix method. Various performance measures including queue length, reliability metrics, long run probabilities, etc. have been obtained using various state probabilities. The application of the model to cellular radio network has been discussed. The cost function has been constructed and optimized using meta heuristic approach. The sensitivity analysis of various performance indices has been performed as an illustration.

Queueing analysis of two unreliable servers machining system with switching and common cause failure

In this paper, we analyse the performance of primary and secondary unreliable servers in a multi-component machining system. For the smooth functioning of the system, there is a provision of warm spares that may not be perfect in switching the failed operating unit. Primary server is prone to complete or partial breakdown whereas secondary server faces only complete breakdown independently or simultaneously due to common cause. The life time and repair time of the operating units, breakdown and the repair time of the servers are exponentially distributed. Various performance indices are formulated to study the behaviour of the queueing model of concerned machining system developed more significantly. By taking an illustration, the sensitivity analysis is carried out. The numerical results are summarised in tabular form and also depicted via graphs.

Transient analysis of machining system with spare provisioning and geometric reneging

In this investigation, we deal with the transient analysis of repairable machining system having multi identical online and warm standby machines. There is facility of repair of failed machines rendered by an unreliable server who is prone to failure and follows the threshold policy in rendering the service and being repaired. The failed machines waiting in the queue may renege and opt sequentially whether to leave the queue or remain in the queue in geometric fashion at the epochs of availability of secondary server. By constructing the transient differential difference equations, the probabilities associated with the system states are determined using the numerical method based on Runge-Kutta method. Various queueing and reliability indices viz. expected number of failed machines in the system, throughput, reliability, mean time to failure, failure frequency, etc., are established and numerically computed by taking illustration. The sensitivity analysis and numerical simulation are performed for exploring the effects of parameters on some performance measures.

Genome wide analysis of Arabidopsis thaliana reveals high frequency of AAAGN7CTTT motif

Sequence specific elements in DNA regulate transcription by recruiting transcription factors. The Dof proteins are a large family of transcription factors that share a single highly conserved zinc finger. The core to which Dof proteins bind has a consensus AAAG or ACTTTA sequence. These motifs have been over represented in many promoters. We performed a genome wide analysis of AAAG repeat elements increasing the spacer length from 0 to 25. Similar analyses was done with AAAG-CTTT motifs. We report unusual high frequency of AAAGN7CTTT in Arabidopsis thaliana genome. We also conclude that there is a preference for A/G nucleotides in spacer sequence between two AAAG repeats.

Vacation queuing model for a machining system with two unreliable repairmen

This investigation is concerned with multi-component machining system having two types of warm standby units and two unreliable heterogeneous repairmen. The life time and repair time of the failed units are exponentially distributed. The first repairman is working according to N (N ≥ 1) policy whereas the second repairman has the privilege of going for a vacation of random length. Both repairmen may also fail while rendering the repair to the failed units either individually or simultaneously. Runge-Kutta method is used to obtain the transient-state probabilities of the system states for which Chapman-Kolmogrov differential equations governing the model are constructed. We have established some indices for the system performance in terms of transient probabilities. The sensitivity analysis is carried out to examine the system efficiency and profitability as per requirements. The numerical results are provided in order to explore the sensitivity of the system descriptors on the performance measures more precisely.

Reliability prediction of fault tolerant machining system with reboot and recovery delay

The present paper deals with the reliability analysis of fault tolerant multi-component machining system having multi-warm spares and reboot provisioning. The time-to-breakdown and repair of active/spare units and server are assumed to be exponentially distributed. The reboot process and recovery delay are also counterfeited exponentially distributed. The spectral method is adapted to compute the transient state probabilities of the system states. In order to predict the transient behavior of the system, various performance measures such as reliability function, mean-time-to-failure

Sensitivity analysis of an inventory model with non-instantaneous and time-varying deteriorating items

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