Qualification: 
Ph.D, MPhil
usha@am.amrita.edu

Dr. Usha Kumari joined Amrita in 2003. She has 18 years of experience in teaching and research. She received her Ph. D. in Mathematics from Cochin University of Science and Technology in 1997. She has an M. Phil. in Statistics from Kerala University. She has qualified CSIR-UGC JRF. Her field of interests include Probability Theory, Stochastic Processes, Operations Research and Statistics.

Dr. Usha is a member of Undergraduate Board of Studies and Board of Studies of Integrated M. Sc. in Mathematics and Physics at Amrita. She has 20 international publications to her credit and 4 papers published in the proceedings and has conducted two national-level workshops, one on Stochastic Processes in 2008 which was sponsored by National Board for Higher Mathematics, and another on Linear Algebra in 2005. She has served as a referee for the Journal of Applied Mathematics & Stochastic Analysis, the Asia Pacific Journal of Operational Research, and the International Journal of Information & Management Systems. She has also presented papers at many international conferences and has been invited to deliver numerous talks.

Dr. Usha ’s academic career started at Union Christian College where she was a lecturer from 1995 to 1998. She subsequently worked as a Research Associate at the Indian Institute of Science, Bangalore (1998-1999) and at Cochin University of Science and Technology (1999-2003) prior to joining Amrita.

Publications

Publication Type: Conference Paper

Year of Publication Title

2021

A. M. Nair, Sreelatha K. S., and Dr. Usha Kumari P. V., “Application of Queuing Theory to a Railway ticket window”, in 2021 International Conference on Innovative Practices in Technology and Management (ICIPTM), 2021.[Abstract]


Waiting time in a queue is a common problem in all the service disciplines and some people may reluctant to join a queue due to long wait. These phenomena can be seen in the case of a railway ticket service also. A well-drafted model is needed for the management to comprehend the circumstances better. This paper centers on a single server queuing model in which the arrival process is a Poisson process and the service times follow an exponential distribution or a constant. In this work, we have studied queue management at a railway ticket counter with a single server. For this, we have collected data for one week from an NSG-3 category railway station and analyzed the data to find the pattern of arrival and service distribution. It has been seen that performance measures and service distributions of neither of the queuing models M/M/1 and M/D/1 conform to reality. So, we propose an approach to apply the mathematical queuing model more efficiently for such systems. We have used an M/G/1 model in which service time is calibrated based on a normal distribution. Based on the data collected from an NSG-3 category railway station for a day, a normal distribution is fitted for the service rate and found that the fit is good statistically. It is found that the resulted performance measures show significant conformity with the observed field data.

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2014

Dr. Usha Kumari P. V., “A retrial Inventory system with an unreliable server”, in International Conference on Operational Research, Sri Venkateswara University,Tirupati, A.P, 2014.

2008

Dr. Maneesha V. Ramesh and Dr. Usha Kumari P. V., “Threshold Based Data Aggregation Algorithm to Detect Rainfall Induced Landslides”, in Proceedings of the 2008 International Conference on Wireless Networks (ICWN’08), 2008, pp. 255-261.

2000

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “Single arrival bulk service single departure queue”, in Proceedings of the Int. Conference on Stochastic Processes and their Applications, Anna University, Madras, 2000.

1998

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “k-out-of-n system with general repair, The N–policy”, in Proc. II International Symposium on Semi-Markov Processes and their Applications, Compiegne, France, 1998.

1995

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the queueing system MD/GD/ ∞”, in International Conference on Stochastic Process and Cmputer Applications., PSG College of Technology, Coimbatore, 1995.

1994

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On an infinite server queue in discrete time”, in 3rd Ramanujam symp. On stochastic processes and their applications, Ramanujan instituterMadras, 1994.

1994

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the GIX(u) /G/ α queue”, in 3rd Ramanujam Symp. On Stochastic Processes and their Applications, Ramamijan institute, Madras, 1994.

Publication Type: Journal Article

Year of Publication Title

2020

Simi Surendran, Dr. Maneesha V. Ramesh, and Dr. Usha Kumari P. V., “Queue size estimation of nodes in a heterogeneous ocean network with multiple priority traffic”, International Journal of Vehicle Information and Communication Systems, vol. 5, no. 1, pp. 26–40, 2020.[Abstract]


Ocean network is a heterogeneous wireless network of fishing vessels at sea to provide internet over sea. The types of messages exchanged between fishing vessels include emergency data, normal data, voice and video messages. As the connectivity is intermittent, it is necessary to select the most appropriate message from the transmission queue for forwarding. This paper focuses on designing a queuing model with multiple priorities to estimate the queue size of each type of message in a node. Solving the steady state equations gives the number of emergency packets, data packets, audio packets and video packets waiting in the node to be transmitted. Hence the message dissemination algorithm can select the appropriate queue for transmitting the message to maximise the available resources with fairness.

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2020

Dr. Usha Kumari P. V., “A stochastic inventory system with two modes of service under N-policy”, Journal of Interdisciplinary Mathematics, vol. 23, no. 1, pp. 127–143, 2020.[Abstract]


We consider a two server stochastic inventory system under N-policy. Demand for the items occurs one at a time according to a Poisson process. Server1 is always available and Server2 is activated on the accumulation of N(>1) demands in the system. As soon as the services of all waiting demands are completed, server2 becomes idle and reactivate only on the accumulation of N units. Assume that service times of both servers are independent and non-identical exponential random variables. We derived the joint probability distribution of the waiting customers, server state and inventory level in the steady state and computed various system performance measures. A cost analysis is carried out and numerical illustrations are provided.

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2020

S. R., C., S., and Dr. Usha Kumari P. V., “Routing Problem In Transportation Of Milk In A Diary-A Case Study”, International journal of Scientific & Technology Research, vol. 9, no. 3, 2020.[Abstract]


Abstract: In this study our attempt is to optimize transportation route for a public sector milk dairy in Kerala. Our aim is to find the minimized route of transportation of milk from the main depot to various delivery locations, minimized transportation charges. The maximized annual profit of the diary is also calculated. The data collection was done in milma milk dairy situated in Punnapra, Alappuzha district, Kerala. We collected the data regarding distance, cost and the time taken by the vehicles to each delivery stations from the depot. The optimization of routes was done using different algorithms such as traveling salesman algorithm, branch and bound technique etc. After comparing the current route and optimized route we made the new optimized route structure. Through this study we found that, if the firm follows the new optimized route, the cost of transportation can be minimized.

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2020

Dr. Usha Kumari P. V., “On a Two Server Reliability System with One Server Idle Below a Threshold”, International Journal of Mathematics in Operational Research (IJMOR) (Accepted), 2020.

2020

Dr. Usha Kumari P. V. and S Krishna, D., “Optimal Server Time Management in a Single Server Queue”, International Journal of Advanced Research in Engineering and Technology, vol. 11, no. 6, 2020.[Abstract]


This paper considers an optimal server time management of a single server queue with -policy in which the server is under vacation until the realization of a random variable . When is realized, the server takes all waiting customers as a batch for service. After the batch service completion, the server shifts to a single service if there is any waiting customer and become idle when the system becomes empty. Such types of models deal with a very important class of real life congestion situations encountered in day-to-day as well as industrial scenario. The problem is to find a policy for selecting the service rate which maximizes the expected net profit per cycle in an M/M/1/K queue. Steady-state solutions and various performance measures are derived and obtained the optimal service rate numerically.

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2018

Dr. Usha Kumari P. V., “Reliability of k out of- n system with repair and Two modes of service under N-policy”, International Journal of Pure and Applied Mathematic, vol. 119, no. 16, pp. 5189-5196, 2018.

2017

Dr. Usha Kumari P. V., “A retrial inventory system with an unreliable server”, Int. J. Mathematics in Operational Research, vol. 10, no. 2 , 2017.

2017

P. Rekha, Dr. Maneesha V. Ramesh, P. Venkat Rangan, Dr. Usha Kumari P. V., and Hemalatha, T., “Energy Efficient Data Acquisition Techniques Using Context Aware Sensing for Landslide Monitoring Systems”, IEEE Sensors Journal, vol. 17, pp. 6006-6018, 2017.[Abstract]


Real-time wireless sensor networks are an emerging technology for continuous environmental monitoring. But real-world deployments are constrained by resources, such as power, memory, and processing capabilities. In this paper, we discuss a set of techniques to maximize the lifetime of a system deployed in south India for detecting rain-fall induced landslides. In this system, the sensing subsystem consumes 77.5%, the communication subsystem consumes 22%, and the processing subsystem consumes 0.45% of total power consumption. Hence, to maximize the lifetime of the system, the sensing subsystem power consumption has to be reduced. The major challenge to address is the development of techniques that reduce the power consumption, while preserving the reliability of data collection and decision support by the system. This paper proposes a wavelet-based sampling algorithm for choosing the minimum sampling rate for ensuring the data reliability. The results from the wavelet sampling algorithm along with the domain knowledge have been used to develop context aware data collection models that enhance the lifetime of the system. Two such models named context aware data management (CAD) and context aware energy management (CAE) have been devised. The results show that the CAD model extends the lifetime by six times and the CAE model does so by 20 times when compared with the continuous data collection model, which is the existing approach. In this paper, we also developed mathematical modeling for CAD and CAE, which have been validated using real-time data collected in the past.

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2016

P. Rekha, Dr. Maneesha V. Ramesh, Dr. Usha Kumari P. V., and P. Venkat Rangan, “Energy Sustenance in Context Aware Landslide Monitoring systems”, Sensys 2015, InfoComm2016, 2016.

2007

Dr. Usha Kumari P. V., “On (s, S) inventory system with random lead time and repeated demands”, International Journal of Stochastic Analysis, vol. 2006, pp. 1-22, 2007.[Abstract]


We consider an (s,S) inventory system with random lead time and repeated demands of unsatisfied demands from the orbit. Whenever the inventory level falls to the level s, an order is placed to bring the level to S. The quantity ordered is M=S−s. Demands to the system are served immediately if there is a positive inventory. Otherwise it will go to a pool of unsatisfied customers called orbit. After a random amount of time, that demand is retried for service. We assume a Markovian setup for the time between consecutive arrivals, replenishments, and retrials. We obtained the condition for ergodicity of the system, steady state system size probabilities, expected length of the busy period of the system, expected inventory level, expected number of customers waiting in the orbit, expected waiting times, and so forth. A control problem is studied and some numerical illusrtations are provided.

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2004

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “k-out-of-n-system with repair: The Max (N, T) Policy”, Performance Evaluation, vol. 57, no. 2, pp. 221–234, 2004.[Abstract]


We consider a k-out-of-n system with repair under the max(N,T) policy. Under this policy, the repair facility is activated for repair of failed units whenever the maximum of an exponentially distributed time duration T and the sum of random variables is realized. The repair times and lifetimes of components are assumed to be independent exponentially distributed random variables. The repaired units are assumed to be as good as new. Failed units are repaired one at a time. The repair facility is switched off the moment all failed units are back to operation. System state probabilities in the long run are derived for (a) cold (b) warm and (c) hot systems. System reliability, the distribution of time during which the server is continuously engaged and its expected duration are computed. Several other system characteristics are also obtained. Determination of the optimal values of N and α is discussed and some numerical illustrations are provided.

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2002

A. Krishnamoorthy, Dr. Usha Kumari P. V., and Lakshmy, B., “k-out-of-n-system with repair: The N-policy”, Asia Pacific Journal of Operational Research, vol. 19, pp. 47–62, 2002.

2002

A. Krishnamoorthy and Dr. Usha Kumari P. V., “GI/M/1/1 queue with finite retrials and finite orbits”, stochastic analysis and applications, vol. 20, no. 2, pp. 357–374, 2002.[Abstract]


In this paper we consider the GI/M/1/1 retrial queue with finite number of retrials to each orbital customer and a finite number of orbits. The interarrival times from outside the system have a general distribution. The sojourn time of a unit in an orbit until its retrial for service and its service time are exponentially distributed with parameters depending on the orbit number. The maximum number of retrials any unit is permitted to take is restricted to k. There are a finite number, say m, of orbits with at most one customer in each orbit. At the time of an arrival if the server is busy and all orbits are occupied, then the customer is lost to the system. If the server is idle at an arrival epoch, the unit directly goes for service. If the server is busy and at least one of the orbits is empty then the arriving customer occupies the first empty orbit. A unit in the orbit retries for service which returns to the same orbit (if the server is busy) with probability P and leaves the system with probability 1−P, 0<P<1. We compute the system state distribution. The distribution of the number of customers reneging and that of the number of units served during an interarrival time are computed. Also waiting time distribution and the idle period distribution are computed. Optimal values of k and m are investigated.

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2001

A. Krishnamoorthy and Dr. Usha Kumari P. V., “k-out-of-n: G system with repair: the D-policy”, Int.Jl. of Computers and Operations Research, vol. 28, no. 10, pp. 973 - 981, 2001.[Abstract]


In this paper we consider a k-out-of-n: G system with repair under D-policy. According to this policy whenever the workload exceeds a threshold D a server is called for repair and starts repair one at a time. He is sent back as soon as all the failed units are repaired. The repaired units are assumed to be as good as new. The repair time and failure time distributions are assumed to be exponential. We obtain the system state distribution, system reliability, expected length of time the server is continuously available, expected number of times the system is down in a cycle and several other measures of performance. We compute the optimal D value which maximizes a suitably defined cost function.Scope and purposeThis paper considers a repair policy, called D-policy, of a k-out-of-n: G system. In a k-out-of-n: G system, the system functions as long as there are atleast k operational units. The server activation cost is high once it becomes idle due to all failed units repaired. Hence it is activated when the accumulated amount of work reaches D. This paper examines the optimal D-value by bringing in costs such as the cost of system being down, the server activation cost. Activating the server the moment the first failure takes place may involve very heavy fixed cost per cycle (a cycle is the duration from a point at which the server becomes idle to the next epoch at which it becomes idle after being activated). The other extreme of server activation only after n−k+1 units fail leads to the system being down for a long duration in each cycle. Hence the need for the optimal D-policy. A brief account of k-out-of-n: G system can be had in Ross (Ross, SM. Introduction to probability models, 6th ed., New York: Academic Press, 1997). The results obtained here find direct applications in reliability engineering, Production systems, Satellite communication, etc.

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2001

S. R. Chakravarthy, Krishnamoorthy, A., and Dr. Usha Kumari P. V., “A k-out-of-n reliability system with an unreliable server and phase type repairs and services: the (N, T) policy”, Journal of Applied Mathematics and Stochastic Analysis, vol. 14, pp. 361–380, 2001.[Abstract]


In this paper we study a k-out-of-n reliability system in which a single unreliable server maintains n identical components. The reliability system is studied under the (N,T) policy. An idle server takes a vacation for a random amount of time T and then attends to any failed component waiting in line upon completion of the vacation. The vacationing server is recalled instantaneously upon the failure of the Nth component. The failure times of the components are assumed to follow an exponential distribution. The server is subject to failure with failure times exponentially distributed. Repair times of the component, fixing times of the server, and vacationing times of the server are assumed to be of phase type. Using matrix-analytic methods we perform steady state analysis of this model. Time spent by a failed component in service, total time in the repair facility, vacation time of the server, non-vacation time of the server, and time until failure of the system are all shown to be of phase type. Several performance measures are evaluated. Illustrative numerical examples are presented.

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2000

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “Single arrival bulk service single departure queue”, Mathematical and Computer Modeling, vol. 31, pp. 99-108, 2000.

2000

A. Krishnamoorthy and Dr. Usha Kumari P. V., “Queues with customers requiring random number of servers”, IAPQR TRANSACTIONS, vol. 25, pp. 97–106, 2000.

1999

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “k-out-of-n-system with repair and retrial”, Spanish Journal of OR, vol. 7, no. 2, pp. 293-304., 1999.

1998

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the queueing system M/MX®/ ∞”, Asia Pacific Jl. Of Operational Research, vol. 15, no. 1, pp. 17-28, 1998.

1998

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the queueing system GID xn/G/α with Markov dependent batch arrivals”, Opsearch, vol. 35, pp. 1-12, 1998.

1998

Dr. Usha Kumari P. V. and Krishnamoorthy*, A., “On the queueing system GIDX/MDR/ ∞”, Optimization, vol. 43, pp. 157–168, 1998.

1998

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On a bulk arrival bulk service infinite service queue”, Stochastic analysis and applications, vol. 16, no. 3, pp. 585–595, 1998.[Abstract]


This paper considers an infinite server queue in continuous time in which arrivals are in batches of variable size X and service is provided in groups of fixed size R. We obtain analytical results for the number of busy servers and waiting customers at arbitrary time points. For the number of busy servers, we obtain a recursive relation for the partial binomial moments both in transient and steady states. Special cases are also discussed

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1996

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On an infinite server queue in discrete time”, Int. Jl. of Inf.and Mgmt. Sciences, vol. 7, no. 3, pp. 71-77., 1996.

1995

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On the queueing system BD/GD/ ∞”, Optimization, vol. 34, pp. 185-193., 1995.

1995

Dr. Usha Kumari P. V., Krishnamoorthy, A., and Kashyap, B. R. K., “On the GIX(u) /G/ ∞ queue”, Int. Jl. of Inf. and Mgmt. Sciences, vol. 6, no. 3, pp. 59-67, 1995.

1995

Dr. Usha Kumari P. V., “On the queueing system Mn x /GD/ α”, Bull. Of Pure and Applied Sciences, vol. 14E, no. 2, pp. 115-125, 1995.

1994

Dr. Usha Kumari P. V. and Krishnamoorthy, A., “On an Infinite Server Queue”, Opsearch, vol. 31, pp. 240–240, 1994.

Publication Type: Conference Proceedings

Year of Publication Title

2008

Dr. Usha Kumari P. V., “ Threshold Based Data Aggregation Algorithm to Detect Rainfall in land Slide”, international Conference on Wireless Networks, vol. 1. pp. 255-261, 2008.[Abstract]


Landslides are one of the environmental disasters that cause massive destruction of human life and infrastructure. Real time monitoring of a landslide prone areas are necessary to issue fore warning. To accomplish real time monitoring, massive amount of data have to be collected and analyzed within a short span of time. This work has developed a method for effective data collection and aggregation by implementing threshold alert levels. The sampling rates of threshold alert levels will determine amount of data collected and aggregated which will reduce the power consumption by each wireless sensor nodes. This work also helps to determine the appropriate sampling rates for each threshold level, and the expected number of data packets in the queue. The time delay in receiving the data packet at the analysis station can be determined by using the value of expected number of data packets in the queue.

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