A. Krishnamoorthy

Cochin University of Science and Technology, Fort Cochin, Kerala, India

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Publications (52)25.47 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we study a MAP/PH/1 queueing model in which the server is subject to taking vacations and offering services at a lower rate during those times. The service is returned to normal rate whenever the vacation gets over or when the queue length hits a specific threshold value. This model is analyzed in steady state using matrix analytic methods. An illustrative numerical example is discussed.
    Applied Mathematical Modelling 03/2013; 37(6):3879–3893. · 2.16 Impact Factor
  • A. Krishnamoorthy, C. Sreenivasan
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    ABSTRACT: This paper analyzes an M / M /2 queueing system with two heterogeneous servers, one of which is always available but the other goes on vacation in the absence of customers waiting for service. The vacationing server, however, returns to serve at a low rate as an arrival finds the other server busy. The system is analyzed in the steady state using matrix geometric method. Busy period of the system is analyzed and mean waiting time in the stationary regime computed. Conditional stochastic decomposition of stationary queue length is obtained. An illustrative example is also provided.
    International Journal of Stochastic Analysis. 01/2012; 2012.
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    ABSTRACT: Server induced interruptions such as server break downs, server attending a high priority customer, and server taking a vacation in queues have been extensively studied in the literature. However, customer-induced interruptions such as customers leaving in the middle of a service due to not having enough information for completing a service and customer breakdowns have not been studied so far. The purpose of this work is to introduce customer interruptions in queueing systems. We consider an infinite capacity queueing system with a single server to which customers arrive according to a Poisson process and the service time follows an exponential distribution. The customer interruption while in service occurs according to a Poisson process and the interruption duration follows an exponential distribution. The self-interrupted customers will enter into a finite buffer of size K. Any interrupted customer, finding the buffer full, is considered lost. Those interrupted customers who complete their interruptions will be placed into another buffer of same size. The interrupted customers waiting for service are given non-preemptive priority over new customers. We investigate the behavior of this queuing system. Several performance measures are evaluated. Numerical illustrations of the system behavior are also provided. An optimization problem of interest will be discussed through an illustrative example.
    Stochastic Analysis and Applications 01/2012; 30(6). · 0.30 Impact Factor
  • A. Krishnamoorthy, B. Lakshmy, R. Manikandan
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    ABSTRACT: A detailed review of inventory models involving positive service time is given. These include classical and retrial cases. A detailed review of inventory models involving positive service time is given. These include classical and retrial cases. Also contributions to production inventory with service time is indicated towards the end. In addition directions for future Also contributions to production inventory with service time is indicated towards the end. In addition directions for future work are indicated. work are indicated. KeywordsInventory with positive service time–Classical inventory–Retrial inventory with/without production KeywordsInventory with positive service time–Classical inventory–Retrial inventory with/without production
    01/2011; 48(2):153-169.
  • A. Krishnamoorthy, V. C. Narayanan
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    ABSTRACT: This paper considers a production inventory with positive service time. The time for producing each item is assumed to follow a “Markovian production scheme”. Because of this, correlation automatically gets into the production process. The customer arrival process follows a Markovian arrival process. When inventory falls to s, the production process is switched on, and is switched off when the on-hand inventory reaches S. The service time to each customer has a phase-type distribution. We investigate the system stability. Under the condition of stability, we investigate the system state distribution. Next, several performance measures are computed, such as the fraction of time server is on vacation; fraction of time the inventory level is zero; fraction of time the production process is On; expected number of customers in the system while server is on vacation and also while it is busy. Numerical results indicate, among other things, the effect of the control variables s and S on the fraction of time the system goes out of inventory and on expected loss rate of customers.
    IMA Journal of Management Mathematics 01/2010; 21(3). · 0.59 Impact Factor
  • Computers & OR. 01/2010; 37:1247-1255.
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    ABSTRACT: A Markovian single server feedback retrial queue with linear retrial rate and collisions of customers is studied. Using generating function technique, the joint distribution of the server state and the orbit length under steady-state is investigated. Some interesting and important performance measures of the system are obtained. Finally, numerical illustrations are provided.
    Computers & Operations Research 01/2010; · 1.91 Impact Factor
  • A. Krishnamoorthy, N. Anbazhagan
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    ABSTRACT: This article presents a perishable stochastic inventory system under continuous review at a service facility in which the waiting hall for customers is of finite size M. The service starts only when the customer level reaches N (
    Stochastic Analysis and Applications 01/2008; 26(1):120-135. · 0.30 Impact Factor
  • Source
    Krishnamoorthy A, K. P. Jose
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    ABSTRACT: We analyze and compare three (s,S) inventory systems with positive service time and retrial of customers. In all of these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. When the inventory level depletes to s due to services, an order of replenishment is placed. The lead-time follows an exponential distribution. In model I, an arriving customer, finding the inventory dry or server busy, proceeds to an orbit with probability γ and is lost forever with probability (1−γ). A retrial customer in the orbit, finding the inventory dry or server busy, returns to the orbit with probability δ and is lost forever with probability (1−δ). In addition to the description in model I, we provide a buffer of varying (finite) capacity equal to the current inventory level for model II and another having capacity equal to the maximum inventory level S for model III. In models II and III, an arriving customer, finding the buffer full, proceeds to an orbit with probability γ and is lost forever with probability (1−γ). A retrial customer in the orbit, finding the buffer full, returns to the orbit with probability δ and is lost forever with probability (1−δ). In all these models, the interretrial times are exponentially distributed with linear rate. Using matrix-analytic method, we study these inventory models. Some measures of the system performance in the steady state are derived. A suitable cost function is defined for all three cases and analyzed using graphical illustrations.
    Journal of Applied Mathematics and Stochastic Analysis 01/2008;
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    ABSTRACT: A transient solution is obtained analytically using continued fractions for the system size in an M/M/1 queueing system with catastrophes, server failures and non-zero repair time. The steady state probability of the system size is present. Some key performance measures, namely, throughput, loss probability and response time for the system under consideration are investigated. Further, reliability and availability of the system are analysed. Finally, numerical illustrations are used to discuss the system performance measures.
    Queueing Systems 01/2007; 56:133-141. · 0.44 Impact Factor
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    ABSTRACT: This paper presents a multiserver retrial queueing system with servers kept apart, thereby rendering it impossible for one to know the status (idle/busy) of the others. Customers proceeding to one channel will have to go to orbit if the server in it is busy and retry after some time to some channel, not necessarily the one already tried. Each orbital customer, independently of others, chooses the server randomly according to some specified probability distribution. Further this distribution is identical for all customers. We assume that the same ‘orbit’ is used by all retrial customers, between repeated attempts, to access the servers. We derive the system state probability distribution under Poisson arrival process of external customers, exponentially distributed service times and linear retrial rates to access the servers. Several system state characteristics are obtained and numerical illustrations provided.
    Annals of Operations Research 01/2006; 141:283-301. · 1.03 Impact Factor
  • Annals OR. 01/2006; 141:67-83.
  • B. Krishna Kumar, D. Arivudainambi, A. Krishnamoorthy
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    ABSTRACT: This paper deals with a generalized M/G/1 feedback queue in which customers are either “positive" or “negative". We assume that the service time distribution of a positive customer who initiates a busy period is G e (x) and all subsequent positive customers in the same busy period have service time drawn independently from the distribution G b (x). The server is idle until a random number N of positive customers accumulate in the queue. Following the arrival of the N-th positive customer, the server serves exhaustively the positive customers in the queue and then a new idle period commences. This queueing system is a generalization of the conventional N-policy queue with N a constant number. Explicit expressions for the probability generating function and mean of the system size of positive customers are obtained under steady-state condition. Various vacation models are discussed as special cases. The effects of various parameters on the mean system size and the probability that the system is empty are also analysed numerically.
    Annals of Operations Research 01/2006; 143(1):277-296. · 1.03 Impact Factor
  • J. R. Artalejo, A. Krishnamoorthy, M. J. Lopez-Herrero
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    ABSTRACT: This paper deals with a continuous review (s,S) inventory system where arriving demands finding the system out of stock, leave the service area and repeat their request after some random time. This assumption introduces a natural alternative to classical approaches based either on lost demand models or on backlogged models. The stochastic model formulation is based on a bidimensional Markov process which is numerically solved to investigate the essential operating characteristics of the system. An optimal design problem is also considered.
    Annals of Operations Research 12/2005; 141(1):67-83. · 1.03 Impact Factor
  • Gautam Choudhury, A. Krishnamoorthy
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    ABSTRACT: We consider an M /G/1 queueing system with a random setup time, where the service of the first unit at the commencement of each busy period is preceded by a random setup time, on completion of which service starts. For this model, the queue size distributions at a random point of time as well as at a departure epoch and some important performance measures are known [see Choudhury, G. An M /G/1 queueing system with setup period and a vacation period. Queueing Sys. 2000, 36, 23–38]. In this paper, we derive the busy period distribution and the distribution of unfinished work at a random point of time. Further, we obtain the queue size distribution at a departure epoch as a simple alternative approach to Choudhury4. Finally, we present a transform free method to obtain the mean waiting time of this model.
    Stochastic Analysis and Applications 01/2005; 22(3):739-753. · 0.30 Impact Factor
  • A. Gómez-Corral, A. Krishnamoorthy, V. C. Narayanan
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    ABSTRACT: This paper deals with multi-server queues with a finite buffer of size N in which units waiting for service generate into priority at a constant rate, independently of other units in the buffer. At the epoch of a unit's priority generation, the unit is immediately taken for service if there is one unit in service that did not generate into priority while waiting; otherwise such a unit leaves the system in search of immediate service elsewhere. The arrival stream of units is a Markovian arrival process (MAP) and service requirements are of phase (PH) type. Our interest is in the continuous-time Markov chain describing the state of the queue at arbitrary times, which constitutes a finite quasi-birth-and-death (QBD) process. We give formulas well suited for numerical computation for a variety of performance measures, including the blocking probability, the departure process, and the stationary distributions of the system state at pre-arrival epochs, at post-departure epochs and at epochs at which arriving units are lost. Illustrative numerical examples show the effect of several parameters on certain probabilistic descriptors of the queue for various levels of congestion.
    Stochastic Models 01/2005; 21:427-447. · 0.47 Impact Factor
  • T. Deepak, V. Joshua, A. Krishnamoorthy
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    ABSTRACT: In this paper a queueing system in which work gets postponed due to finiteness of the buffer is considered. When the buffer is full (capacityK) further arrivals are directed to a pool of customers (postponed work). An arrival encountering the buffer full, will join the pool with probability γ (0
    Top 02/2004; 12(2):375-398. · 0.84 Impact Factor
  • A.N Dudin, A Krishnamoorthy, V.C Joshua, G.V Tsarenkov
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    ABSTRACT: We consider a single server retrial queuing model in which customers arrive according to a batch Markovian arrival process. Any arriving batch finding the server busy enters into an orbit. Otherwise one customer from the arriving batch enters into service immediately while the rest join the orbit. The customers from the orbit try to reach the service later and the inter-retrial times are exponentially distributed with intensity depending (generally speaking) on the number of customers on the orbit. Additionally, the search mechanism can be switched-on at the service completion epoch with a known probability (probably depending on the number of customers on the orbit). The duration of the search is random and also probably depending on the number of customers in the orbit. The customer, which is found as the result of the search, enters the service immediately if the server is still idle. Assuming that the service times of the primary and repeated customers are generally distributed (with possibly different distributions), we perform the steady state analysis of the queueing model.
    European Journal of Operational Research 02/2004; · 2.04 Impact Factor
  • P.V. Ushakumari, A. Krishnamoorthy
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    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 N(1≤N≤n−k) 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.
    Performance Evaluation. 01/2004;
  • T. V. Varghese, A. Krishnamoorthy
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    ABSTRACT: We discuss a single commodity continuous review (s, S) inventory system in which commodities get damaged due to external disaster. Shortages are not permitted and lead time is assumed to be zero. The interarrival times of demands constitute a family of i.i.d. random variables with a common arbitrary distribution. The quantity demanded at a demand epoch is arbitrarily distributed which depends only on the time elapsed since the last demand epoch. Transient and steady state probabilities of the inventory levels are derived by identifying suitable semi-regenerative process. In the case when the demand is for unit item and the disaster affects only an exhibiting item, the steady state probability distribution is obtained as uniform. An optimization problem is discussed and numerical examples are provided.
    Stochastic Analysis and Applications 01/2004; No. 5(pp. 1315–1326):1315-1326. · 0.30 Impact Factor

Publication Stats

104 Citations
25.47 Total Impact Points

Institutions

  • 1984–2013
    • Cochin University of Science and Technology
      • Department of Mathematics
      Fort Cochin, Kerala, India
  • 1996
    • Annamalai University
      • Department of Statistics
      Anamalainagar, Tamil Nādu, India