# Balasubramanian Krishna KumarVIT University | VIT

Balasubramanian Krishna Kumar

M.Sc., M.Phil., Ph.D.

## About

93

Publications

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1,396

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Introduction

Additional affiliations

January 2000 - December 2012

January 1991 - December 1993

## Publications

Publications (93)

This article investigates the transient probabilities associated with the number of users’ requests in a service facility for a finite-source computer queueing network, employing a novel analytic approach. Key real-time performance metrics such as the mean and variance pertaining to the number of requests in the service facility are obtained, along...

This article deals with the steady-state behaviour of a finite orbit capacity multiserver call center retrial queue with Bernoulli vacation schedule in which the servers not only accept incoming calls but also make outgoing calls after some exponentially distributed idle time. In addition, upon each service completion of the outgoing call, the serv...

This paper designs and analyzes a novel single-channel cognitive radio retrial queueing network wherein a waiting line buffer is deployed for secondary users (SUs). A finite source system generates the primary users (PUs). Apart from these, PUs having preemptive priority over SUs, the effect of retrial/repeated attempts of PUs is taken into conside...

This article deals with a new class of fluid flow queue regulated by an \begin{document}$ M/M/1 $\end{document} queueing system in the presence of active catastrophic failures and subsequent repairs of the server. The distribution of the stationary buffer-content is determined in terms of modified Bessel function of first kind. Besides, an explicit...

This paper studies a Markov model of a queuing-inventory system with primary, retrial, and feedback customers. Primary customers form a Poisson flow, and if an inventory level is positive upon their arrival, they instantly receive the items. If the inventory level is equal to zero upon arrival of a primary customer, then this customer, according to...

We analyze a multi-processor two-stage tandem call center retrial queueing network in which the processors are subject to active breakdowns and repairs at stage-I. A level-dependent quasi-birth-and-death (LDQBD) process is formulated and a sufficient condition for ergodicity of the system is discussed. Under the stability condition, the stationary...

In this paper, we analyze the transient behavior of a novel single server queueing system with hybrid arrivals of single and state-dependent batch of customers. Whenever the system becomes empty the server undergoes the switch-off state for random duration of time. Explicit expressions for transient probabilities of the status of the server and sys...

In this article, we propose a dynamic operating of a single server service system between conventional and retrial queues with impatient customers. Necessary and sufficient conditions for the stability, and an explicit expression for the joint steady-state probability distribution are obtained. We have derived some interesting and important perform...

An M/G/1 retrial queueing system with two phases of service of which the second phase is optional and the server operating under Bernoulli vacation schedule is investigated. Further, the customer is allowed to balk upon arrival if he finds the server unavailable to serve his request immediately. The joint generating functions of orbit size and serv...

This paper analyses a Markovian retrial queue where the server is subject to breakdowns and repairs. It is assumed that the breakdowns/repairs behaviour when the server is idle is different from the one when it is busy. Under the steady-state condition, explicit expressions for the partial probability generating functions of the server status and t...

We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of t...

We consider a time-non-homogeneous double-ended queue subject to catastrophes and repairs. The catastrophes occur according to a non-homogeneous Poisson process and lead the system into a state of failure. Instantaneously, the system is put under repair, such that repair time is governed by a time-varying intensity function. We analyze the transien...

We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods. We first obtain the steady-state distribution of t...

Multiprogramming and Multiporgramming Retrial Queue with Berenoulli Vacation of CPU servers is discussed

We consider the transmission of protocol data units in an LTE eNodeB in downlink direction and focus on the radio link control (RLC) and hybrid Automatic-Repeat-Request functionality at layer 2 of the
transmission system. We model the associated window flow control of RLC frames in terms of an open queueing network with two stations and describe RL...

This paper deals with retrial queueing models having an unlimited/a finite orbit capacity with control retrial policy of a multiprogramming–multiprocessor computer network system. Under the Markovian assumptions and light-traffic condition, the steady-state probabilities of the number of programs in the system and the mean number of programs in the...

A single server queue subject to maintenance of the server and the close down period is considered. We obtain explicit expressions for the transient probabilities of the system size, the server under maintenance state and the close down period. The time-dependent performance measures of the system and the probability density function of the first-p...

Sudhesh (2010) has discussed the transient probabilities for queueing systems subject to catastrophic failures and impatience of customers. However, it contains some errors concerning the terminology and the final forms of the transient probabilities of the system size. In this paper, we correct the errors and obtain the correct results in the work...

This paper is concerned with the analysis of a single server queueing system subject to Bernoulli vacation schedules with server setup and close down periods. An explicit expression for the probability generating function of the number of customers present in the system is obtained by using imbedded Markov chain technique. The steady state probabil...

This paper deals with a single server Markovian queue subject to maintenance of the server. A batch of customers is allowed
whenever the server is idle such that each individual customer in the batch is subject to a control admission policy upon
arrival. Explicit expressions are obtained for the time dependent probabilities of the system size in te...

A non-Markovian feedback single-server retrial queue with collisions and general retrial times is investigated. A necessary and sufficient condition for the system to be stable is studied. Using the supplementary variable technique, the joint distribution of the server state and the orbit length under steady-state is obtained. Some interesting and...

A single server retrial queue with negative customers and two types of Bernoulli feedback is considered. A necessary and sufficient
condition for the system to be stable is investigated. The system size probabilities at output epochs are obtained by using
an embedded Markov chain. Further, the joint generating functions of queue length and server s...

Consider a system performing a continuous-time random walk on the integers,
subject to catastrophes occurring at constant rate, and followed by
exponentially-distributed repair times. After any repair the system starts anew
from state zero. We study both the transient and steady-state probability laws
of the stochastic process that describes the st...

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...

In this paper, a steady-state Markovian multi-server retrial queueing system with Bernoulli vacation scheduling service is studied. Using matrix-geometric approach, various interesting and important system performance measures are obtained. Further, the probability descriptors like ideal retrial and vain retrial are provided. Finally, extensive num...

In this paper, a Markovian multiple server queue in which each server takes vacation according to Bernoulli scheduling service has been studied. For this system, the stationary queue length distribution and several performance characteristics are obtained using the matrix geometric solution technique. The system busy period and waiting time distrib...

This paper deals with a multiserver feedback retrial queueing system with finite waiting position and constant retrial rate. This system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition for stability of the system is investigated. Some important system performance measures are obtained using matrix geo...

Queueing systems with state-dependent arrival and service rates along with catastrophes are investigated. Explicit expressions for the transient probabilities of system size are obtained. The corresponding steady-state probabilities are deduced. Busy period distribution is also found. Some performance measures are obtained for the system. Extensive...

We consider a
two-heterogeneous-server queueing system with
Bernoulli vacation in which customers arrive according to a Markovian arrival
process (MAP). Servers returning from vacation immediately take another vacation
if no customer is waiting. Using matrix-geometric method, the steady-state
probability of the number of customers in the system is...

Queueing systems with catastrophes and state-dependent arrival and service rates are considered. For two types of queueing systems namely, queues with discouraged arrivals and infinite server queue, explicit expressions for the transient probabilities of system size are obtained by using continued fractions technique. Some system performance measur...

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
co...

This paper presents a transient solution for the system size in an M/M/2 queue where the service rates of the servers are not identical with the possibility of catastrophes in the system. The time dependent probabilities for the number in the system are obtained. The steady state probabilities of the system size are also provided. Some important pe...

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)....

This paper discusses multiserver feedback retrial queues with balking and control retrial rate. This system is analyzed as
a quasi-birth-and-death (QBD) process and the necessary and sufficient condition for stability of the system is discussed.
Some interesting system performance measures are obtained using matrix geometric method. The effects of...

In this paper, a Markovian queue with two heterogeneous servers and multiple vacations has been studied. For this system, the stationary queue length distribution and mean system size have been obtained by using matrix geometric method. The busy period analysis of the system and mean waiting time distribution are discussed. Extensive numerical illu...

A transient solution for the system size in the M/M/1 queueing system with the possibility of catastrophes and server failures is analyzed. The steady state probabilities of the system size are also derived. Some important performance measures are discussed. Finally, the reliability and availability of the system are obtained.

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival ofall the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using
the regeneration point technique. The mean number of cells which die in timet and its asymptotic behaviour...

This paper is concerned with the analysis of a single-server batch arrival retrial queue with two classes of customers. In the case of blocking, the class-1 customers leave the system forever whereas the class-2 customers leave the service area and enter the orbit and wait to be served later. The necessary and sufficient condition for the system to...

This paper is concerned with the analysis of a single-server batch arrival retrial queue with Bernoulli service schedule and multiple vacation with general retrial times and the server being subject to starting failures. We assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS (first-come-first-served...

An M/G/1 queue with Bernoulli feedback and general setup time under a control policy is analyzed. The customers arrival rate at service station varies according to the system status: buildup, setup and busy states. The probability generating function for system size and mean number of customers in the system are obtained under steady-state conditio...

This paper discusses a retrial queue with Bernoulli feedback, where the server is subjected to starting failure. The retrial time is assumed to follow an arbitrary distribution and the customers in the orbit access the server under FCFS discipline. The necessary and sufficient condition for the stability of the system is derived. Various performanc...

An M/G/1 retrial queueing system with additional phase of service and possible preemptive resume service discipline is considered. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the...

An M/G/1 queueing system with no waiting room is considered. The server is assumed to provide two types of services-regular and optional with the provision of server breakdown. Explicit expressions for the transient probabilities for the system being idle, busy and breakdown are obtained. The reliability and availability analysis of the system are...

This paper is concerned with the analysis of a single-server queue with Bernoulli vacation schedules and general retrial times. We assume that the customers who find the server busy are queued in the orbit in accordance with an FCFS (first-come-first-served) discipline and only the customer at the head of the queue is allowed access to the server....

This paper presents a transient solution for the system size in the M/M/2 queue with the possibility of catastrophes at the service stations. The state probability of the system size at time t, where the queue starts with any number of customers, in obtained. Asymptotic behaviour of the probability of the server being idle and mean system size are...

This paper analyses a multi-channel Markovian queueing system with heterogeneous servers and balking behaviour. For the system initiated with a random number of customers, the transient solution for the system size distribution is obtained explicitly in a direct way and the steady state probabilities are deduced. Some special cases are also discuss...

This paper discusses an M/G/1/1 queue where customer after regular service completion may leave the system or feedback to regular service again or opt for specialised services. Explicit expressions for the transient probabilities that the server is idle and the server is providing the regular service or optional services are obtained.

A transient solution for the system size in the M/M/1 queueing model with the possibility of catastrophes at the service station is derived in the direct way. Asymptotic behavior of the probability of the server being idle and mean queue size are discussed. Steady-state probabilities are also obtained.

A semi-Markov cornpartmental model with branching particies is considered. The notion of disaster is incorporated into the structure. The means of (i) the total sojourn time, (ii) the number of deaths, (iii)the number of births and (iv)the number of emigrant particles in the system are analysed. Some interesting relations connecting these means are...

The total number of deaths and total sojourn times of African honey bees are studied using semi-markov compartment analysis.
This generalizes many existing biological models.

A multitype Markov branching process under the influence of disasters (catastrophes) arriving as a renewal process leading to possible mutation of particles to other types is considered. The integral equations for the probability generating function of the number of particles of each type are derived incorporating time dependent mutation rates. The...

We consider a multitype Markov branching process under the influence of disasters occurring as a renewal process. For the branching particles in the system, the disasters may lead to possible death or mutation to other types of particles. For such a process, the total mean sojourn time of all the particles in the system is analysed using the regene...

A semi-Markov multi-compart mental system in which particles reproduce similar particles as a Markov branching process and being subjected to disasters is studied. Expressions for the mean number of particles alive at time t in each compartment are obtained. The results concerning irreversible, mammillarian and catenary compartmental systems have b...

The analysis for busy period of an infinite capacity M/M/1 queue with balking is discussed. Defining the generating function in an unusual and direct way, the time-dependent solution for the density function of busy period is obtained elegantly.

In this paper we consider a discrete-time cyclic-service system consisting of multiple stations visited by a single server. Several priority classes of customers arrive at each station according to independent batch Bernoulli processes. The head-of-the-line (HL) priority rule and non-zero switch-over times between stations are assumed. The customer...

We consider a stochastic compartmental model in which cells reproduce in accordance with a regulated birth and death process. We find expressions for the mean vector and covariance matrix for the number of cells in these compartments. We obtain the asymptotic behavior of the mean vector in the general case and explicit expressions for two compartme...

We consider a discrete-time cyclic-service system consisting of multiple stations visited by a single server. Customers from several priority classes arrive at an individual station according to independent batch Bernoulli processes. We assume a non-preemptive priority rule and non-zero switch-over times of the server between consecutive stations....

An infinite capacityM/M/1 queue with balking is discussed. Defining the generating function in an unusual and direct way, the time-dependent solution for the system size is obtained elegantly.

A semi‐Markov compartmental system in which the particles reproduce according to the Markov branching process, apart from transitions between the compartments, is considered. Asymptotic behaviour of the mean matrix of the number of particles alive at time t is studied. Explicit expressions for some special cases are discussed.

A density‐dependent birth and death process with immigration is considered. An explicit expression is obtained for the population size {X(t)}in terms of the modified Bessel functions. Asymptotic behaviours of the mean and P(X(t) =0) are discussed. A Martingale function is constructed and the probability of population becoming extinct before reachin...

We consider a semi-Markov compartroental system with branching particles, Me study the total sojourn time of all the particles and obtain the asymptotic behaviour of its mean. We also discuss some special systems.

A density–dependent birth and death process in which immigration is permitted only when the number of particles in the system is less than a positive integer kis considered. An explicit expression for the probability generating function of the population size is obtained by using a direct and unconventional approach. Special cases are discussed.

A density-dependent birth and death process is considered, in which immigration is allowed whenever the population size reaches zero. An explicit expression is obtained for the population size in terms of the modified Bessel functions. Asymptotic behaviour of extinction probability and the mean are established.

An age-dependent branching process where each cell produces offspring only if its life length is greater than τ1 > 0 is considered. Asymptotic behaviours of the mean number of cells that die after time τ2 > 0 for an age-dependent branching process are studied for the different cases and exact expressions for a Markov branching process are given. Su...

An example of density dependent-birth and death process whose mean satisfies the logistic equation as proposed by Gompertz is given. Explicit expressions for the probability generating function and non-trivialstationarydistribution are obtained.

Two examples of density dependent birth and death processes whose means satisfy the logistic equation as proposed by Verhulst and Gompertz are given. Explicit expressions for the probability generating functions and non-trivial stationary distributions are obtained.

For an age-dependent branching process, we consider cells at time t whose lifetimes lie in an interval. The asymptotic behaviour of the mean of these cells is given and the sum of their lifetimes is discussed.