Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service
Pikkala Vijaya Laxmi Obsie Mussa Yesuf
Journal of Industrial & Management Optimization 2010, 6(4): 929-944 doi: 10.3934/jimo.2010.6.929
Queues with Markovian service process ($MSP$) are mainly useful in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode (ATM) environment. This paper analyzes a finite buffer single server batch service ($a, b)$ queue with general input and Markovian service process ($MSP$). The server accesses new arrivals even after service has started on any batch of initial number $a$. This operation continues till the service time of the ongoing batch is completed or the maximum accessible capacity $d ~(a\le d < b)$ of the batch being served is attained whichever occurs first. Using the embedded Markov chain technique and the supplementary variable technique we obtain the steady state queue length distributions at pre-arrival and arbitrary epochs. The primary focus is on the various performance measures of the steady state distribution of the batch service, special cases and also on numerical illustrations.
keywords: Batch Service. Accessible Batch Markovian Service Process Queue Supplementary Variable
Performance analysis of renewal input $(a,c,b)$ policy queue with multiple working vacations and change over times
Pikkala Vijaya Laxmi Seleshi Demie
Journal of Industrial & Management Optimization 2014, 10(3): 839-857 doi: 10.3934/jimo.2014.10.839
This paper analyzes a renewal input multiple working vacations queue with change over times under $(a,c,b)$ policy. The service and vacation times are exponentially distributed. The server begins service if there are at least $c$ units in the queue and the service takes place in batches with a minimum of size $a$ and a maximum of size $b~ (a\leq c \leq b)$. The steady state queue length distributions at arbitrary and pre-arrival epochs are obtained along with some special cases of the model. Performance measures and optimal cost policy is presented with numerical experiences for some particular values of the parameters. The genetic algorithm is employed to search the optimal values of some important parameters of the system.
keywords: queue genetic algorithm. Multiple working vacations infinite buffer supplementary variable cost
Analysis of renewal input bulk arrival queue with single working vacation and partial batch rejection
Veena Goswami Pikkala Vijaya Laxmi
Journal of Industrial & Management Optimization 2010, 6(4): 911-927 doi: 10.3934/jimo.2010.6.911
This paper analyzes a finite buffer bulk arrival queueing system with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrarily and exponentially distributed. Using the supplementary variable and the imbedded Markov chain techniques, we obtain the system length distributions at pre-arrival and arbitrary epochs. We also present Laplace-Stiltjes transform of the actual waiting time distribution in the system. Finally, several performance measures and a variety of numerical results in the form of tables and graphs are discussed.
keywords: Finite buffer Working vacation. Bulk arrival Waiting time Queue
Ant colony optimization for optimum service times in a Bernoulli schedule vacation interruption queue with balking and reneging
Pikkala Vijaya Laxmi Singuluri Indira Kanithi Jyothsna
Journal of Industrial & Management Optimization 2016, 12(4): 1199-1214 doi: 10.3934/jimo.2016.12.1199
This paper analyzes a finite buffer multiple working vacations queue with balking, reneging and Bernoulli schedule vacation interruption. Arriving customers decide either to join the system or to balk. After joining the queue the customers may renege based on their desire for service or their unwillingness for waiting. At a service completion instant during working vacations, the server can decide either to continue the vacation with probability $q$ or interrupt the vacation and resume regular service period with probability $1-q$. The inter-arrival times of customers are assumed to be arbitrarily distributed. Service times during a regular service period, during a working vacation period and vacation times are assumed to be exponentially distributed. Using recursive technique, the steady state system length distributions at various epochs are obtained. Some performance measures of the model and cost analysis using ant colony optimization are presented. Finally, numerical results showing the effect of model parameters on key performance measures are presented.
keywords: Bernoulli schedule vacation interruption balking ant colony optimization. reneging multiple working vacations

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