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Sensitivity Analysis of Markovian Queue with Discouragement, Additional Servers and Threshold Policy


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1 World College of Technology and Management, Gurugram, Haryana, India
     

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In the present paper, an attempt has been made to study the optimal threshold policy for Markovian queueing model having additional servers along with permanent server. The incorporation of customer's balking and reneging behavior has been done. The customers arrive in Poisson fashion and their service times are exponentially distributed. The first server starts service when N (≥1) or more customers are accumulated and turns off when the system is empty. The (j+1)th (j=1, 2,...., r-1) server turns on when there are Nj+1 customers in the system and will be removed as soon as the number of customers drops to threshold level Nj. We use Laplace transform technique to derive transient probabilities and some other system characteristics such as the expected number of jobs in the system, throughput, and probability that jth (j=1,2,3,…,r) server being busy in rendering the service, etc.. The effects of system parameters on the performance characteristics have been examined by taking numerical illustrations.

Keywords

Threshold Policy, Markovian Queue, Balking, Reneging, Additional Servers, Transient Analysis, Throughput, Delay Time.
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  • Sensitivity Analysis of Markovian Queue with Discouragement, Additional Servers and Threshold Policy

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Authors

Neetu Singh
World College of Technology and Management, Gurugram, Haryana, India

Abstract


In the present paper, an attempt has been made to study the optimal threshold policy for Markovian queueing model having additional servers along with permanent server. The incorporation of customer's balking and reneging behavior has been done. The customers arrive in Poisson fashion and their service times are exponentially distributed. The first server starts service when N (≥1) or more customers are accumulated and turns off when the system is empty. The (j+1)th (j=1, 2,...., r-1) server turns on when there are Nj+1 customers in the system and will be removed as soon as the number of customers drops to threshold level Nj. We use Laplace transform technique to derive transient probabilities and some other system characteristics such as the expected number of jobs in the system, throughput, and probability that jth (j=1,2,3,…,r) server being busy in rendering the service, etc.. The effects of system parameters on the performance characteristics have been examined by taking numerical illustrations.

Keywords


Threshold Policy, Markovian Queue, Balking, Reneging, Additional Servers, Transient Analysis, Throughput, Delay Time.

References